Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of (...) provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. (shrink)

PurposeDrawing upon the stimulus-organism-response model, this paper aims to investigate the effects of stores’ environmental components on Chinese consumers’ emotions and intentions to purchase luxury brands.Design/Methodology/ApproachData were collected from Chinese consumers who have purchased luxury brands from retail stores. Partial least squares-structural equation modeling and fuzzy-set qualitative comparative analysis were employed for data analysis.FindingsThe results of PLS-SEM indicated that three dimensions of the store environment directly and significantly influenced Chinese consumers’ emotions. However, fsQCA revealed greater heterogeneity among respondents by (...) highlighting stores’ environmental components and Chinese consumers’ emotions.Originality/ValueThis study makes significant contributions to the marketing literature by examining the S-O-R model alongside fsQCA approach to conditionally predict outcomes in a luxury brand context. The present study may be one of the first to examine the effects of stores’ environmental components on Chinese consumers’ emotions and purchase intentions, applying both symmetrical test and asymmetrical test approaches to determine significant components of the store environment as well as component combinations that predict Chinese consumers’ emotions and purchase intentions. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical (...) situations involving more than one maximal value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A, where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U- uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U = 1/h 0 h log [1+]d, where h is the largest membership value obtained by any element of A and is the measure of the -cut of A defined by the Lebesge integral of its characteristic function. (shrink)

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.

We consider time as a fuzzy concept. Based on this, the Fuzzy Time-Particle interpretation Of Quantum Mechanics is introduced as an interpretation of Quantum Mechanics [4],[5],[6]. Here, we show how to compute the function associated to Fuzzy time.

An algebra with fuzzy equality is a set with operations on it that is equipped with similarity ≈, i.e. a fuzzy equivalence relation, such that each operation f is compatible with ≈. Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic. On the other hand, they are the formal counterpart to the intuitive (...) idea of having functions that are not allowed to map similar objects to dissimilar ones. In this paper, we present a generalization of the well-known Birkhoff’s variety theorem: a class of algebras with fuzzy equality is the class of all models of a fuzzy set of identities iff it is closed under suitably defined morphisms, substructures, and direct products. (shrink)

The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like “antitone” or “isotone” concepts constructed from fuzzy binary relations, but also to allow the two universes to be equipped each with its own truth structure. Perhaps the most important feature of our approach is that we do not commit ourselves to any kind of logical connector, covering (...) thus the case of a possibly non-commutative conjunction too. (shrink)

We consider the equationally orderable quasivarieties and associate with them deductive systems defined using the order. The method of definition of these deductive systems encompasses the definition of logics preserving degrees of truth we find in the research areas of substructural logics and mathematical fuzzy logic. We prove several general results, for example that the deductive systems so defined are finitary and that the ones associated with equationally orderable varieties are congruential.

In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.

Il est assez commun de se représenter le bûcheron comme un être plutôt fruste, qualifié avant tout par sa force au service d’une tâche peu valorisée. Or cette représentation se révèle tronquée, car l’équation qui associe la force à l’outil ne peut se réaliser sans le contrôle du geste. Plus encore, l’écoute des témoignages recueillis auprès des forestiers nous apprend que ce travail réclame d’efficaces systèmes de précision. C’est là une qualification oubliée, pourtant reconnue à part entière dès l’Iliade, qui (...) nous en donne deux témoins privilégiés par l’anthropologie historique de la Grèce, la mètis, l’« intelligence rusée », prêtée au kybérnêtês, le pilote du navire, au conducteur de char et, en bonne première place, au bûcheron. La théorie du contrôle nous permet maintenant de dépasser le flou conceptuel de la notion historiquement pré-théorique de mètis, la ruse s’appliquant à des cas bien trop divers, pour lui préférer les développements les plus récents d’une science du contrôle de l’action, théorisée depuis Wiener, nourrissant aujourd’hui les projets les mieux financés de cyber-cerveaux informatiques, au service des neurosciences et de la médecine. Le travail forestier, qui réclame une coordination maîtrisée des gestes, y compris de leurs commandes vocales dans le chant de travail — qu’un seul ou plusieurs bûcherons en équipe soient mobilisés —, nous en fournit une parfaite illustration. The woodcutter is commonly represented as a fairly boorish person, reduced to brute force and low-level tasks. But this representation is partial because a simplistic inferential link between an axe and strength obliterates that nothing can happen without any modus operandi, i.e. a set of neural controls over gestures. Indeed, listening to woodcutter’s testimonies led us to elicit that this work needs efficient precision systems. This high level of qualification was acknowledged at least since Homer’s Iliad as evidenced by two favourite telltales from historical anthropology of Ancient Greece: mètis ascribed to kybérnêtês, the ship’s pilot as to the chariot-driver and in the first rank to the woodcutter. Control theory allows now to avoid the fuzziness of meaning of the pre-theoretical notion of mètis to focus on a domain steadily developed since Wiener, now part of costly cyber-brain projects in informatics, for neuroscience and medicine. Forest work, which requires skilled gesture coordination, with vocal commands in a worksong—for one or more woodcutters being engaged in the task—is such a telling case. (shrink)

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, (...) are considered. In their abstract form, thus,deductive relationsare defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic. (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Every emerging technology has its pros and cons; health-conscious users pay more importance to healthy and environment-friendly technologies. Based on the UTAUT2 model, we proposed a comprehensive novel model to study the factors influencing consumers’ decision-making to adopt the technology. Compared to prior studies that focused on linear models to investigate consumers’ technology adoption intentions and use behavior. This study used a Structural Equation Modeling-fuzzy set qualitative comparative analysis approach to account for the complexity of customers’ decision-making processes in (...) adopting new technology. We collected valid responses from 830 consumers, analyzed them, and evaluated them using a deep learning SEM-fsQCA technique to capture symmetric and asymmetric relations between variables. We have extensively incorporated a health-consciousness attitude as a predictor and mediator to understand better the decision-making toward technology adoption, specifically 5G technology. All the factors tested in our model are statistically significant except the economic factors. Health-consciousness attitude and behavioral intention found significant predictors and valid mediators in the process of 5G technology adoption. FsQCA provided six configurations to achieve high 5G adoption. The findings have significant practical ramifications for telecom corporations, advertisers, government officials, and key policymakers. Additionally, the study added substantial theoretical literature to technology adoption, particularly the adoption of 5G technology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 10.1 (2003) 57-62 [Access article in PDF] Listening to People Or Listening to Prozac?Another Consideration of Causal Classifications Jennifer Hansen Keywords causal classification, descriptivism, melancholia, neurasthenia, depression, cultural relativism. The shape and detail of depression have gone through a thousand cartwheels, and the treatment of depression has alternated between the ridiculous and the sublime, but the excessive sleeping, inadequate eating, suicidiality, withdrawal from social interaction, (...) and relentless despair are all as old as the hill tribes, if not as old as the hills. In the years since man achieved the capacity for self-reference, shame has come and gone; treatments for bodily complaints have alternated and crossed with treatments for spiritual ones; pleas to external gods have echoed pleas to internal demons. To understand the history of depression is to understand the invention of human being as we now know and are him. Our Prozac-popping, cognitively focused, semi-alienated postmodernity is only a stage in the ongoing understanding and control of mood and character. (Solomon 2001, 286) ALTHOUGH ANDREW SOLOMON clearly believes that "the shape and detail of depression have gone through a thousand cartwheels," Jennifer Radden gives us pause before assuming that depression is just another name for Dame Melancholy. Solomon's claim depends on a deeper metaphysical claim about the nature of depression and its causes. The current method of psychiatric nosology, descriptivism, does not necessarily support equating melancholia and depression. Furthermore, it appears that adopting descriptivism as the sole method of classifying mental disorders commits us to cultural relativist psychiatry. Below I reconsider whether we want to rule out causal classifications and suggest that embracing both descriptivism and causal classifications offer us greater possibilities in understanding human illness and culture.Although the occasion for Jennifer Radden's essay is to investigate whether or not melancholia and depression refer to the same thing, her essay detours into a consideration of extra-descriptivist models of psychiatric illness versus the descriptivism of current psychiatric nosology. This detour turns out to be warranted; her purely academic question yields to a timelier question concerning the proper methodology for classifying mental disorders. Whereas debates about psychiatric nosology are perennial, the recent success of the new generation of antidepressants [End Page 57] is reviving biological psychiatry and its search for the neurochemical origins of depression. Hence, embedded in Radden's question concerning whether or not melancholia is the same thing as clinical depression, is another important question concerning the causes of mental illness, particularly depression.Currently, with its descriptivist approach, the Diagnostic and Statistical Manual of Mental Disorders (DSM) does not classify mental illness, such as clinical depression, based on underlying causes. The cluster of symptoms and behavioral signs that lead a clinician to diagnose one as depressed that are contained in either the DSM or the International Classification of Diseases (ICD) may be too fuzzy or elusive to give any clear distinction between major depression, mild depression, and the blues. For example, one group of epidemiologists points out that [t]he DSM-III, DSM-III-R, and DSM-IV acknowledge that depression, like many mental disorders, has no currently obvious natural classes... If natural classes of depression exist, then their nosology awaits the discovery of distinct and reliable genetic, biological, clinical, or other predictors of risk, severity, or clinical course. Clinicians have a tradition of separating depressions into subtypes; however, this subtyping has not yet led to clear-cut delineations of syndromes in populations. (Kaelber 1995, 4) The evidence is still insufficient to establish the biological or psychological origins of depression. Although many theories exist that explain why people become depressed, scientifically we are not yet in a position to determine which is the right theory. From a pragmatic perspective, however, whether or not we know what causes depression, we can nonetheless attempt to alleviate suffering from depression. And it is with this goal in mind that the DSM-IV and ICD-10 classify mental disorders.Now, given that our current methodology for psychiatric nosology does not establish causes, it is also insufficient for determining what... (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

The present book of proceedings includes chapters related to the areas of pure, applied and inter-disciplinary mathematics reflecting the potential applications in the domains of sciences and engineering. The main areas include algebra and its applications, analysis and approximation theory, cryptography, computational fluid dynamics, continuum mechanics and vibrations, differential equations and applications, graph theory, fuzzy mathematics and logic, numerical analysis, optimization and its applications, wave propagation, etc. The scientists, engineers, academicians and researchers working in the proposed areas of (...) coding and information theory, computational fluid dynamics, differential equations, fuzzy sets and systems, numerical analysis, optimization, vibrations, etc. looking for new insight and ideas in these areas will be benefitted by the contents of this book. In fact, it will be useful to a large class of readers interested in recent findings related to mathematical sciences and their applications to the diverse domains of knowledge. The book will be a fruitful contribution to all knowledge seekers and researchers in the concerned areas who are looking for new insight and ideas. As it consists of updated research articles on emerging areas of mathematical sciences and their applications, it will be a valued addition to the learning resource centres of various universities, industries, and research and development organizations across the globe. (shrink)

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered (...) here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Four Philosophical Models of the Relation Between Theory and PracticeEstelle R. JorgensenSince music education straddles theory and practice, my purpose is to sketch the strengths and weaknesses of four philosophical models of the relationship between theory and practice. I demonstrate that none of them suffices when taken alone; each has something to offer and its own detractions. And I conclude with four suggested ways in which the analysis can (...) be helpful to music teachers and those interested in their work.Clarifying what is meant by theory and practice raises a nest of conceptual problems. Concerning theory, it may be tempting to equate the terms "theory" and "philosophy." Among their shared properties, these terms deal with conceptual and abstract entities that, from the Enlightenment at least, have been held to be distinct from the phenomenal world. They also clarify ideas and distinguish one concept from another. Among their different purposes, the object of philosophy is the asking of questions in a search for wisdom or truth whereas theory is formulated for explanatory purposes, especially within the frame of scientific propositions that can be refuted through empirical observations. The tests of philosophy are, therefore, those of symbolic logic evidenced in principles such as [End Page 21] internal consistency, correspondence with evidence (deductive, inductive, or analogical), and coherence within a unity or whole. Although logical criteria may also be important in formulating and testing theory,1 it is tested and refuted primarily through means of qualitative descriptions and quantitative assessments of observable phenomena.Regarding practice, one is also confronted with an ambiguous construct that may be interpreted descriptively (what is done in the phenomenal world or taken to be the general state of affairs) or normatively (what is desirable or ideal). There is also the distinction between the practice of a seasoned performer and practice in the sense of striving towards the mastery of a competent and expert practice. In this regard, Vernon Howard distinguishes between "practice" (or the skills exemplified by proficient or expert performers) and "practise (or acquiring the level of mastery of proficient or expert performance)."2 For him, the ambiguous and paradoxical nature of artistic practice highlights the complexity of degrees of attaining mastery of skills or exemplary practice and the diverse array of skills ranging from habit to critical thinking involved in the practice of any art. Although each practice is distinguished by its own belief systems, rituals, expectations, and commonsense, boundaries between differing practices are sometimes "soft" or fuzzy, as one seeps into another.3 Consequently, it is often difficult to distinguish one from another at the margins where one practice becomes another.DichotomyThe notion of theory and practice as independent or a dichotomous relationship between the phenomenal world on the one hand and the mind and spirit on the other has its roots in the ancient world. For Plato, the world of "appearances," referring to the phenomenal world understood by imagination (eikasia) and belief (pistis), should be distinguished from the higher, abstract "intelligible world" grasped through thinking (dianoia), knowledge (episteme), and intelligence (noesis).4 René Descartes' later bifurcation of the inner and outer worlds and inversion of Platonic values and understandings resulted in the ascendancy of careful and deliberate observation of the phenomenal world over philosophical reflection.5 His ideas helped to set the stage for the Enlightenment and the Industrial, Scientific, and Information Revolutions. Empiricism, science, and technology gradually displaced philosophy as primary ways of knowing the phenomenal world and understanding the nature of mind, human cognition, feeling, and being. Making hard-boundaried distinctions between within and without one's self, the phenomenal world and the world of spiritual things, and theory and practice were important insights. These distinctions provided for limits on the sorts of ways in which truth could be known. Reasoned deliberation [End Page 22] and imaginative thought have particular usefulness in the world of theory while sensory perception and careful observation are especially useful in the phenomenal world of practice. So while the scholar might speculate about phenomena, observational tools are also useful in coming to know and understand them. Reason and observation each have particular strengths, and it ought not be assumed that philosophy or scientific observation... (shrink)

Taking university-enterprise collaborative innovation in five southern coastal provinces of China as subjects, empirical research is implemented by constructing a theoretical model of the effects of interface resource integration, interface conflict management, interface connection mechanisms, and enterprise absorptive capacity on the university-enterprise collaborative innovation performance with the partial least squares structural equation modeling and fuzzy-set qualitative comparative analysis. A total of 245 valid questionnaires were collected from five coastal provinces in south China. The research results show that the interface (...) resource integration, interface connection mechanisms, and enterprise absorptive capacity has direct significant positive impacts on the collaborative innovation performance. Interface conflict management has no significant impact on school-enterprise collaborative innovation performance. Moreover, the interface connection mechanism acts as an intermediary. Therefore, it is suggested that university-enterprise should integrate resources with complementing, interacting, and sharing resources; construct the profit and risk-sharing mechanism, communication and trust mechanism, and organizational learning mechanism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Four Philosophical Models of the Relation Between Theory and PracticeEstelle R. JorgensenSince music education straddles theory and practice, my purpose is to sketch the strengths and weaknesses of four philosophical models of the relationship between theory and practice. I demonstrate that none of them suffices when taken alone; each has something to offer and its own detractions. And I conclude with four suggested ways in which the analysis can (...) be helpful to music teachers and those interested in their work.Clarifying what is meant by theory and practice raises a nest of conceptual problems. Concerning theory, it may be tempting to equate the terms "theory" and "philosophy." Among their shared properties, these terms deal with conceptual and abstract entities that, from the Enlightenment at least, have been held to be distinct from the phenomenal world. They also clarify ideas and distinguish one concept from another. Among their different purposes, the object of philosophy is the asking of questions in a search for wisdom or truth whereas theory is formulated for explanatory purposes, especially within the frame of scientific propositions that can be refuted through empirical observations. The tests of philosophy are, therefore, those of symbolic logic evidenced in principles such as [End Page 21] internal consistency, correspondence with evidence (deductive, inductive, or analogical), and coherence within a unity or whole. Although logical criteria may also be important in formulating and testing theory,1 it is tested and refuted primarily through means of qualitative descriptions and quantitative assessments of observable phenomena.Regarding practice, one is also confronted with an ambiguous construct that may be interpreted descriptively (what is done in the phenomenal world or taken to be the general state of affairs) or normatively (what is desirable or ideal). There is also the distinction between the practice of a seasoned performer and practice in the sense of striving towards the mastery of a competent and expert practice. In this regard, Vernon Howard distinguishes between "practice" (or the skills exemplified by proficient or expert performers) and "practise (or acquiring the level of mastery of proficient or expert performance)."2 For him, the ambiguous and paradoxical nature of artistic practice highlights the complexity of degrees of attaining mastery of skills or exemplary practice and the diverse array of skills ranging from habit to critical thinking involved in the practice of any art. Although each practice is distinguished by its own belief systems, rituals, expectations, and commonsense, boundaries between differing practices are sometimes "soft" or fuzzy, as one seeps into another.3 Consequently, it is often difficult to distinguish one from another at the margins where one practice becomes another.DichotomyThe notion of theory and practice as independent or a dichotomous relationship between the phenomenal world on the one hand and the mind and spirit on the other has its roots in the ancient world. For Plato, the world of "appearances," referring to the phenomenal world understood by imagination (eikasia) and belief (pistis), should be distinguished from the higher, abstract "intelligible world" grasped through thinking (dianoia), knowledge (episteme), and intelligence (noesis).4 René Descartes' later bifurcation of the inner and outer worlds and inversion of Platonic values and understandings resulted in the ascendancy of careful and deliberate observation of the phenomenal world over philosophical reflection.5 His ideas helped to set the stage for the Enlightenment and the Industrial, Scientific, and Information Revolutions. Empiricism, science, and technology gradually displaced philosophy as primary ways of knowing the phenomenal world and understanding the nature of mind, human cognition, feeling, and being. Making hard-boundaried distinctions between within and without one's self, the phenomenal world and the world of spiritual things, and theory and practice were important insights. These distinctions provided for limits on the sorts of ways in which truth could be known. Reasoned deliberation [End Page 22] and imaginative thought have particular usefulness in the world of theory while sensory perception and careful observation are especially useful in the phenomenal world of practice. So while the scholar might speculate about phenomena, observational tools are also useful in coming to know and understand them. Reason and observation each have particular strengths, and it ought not be assumed that philosophy or scientific observation... (shrink)

This paper introduces a logic to reason about a well-known model of opinion dynamics in socialnetworks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, (...) developing a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis. (shrink)

The “Asian disease” problem (Tversky & Kahneman, 1981) demonstrated behaviour in contradiction to the invariance axiom of EU theory. However, the risky choice behaviour was simply seen by the equate-to-differentiate model as a choice between the best possible outcomes or a choice between the worst possible outcomes. It was then argued that a way in which frame influences choice is through the perceived difference between possible outcomes. A “judgement” task was designed to examine whether the knowledge of “the value difference (...) between each possible outcome and the certain outcome” will permit prediction of preference in the choice pattern related to the Asian disease problem. Participants were exposed to an anthrax disease problem (the original or probabilistic version of the Asian disease problem) and a SARS problem (the fuzzy version of the Asian disease problem). It was shown that the empirical evidence in relation to the Asian disease problem could be satisfactorily accounted for by the generalised weak dominance strategy revealed by the judgement results. (shrink)

We study the different solution strategy for solving epidemic model in different imprecise environment, that is, a Susceptible-Infected-Susceptible model in imprecise environment. The imprecise parameter is also taken as fuzzy and interval environment. Three different solution procedures for solving governing fuzzy differential equation, that is, fuzzy differential inclusion method, extension principle method, and fuzzy derivative approaches, are considered. The interval differential equation is also solved. The numerical results are discussed for all approaches in different imprecise environment.

Taking university-enterprise collaborative innovation in five southern coastal provinces of China as subjects, empirical research is implemented by constructing a theoretical model of the effects of interface resource integration, interface conflict management, interface connection mechanisms, and enterprise absorptive capacity on the university-enterprise collaborative innovation performance with the partial least squares structural equation modeling and fuzzy-set qualitative comparative analysis. A total of 245 valid questionnaires were collected from five coastal provinces in south China. The research results show that the interface (...) resource integration, interface connection mechanisms, and enterprise absorptive capacity has direct significant positive impacts on the collaborative innovation performance. Interface conflict management has no significant impact on school-enterprise collaborative innovation performance. Moreover, the interface connection mechanism acts as an intermediary. Therefore, it is suggested that university-enterprise should integrate resources with complementing, interacting, and sharing resources; construct the profit and risk-sharing mechanism, communication and trust mechanism, and organizational learning mechanism. (shrink)

After a chapter which is an introduction to and summary of the rest of the book, chapter 2 begins by criticizing various attempts to do away with theories, such as the Reichenbach-Salmon conception of theoretical truth in terms of observational consequences, and the Ramsey strategy of replacing first-order theoretical sentences by second-order nontheoretical ones; it then argues against hypothetico-deductivist theories of confirmation on the grounds that they are unable to handle the relevance of evidence to theory, whether or not other (...) formal constraints or even nonformal ones such as simplicity and explanatory power are added to those theories; it ends with an exposition of the Reichenbach-Carnap conventionalist thesis that the confirmation of hypotheses with evidence presupposes analytic principles connecting hypothetical and empirical concepts. Chapter 3 criticizes Bayesian theories of confirmation on such grounds as that the a priori arguments for Bayesian restrictions on beliefs are insufficient; that the Bayesian explanations of notions like variety of evidence, ad hocness, and simplicity are inadequate; and that they cannot account, without drastic revisions, for the relevance of evidence to theory, especially old evidence to new theory. Chapter 4 is an unsympathetic account of historically oriented philosophies of science; Lakatos’s notion of progressive research programs and Laudan’s theory of problem-solving effectiveness are found to be insufficiently precise and dubbed examples of "new fuzziness", while the Sneed-Stegmüller dynamics of theories is regarded as "a paradigm of misplaced rigor" ; and all three are criticized as unable to explicate the concept of evidential relevance. Chapter 5 is a formal and informal elaboration of the basic idea in Glymour’s account of theory and evidence, namely that confirmation or support is a three-term relation among evidence, hypothesis, and theory, so that evidence confirms an hypothesis only relative to a theory, and such that evidence e confirms hypothesis h relative to T if T with e implies, but T without e does not imply, an instance of h, and T with e does not imply a comparable hypothesis h’ different from h; the most interesting part of this chapter is a series of discussions showing how such an idea makes sense of the "methodological truisms" that it is possible selectively to test certain parts of a theory but not others, that a theory is supported better by a greater variety of evidence, that redundant or physically meaningless quantities are an undesirable feature of theories, that there are no inviolable rules, that a "white shoe" does not confirm "all ravens are black," that a theory is more useful and better supported than the set of its observational consequences, and that the hypothetico-deductive method often works. Since Glymour claims no originality for the conception of this general account, but only for its description, he plausibly thinks it necessary to apply it to some important historical cases of actual science; he does so in the next chapter by discussing at some length the structure and merits of Ptolemaic and Copernican astronomy, of Newton’s universal gravitation, of nineteenth century atomism, of Freud’s Rat Man, and of general relativity. For example, he argues convincingly that Copernicanism was better supported by the evidence available even before the telescope because it alone, and not the Ptolemaic theory, can determine some planetary properties which are presupposed by both theories, can test and confirm some common hypotheses, and can be confirmed in an essential rather than incidental manner; and though Glymour admits that the Copernicans tended to argue in terms of explanatory rather than confirmatory superiority, he sketches an interesting account of the relation between explanation and confirmation which strengthens his case. He also analyzes the text at the beginning of book 3 of Newton’s Principia and compiles a reconstruction of the intricate details of the inferential structure of the argument to universal gravitation; his impressive reconstruction clearly shows that Newton’s method is neither the inductivist one he himself thought he was following, nor the one attributed to him by Pierre Duhem, but rather one in accordance with Glymour’s so-called "bootstrap strategy" of repeatedly using the evidence from Kepler’s second and third laws, from lunar data, and from falling bodies, together with the theory consisting of the second and third laws of motion, to arrive at increasingly general instances of the principle of universal gravitation. Glymour’s account of arguments for and against the atomic theory from Thomson to Cannizzaro is his longest historical example, but he himself admits that this illustration of the bootstrap strategy is "certainly not the neatest", and rather "diffuse, and perhaps disconnected". Chapter 7 is a detailed application of the same principles to the technique known among social scientists as "causal modeling"; since such "causal models" are essentially systems of algebraic equations, Glymour’s account shows indirectly that the bootstrap strategy is applicable to any scientific theory presented as a set of algebraic equations; this, of course is not surprising, since the formal considerations with which Glymour begins the exposition of his theory in chapter 5 involve systems of algebraic equations. Chapter 8 is an attempt to apply Glymour’s theory of evidence to the very common scientific practice of curve-fitting, where one measures values of two or more quantities and then infers a functional relationship; Glymour argues that simpler polynomials are preferred because they are tested more frequently and more severely by the data and because they are more informative; but then he criticizes his own explanation and concludes that "the bootstrap procedures of chapter 5 do not seem to help the problem much more than a whit" ; this is admirably honest, but if one wants an additional logical or methodological rationale, then one would perhaps have to go to the meta-level and say that Glymour is here testing his own theory, and he is more interested in a further illustration of the bootstrap methodology even with a failed test, than he is to claim universal or exclusive validity for it. In chapter 9 Glymour uses his bootstrap theory of confirmation to criticize geometrical conventionalism; he considers the alternative theories of space or space-time proposed by conventionalists to show the radical undetermination of geometries by evidence, for example, a non-Euclidean geometry with no universal force instead of Newtonian gravitation with Euclidean geometry; he argues that such alternatives are simply not as well tested as the originals and that their equivalence to the originals is questionable. The last chapter is a brief discussion of further problems worthy of future investigation. (shrink)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...) the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown’s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard’s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above. (shrink)

One of the long-standing problems in particle physics is the covariant description of higher spin states. The standard formalism is based upon totally symmetric Lorentz invariant tensors of rank-K with Dirac spinor components, $\psi _{\mu _1 \cdots \mu _K } $ , which satisfy the Dirac equation for each space time index. In addition, one requires $\partial ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0{\text{ }}and{\text{ }}\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } (...) = 0$ . The solution obtained this way (so called Rarita–Schwinger framework) describes “has–been” spin-(K+ $ - \frac{1}{2}$ ) particles in the rest frame and particles of indefinite (fuzzy) spin elsewhere. Problems occur when $\psi _{\mu _1 \cdots \mu _K } $ constrained this way are placed within an electromagnetic field. In this case, the energy of the spin-(K+ $ - \frac{1}{2}$ ) state becomes imaginary and it propagates acausally (Velo–Zwanziger problem). Here I consider two possible avenues for avoiding the above problems. First I make the case that specifically for baryon excitations there seems to be no urgency so far for a formalism that describes isolated higher-spin states as all the observed nucleon and Δ(1232) excitations (up to Δ(1600)) are exhausted by unconstrained ψ μ , $\psi _\mu ,\psi _{\mu _1 \cdots \mu _3 } {\text{ }}and{\text{ }}\psi _{\mu _1 \cdots \mu _5 } ,$ , structures which originate from rotational and vibrational excitations of an underlying quark–diquark string. Second, I show that the $\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0$ constraint is a short-hand of a more general definition of the parity-singlet invariant subspace of the squared Pauli–Lubanski vector, W 2. I consider the simplest case of K=1 and construct the covariant projector onto that very state as $ - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4})$ . I suggest to work in the sixteen dimensional vector space, Ψ, of the direct product of the four-vector, A μ , with the Dirac spinor, ψ, i.e., Ψ=A μ ⊗ψ, rather than keeping space-time and spinor indices separated and to consider $( - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4}) - 1)\Psi = 0$ as the principal wave equation without invoking any further supplementary conditions. In gauging the equation minimally and, in calculating the determinant, one obtains the energy-momentum dispersion relation. The latter turned out to be well-behaved and free from pathologies, thus avoiding the classical Velo–Zwanziger problem. (shrink)

Standard models of adolescent risk taking posit that the cognitive abilities of adolescents and adults are equivalent, and that increases in risk taking that occur during adolescence are the result of socio emotional differences in impulsivity, sensation seeking, and lack of self-control. Fuzzy-trace theory incorporates these socio emotional differences. However, it predicts that there are also cognitive differences between adolescents and adults, specifically that there are developmental increases in gist-based intuition that reflects understanding. Gist understanding, as opposed to verbatim-based (...) analysis, generally has been hypothesized to have a protective effect on risk taking in adolescence. Gist understanding is also an essential element of informed consent regarding risks in medical decision- making. Evidence thus supports the argument that adolescents’ status as mature minors should be treated as an exception rather than a presumption, because accuracy in verbatim analysis is not mature gist understanding. Use of the exception should be accompanied by medical experts’ input on the bottom-line gist of risks involved in treatment. (shrink)

Although machine intelligence is increasingly employed in healthcare, the realm of decision-making in medical ethics remains largely unexplored from a technical perspective. We propose an approach based on fuzzy cognitive maps (FCMs), which builds on Beauchamp and Childress’ prima-facie principles. The FCM’s weights are optimized using a genetic algorithm to provide recommendations regarding the initiation, continuation, or withdrawal of medical treatment. The resulting model approximates the answers provided by our team of medical ethicists fairly well and offers a high (...) degree of interpretability. Possible applications of such a system include informal guidance on medical ethics dilemmas as well as educational purposes. (shrink)

A clear account of the principles of fuzzy logic-based design, from a computer/electronics engineering perspective. This pedagogical work incorporates current fuzzy logic techniques, emphasizing hardware/software design for fuzzy systems and fuzzy logic development tools.

The notions of health, illness, and disease are fuzzy-theoretically analyzed. They present themselves as non-Aristotelian concepts violating basic principles of classical logic. A recursive scheme for defining the controversial notion of disease is proposed that also supports a concept of fuzzy disease. A sketch is given of the prototype resemblance theory of disease.

I aim to develop a tool for comparing theories of vagueness, using Structured Query Language. Relevant SQL snippets will be used throughout.

Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description (...) logic as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.” . (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in (...) as a fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one-to-one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by Galois connections is provided.

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

In empiricism, there are only two answers for a question: black or white. Yet, subjective meanings of human behaviours and responses toward health and illness cannot be simply explained with black and white. Gray zones are needed because they are characterized by complexity and require a contextual understanding. In this paper, we present and suggest fuzzy logic as an example of theoretical bases that help transcend the conflicts between objectivity and subjectivity, respect gray zones between black and white answers (...) for questions, and provide a contextual understanding of complex nursing phenomenon. A historical review of fuzzy logic is followed by a definition of fuzzy logic. Then, fuzzy logic is discussed in terms of its compatibility with nursing epistemological views and philosophical thoughts. Fuzzy logic agrees with three categories of epistemological views of nursing, including correspondence, coherence and pragmatism. Fuzzy logic also agrees with four major philosophical thoughts in nursing, including postempiricism, pragmatism, feminism, and postmodernism. Based on the discussion, we propose that fuzzy logic be further explored, used and developed in research and practice in the nursing areas/situations/phenomena that are characterized by complexity, ambiguousness, and vagueness. (shrink)

It is proposed to analyze fuzzy concepts and relations between them in the frame of triplet concept modeling. Fuzzy concepts are introduced by means of the so-called fuzzification of dichotomous concepts. The cognitive and psychological aspects of concept possession are separated and studied.