We introduce a new theorem in social choice theory built on a path integral approach which will show that, under some reasonable conditions, there is a unique way to aggregate individual preferences based on fuzzy sets into a social preference based on probabilities, and that this way is invariant under any permutation of alternatives. We then apply this theorem to the case of democratic decision making with data of the behaviour and voting preferences of voting agents and show that there (...) is a tradeoff between fairness and efficiency and that no voting system can achieve both simultaneously. (shrink)

This hands-on guide offers clear explanations of fuzzy logic along with practical uses and detailed examples. Written by an award-winning engineer and experienced author, Fuzzy Logic: Applications in Artificial Intelligence, Big Data, and Machine Learning is aimed at improving competence and skills in students and professionals alike. Inside, you will discover how to apply fuzzy logic and migrate to a new man-machine relationship in the context of pervasive digitization and big data across emerging technologies. The book lays out real-world applications (...) in intelligent energy systems with demand response, smart homes, electrification of transportation, supply chain efficiencies, smart cities, e-commerce, education, healthcare, and decarbonization. (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. (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)

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)

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...) for t-norms without non-trivial zero divisors, $\neg$ is Gödel negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial zero divisors and extended with an involutive negation. (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.

Substructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0.1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) ∨ ((B → A) ∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MTL and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are (...) provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1]. (shrink)

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.

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.

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)

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)

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)

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)

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies and satisfiable sentences as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.

A novel fuzzy control scheme with adaptation algorithms is developed for robot manipulators’ system. At the beginning, one adjustable parameter is introduced in the fuzzy logic system, the robot manipulators system with uncertain nonlinear terms as the master device and a reference model dynamic system as the slave robot system. To overcome the limitations such as online learning computation burden and logic structure in conventional fuzzy logic systems, a parameter should be used in fuzzy logic system, which composes fuzzy logic (...) system with updated parameter laws, and can be formed for a new fashioned adaptation algorithms controller. The error closed-loop dynamical system can be stabilized based on Lyapunov analysis, the number of online learning computation burdens can be reduced greatly, and the different kinds of fuzzy logic systems with fuzzy rules or without any fuzzy rules are also suited. Finally, effectiveness of the proposed approach has been shown in simulation example. (shrink)

In many applications we have a set of objects together with their properties. Since the available information is usually incomplete and/or imprecise, the true knowledge about subsets of objects can be determined approximately only. In this paper, we discuss a fuzzy generalisation of two pairs of relation-based operators suitable for fuzzy set approximations, which have been recently investigated by Düntsch and Gediga. Double residuated lattices, introduced by Orlowska and Radzikowska, are taken as basic algebraic structures. Main properties of these operators (...) are presented. (shrink)

Recently, a new movement has arisen in the philosophy of perception: one that views perception as a natural kind. Strangely, this movement has neglected the extensive work in philosophy of science on natural kinds. The present paper remedies this. I start by isolating a widespread and influential assumption, which is that we can give necessary and sufficient conditions for perception. I show that this assumption is radically at odds with current philosophy of science work on natural kinds. I then develop (...) an alternative, new view of perception. This new view takes as its starting point the dominant position on kinds in the life sciences: the homeostatic property cluster account. I show that, if you accept this view, then all of the putative cases of unconscious perception are more plausibly seen as cases where it is indeterminate whether the mental episode in question is an instance of perception. (shrink)

Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided (...) for CRL and used to establish co-NP completeness results for these logics. (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.

The major point in [1] chapter 2 is the following claim: “Any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction.” So, in the case we wish to save Classical Logic we should change our Computational Model. As we see in chapter two, the mentioned contradiction is about and around the concept of time, as it is in the contradiction of modified version of paradox. It is natural to (...) try fabricating the paradox not by time but in some other linear ordering or the concept of space. Interestingly, the attempts to have similar contradiction by the other concepts like space and linear ordering, is failed. It is remarkable that, the paradox is considered either Epistemological or Logical traditionally, but by new considerations the new version of paradox should be considered as either Logical or Physical paradox. Hence, in order to change our Computational Model, it is natural to change the concept of time, but how? We start from some models that are different from the classical one but they are intuitively plausible. The idea of model is somewhat introduced by Brouwer and Husserl [3]. This model doesn’t refute the paradox, since the paradox and the associated contradiction would be repeated in this new model. The model is introduced in [2]. Here we give some more explanations. (shrink)

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of \((\in, \in)\) and \((\in, \in\! \vee \, {q})\)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of \((\alpha,\beta)\)-fuzzy subalgebras and \((\alpha,\beta)\)-fuzzy ideals on equality algebras. (...) Also, by using the notion of \((\in, \in)\)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of \(X\), and we proved that the set of all classes of \(X\) by these order is a poset. (shrink)

This chapter contains sections titled: Origin Many‐Valued Logic Fuzzy Logic in a Broad and Narrow Sense The Basic Fuzzy Propositional Calculus The Basic Fuzzy Predicate Calculus Similarity The Liar and Dequotation Very True Probability Conclusion.

S.Haack has defended the idea that in fuzzy logic it cannot be affirmed that the true values of a statement are themselves blurry. This article analyzes Haack position in the light of some current approaches of classic philosophy of logic, and from the cognitive point of view of philosophy of logic, especially from the theory of concepts. Under the said approaches, the thesis on non-gradation of truth appears significantly weakened.

The major reason given in the philosophical literature for dissatisfaction with theories of vagueness based on fuzzy logic is that such theories give rise to a problem of higherorder vagueness or artificial precision. In this paper I first outline the problem and survey suggested solutions: fuzzy epistemicism; measuring truth on an ordinal scale; logic as modelling; fuzzy metalanguages; blurry sets; and fuzzy plurivaluationism. I then argue that in order to decide upon a solution, we need to understand the true nature (...) and source of the problem. Two possible sources are discussed: the problem stems from the very nature of vagueness—from the defining features of vague predicates; or the problem stems from the way in which the meanings of predicates are determined—by the usage of speakers together with facts about their environment and so on. I argue that the latter is the true source of the problem, and on this basis that fuzzy plurivaluationism is the correct solution. (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)

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.

The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting.

This paper deals with good fuzzy preorders on fuzzy power structures. It is shown that a fuzzy preorder R on an algebra ${(X,\mathbb{F})}$ is compatible if and only if it is Hoare good, if and only if it is Smyth good.

It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. I question this assumption, showing that there is an intelligible motivation for adopting a (...) many-valued semantics even if one accepts a form of epistemicism. The resulting hybrid view has advantages over both classical epistemicism and traditional many-valued approaches. (shrink)

Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.

In this paper, notions of fuzzy closure system and fuzzy closure L—system on L—ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

This paper proposes a novel adaptive fuzzy super-twisting sliding mode control scheme for microgyroscopes with unknown model uncertainties and external disturbances. Firstly, an adaptive algorithm is used to estimate the unknown parameters and angular velocity of microgyroscopes. Secondly, in order to improve the performance of the system and the superiority of the super-twisting algorithm, this paper utilizes the universal approximation characteristic of the fuzzy system to approach the gain of the super-twisting sliding mode controller and identify the gain of the (...) controller online, realizing the adaptive adjustment of the controller parameters. Simulation results verify the superiority and the effectiveness of the proposed approach, compared with adaptive super-twisting sliding mode control without fuzzy approximation; the proposed method is more effective. (shrink)

The paper deals with fuzzy Horn logic which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w.r.t. semantics over the unit interval [0, 1] with left-continuous t-norm and a residuated implication, provided that only certain fuzzy sets of formulas are considered. The model classes of fuzzy structures of FHL are characterized by closure properties. We also give (...) comments on related topics proposed by N. Weaver. (shrink)

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a (...) new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm. (shrink)

Conservative agriculture practice adoption literature advocates that adoption is caused by many factors comprising cognitive, social, economic, personal, and CAP-related factors. Evaluating the adoption of CAPs as the outcome is complex and challenging with regression-based models as the systemic interdependencies of the factors offer diverse or varying results. Farmer production and environmental orientations as cognitive stances are notable interpreters of CAP adoption. The appetite level for risk-taking, innovativeness, and trust facilitates the adoption of CAPs. However, a causal-predictive technique should be (...) used to investigate the adoption of CAP. Hence, this study engages in a configuration approach using a fuzzy-set qualitative comparative analysis to analyze the patterns of different types of farmers' orientations, personal level of trust on extension services, and innovativeness risk-taking attitude on the intention to adopt CAPs. The analysis is based on the 155-farmer data collected employing a structured interview from Pakistan. The results suggest that a higher level of environment orientation and innovativeness is sufficient to increase the intention to adopt CAPs. Moreover, a higher intention to adopt CAPs is achieved with a lower production orientation, a higher personal level of innovativeness, and a risk-taking attitude of the farmer. The innovativeness can help to develop the intention to adopt the CAPs among the environment and production-oriented farmers. Causal solutions offer a unique understanding that the farmers' environment and production orientation can combine to suggest inclined to adopt CAPs by having an attitude of innovativeness and risk-taking. The causal solutions achieved significant predictive validity in the holdout samples. Policy and farmer-level suggestions were made to raise the intention to adopt CAPs among the farmers. (shrink)

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.

This contribution to the Common Knowledge symposium “Fuzzy Studies” argues, on the basis of recent research, that religious polemic is a phenomenon closely associated only with monotheist traditions. Focusing on religious polemics in medieval and early modern Islamic and Christian Spain, it analyzes polemical texts of diverse natures and from different centuries to see how their authors, by attacking both dogmatic and legal opinion, aimed to harden the amorphous boundaries between groups. On the Christian side, polemicists argued for the restriction (...) of the rights of Muslims and Jews in Christian territories, or for the outright expulsion or conversion of these groups. On the Islamic side, a number of Muslim authors voiced the claim that Muslims should emigrate from Christian territories. The article seeks to show how these polemical voices argued against known opponents but also against anonymous Christians, Muslims, and Jews who, untouched by such polemics, had lived close to one another and, without conflict, had accepted the undefined character of their daily life together. In support of this argument, the author makes use of hitherto unknown archival documents regarding how adherents of the three religions interacted in medieval Christian Spain. (shrink)

Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge (...) and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start. (shrink)

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of (...) occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state. (shrink)

Medical knowledge as well as clinical practice are characterized by inescapable uncertainty. There are many reasons this is the case, but foremost among them is that almost everything in medicine is inevitably vague, be it something linguistic such as the term “illness”, or something extra-linguistic such as the condition referred to as illness. If we ask ourselves, then, what the term “illness” means exactly, on the one hand; and how we may precisely delimit the condition illness, on the other; we (...) shall realize that to answer these and similar questions requires specific methods that enable us to adequately cope with vagueness. As we shall see below, fuzzy logic provides us with just such methods. (shrink)

Farmers are key actors in the transition towards sustainable agricultural practices. Therefore, it is important to understand farmers’ motivations to encourage lasting change. This study investigated how farmers from the two different social contexts of the northeast US and Denmark perceive sustainability. Twenty farmers constructed Fuzzy Cognitive Maps to model their practices and perceived outcomes. The maps were analyzed using social capital as an analytical framework. The results showed that sustainability perceptions differed between US and Danish farmers. Specifically, Danish farmers (...) focused mainly on environmental sustainability while US farmers distributed their focus more evenly across environmental, social, and economic factors. Further, US and Danish farmers had different notions of community engagement. US farmers emphasized the importance of interdependence with their non-farmer community members, where farmers contributed to the wellbeing and livelihoods of non-farmers and vice versa. For Danish farmers, the importance of community engagement lay mainly in localizing food systems, the public image of farming, and the cultural value of farms. Differences in the dominant types of social capital (farmer-to-government vs. farmer-to-non-farmer-community) can explain this pattern. We argue that understanding social capital and primary level of influence can lead to more effective and efficient policies. (shrink)

This book brings together classic and recent papers in the philosophical and linguistic analysis of fuzzy grammar, gradience in meaning, word classes, and syntax. Issues such as how many grains make a heap, when a puddle becomes a pond, and so forth, have occupied thinkers since Aristotle and over the last two decades been the subject of increasing interest among linguists as well as in fields such as artificial intelligence and computational linguistics. The work is designed to be of use (...) to students in all these fields. It has a substantial introduction, is divided into thematic parts, contains annotated sections of further reading, and is fully indexed. (shrink)

Prioritization of activities is a multicriteria problem that includes both quantitative and qualitative factors. Moreover, due to the nature of organizations and activities, the impact of activities on each other is fuzzy. Prioritizing activities in real and fuzzy situations will help an organization’s decision makers to make the right decisions. In this paper, a new fuzzy hybrid methodology is proposed to describe and prioritize the activities of the organization in fuzzy conditions. First, the activities of the organization are described in (...) a new fuzzy format based on activity model of the C4ISR framework. Furthermore, fuzzy DEMATEL is used to calculate the interdependencies between activities, and then fuzzy ANP is used to calculate the weight of each activity. Finally, by combining the results of the two methods, the priority of activities was calculated. Additionally, an empirical study is presented to illustrate the application of the proposed method. (shrink)

Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised quantifiersGeneralised quantifiers for natural language. That technique requires one to construct the vector space over powersets, and therefore is computationally costly. In this paper, we overcome this problem by considering fuzzy versions of quantifiers along the lines of ZadehZadeh, L. A., within the category of many valued relationsMany valued relations. We show that this category is a concrete instantiation of the (...) compositional distributional model. We show that the semantics obtained in this model is equivalent to the semantics of the fuzzy quantifiers of ZadehZadeh, L. A.. As a result, we are now able to treat fuzzy quantification without requiring a powerset construction. (shrink)

In this article, the main definitions and differentiation concepts of neutrosophic fuzzy environment will be reviewed. This article will introduce an analytical methodology for solving the second-order linear ordinary differential problem with neutrosophic fuzzy boundary values, this analysis will be under generalized Hukuhara differentiability to show the analytical solutions from a different point of view for the uncertain system, some of these solutions may be decreasing in uncertainty or maybe reflecting the behavior of some real-world systems better. Some applications and (...) numeral examples will be solved to show the behavior of the solution. (shrink)