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

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

Power structures are obtained by lifting some mathematical structure (operations, relations, etc.) from an universe X to its power set ${\mathcal{P}(X)}$ . A similar construction provides fuzzy power structures: operations and fuzzy relations on X are extended to operations and fuzzy relations on the set ${\mathcal{F}(X)}$ of fuzzy subsets of X. In this paper we study how this construction preserves some properties of fuzzy sets and fuzzy relations (similarity, congruence, etc.). We define the (...) notions of good, very good, Hoare good and Smith good fuzzy relation and establish some connections between them, generalizing some results of Brink, Bošnjak and Madarász on power structures. (shrink)

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.

Earthquake is a kind of natural disaster, which will have a great impact on the building structure. In the vibration control field of building structures, the timeliness of system stability is extremely important. In traditional control methods, the timeliness is not paid enough attention for systems with uncertain seismic waves. For setting this problem, fuzzy adaptive compensation control for uncertain building structural systems by sliding-mode technology is proposed. It is combined with fuzzy adaptive control and sliding-mode control (...) to ensure that the system can be stable with satisfied timeliness. Also, saturation function is used to ensure the feasible physical implementation of the control system. Compared with the traditional LQR control, the simulation results showed that the proposed method can make the system reach a stable state with rapid convergence performance and has a feasible physical implementation. (shrink)

The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanché’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are linguistic expressions such (...) as “most”, “many”, “a few”, and “almost all”, and they correspond to what are often called “fuzzy quantifiers” in the literature. The graded Peterson’s cube of opposition, which describes properties between two graded squares, will be discussed at the end of this paper. (shrink)

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α, δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to (...) a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ. (shrink)

Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists (...) an order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism. (shrink)

Substructural logics are obtained from the sequent calculi for classical or intuitionistic logic by suitably restricting or deleting some or all of the structural rules (Restall, 2000; Ono, 1998). Recently, this field of research has come to encompass a number of logics - e.g. many fuzzy or paraconsistent logics - which had been originally introduced out of different, possibly semantical, motivations. A finer proof-theoretical analysis of such logics, in fact, revealed that it was possible to subsume them under the (...) previous definition (see e.g. Aguzzoli and Ciabattoni, 2000).Although proof systems for substructural logics are currently being investigated with remarkable success, their algebraic models do not seem equally satisfactory. In fact:(i) such structures are often very weak, i.e. they do not possess many interesting algebraic properties;(ii) as a consequence, their theories of ideals, congruences, and representation are as a rule scarcely developed, or even lacking.In this paper, we address these difficulties. (shrink)

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

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.

In a series of articles we try to show the need of a novel Theory for Theory of Computation based on considering time as a Fuzzy concept. Time is a central concept In Physics. First we were forced to consider some changes and modifications in the Theories of Physics. In the second step and throughout this article we show the positive Impact of this modification on Theory of Computation and Complexity Theory to rebuild it in a more successful and (...) fruitful approach. We call this novel Theory TC*. (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)

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 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.

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 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)

While the past century of neuroscientific research has brought considerable progress in defining the boundaries of the human cerebral cortex, there are cases in which the demarcation of one area from another remains fuzzy. Despite the existence of clearly demarcated areas, examples of gradual transitions between areas are known since early cytoarchitectonic studies. Since multi-modal anatomical approaches and functional connectivity studies brought renewed attention to the topic, a better understanding of the theoretical and methodological implications of fuzzy boundaries (...) in brain science can be conceptually useful. This article provides a preliminary conceptual framework to understand this problem by applying philosophical theories of vagueness to three levels of neuroanatomical research. For the first two levels (cytoarchitectonics and fMRI studies), vagueness will be distinguished from other forms of uncertainty, such as imprecise measurement or ambiguous causal sources of activation. The article proceeds to discuss the implications of these levels for the anatomical study of connectivity between cortical areas. There, vagueness gets imported into connectivity studies since the network structure is dependent on the parcellation scheme and thresholds have to be used to delineate functional boundaries. Functional connectivity may introduce an additional form of vagueness, as it is an organizational principle of the brain. The article concludes by discussing what steps are appropriate to define areal boundaries more precisely. (shrink)

The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express (...) their hopes for the future. (shrink)

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)

This unique compendium presents a comprehensive and self-contained theory of material development under imperfect information and its applications. The book describes new approaches to synthesis and selection of materials with desirable characteristics. Such approaches provide the ability of systematic and computationally effective analysis in order to predict composition, structure and related properties of new materials. The volume will be a useful advanced textbook for graduate students. It is also suitable for academicians and practitioners who wish to have fundamental models (...) in new material synthesis and selection. (shrink)

This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The algebraic (...) structures corresponding to the systems are then defined, and completeness results are provided. We next consider fuzzy systems satisfying new relevance principles introduced by Yang. We show that the weakening-free uninorm systems and some extensions and neighbors of R satisfy the new relevance principles. (shrink)

Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and (...) residuated lattice. It contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details; besides semantics, syntax and completeness of this logic, a lot of examples are given. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices. (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)

The study of weighted structures is one of the important trends in recent computer science. The aim of the article is to provide a weighted, many-valued version of classical intensional semantics formalised in the framework of higher-order fuzzy logics. We illustrate the apparatus on several variants of fuzzy S5-style modalities. The formalism is applicable to a broad array of weighted intensional notions, including alethic, epistemic, or probabilistic modalities, generalised quantifiers, counterfactual conditionals, dynamic and non-monotonic logics, and some more.

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)

A dam is a complex and important water-retaining structure. Once the dam is broken, the flood will cause immeasurable damage to the lives and properties of the downstream people, so it is particularly important to have the dam risk management. Since the dam-break flood is a severe-consequence low-frequency event, the corresponding fatalities caused by it are difficult to estimate due to the lack of relevant data and poor data continuity. This paper analyzes the direct and indirect factors affecting the (...) risk of life loss in dam failures and studies the characteristics, distribution rules, and membership functions of each factor. An adaptive differential evolution method is constructed through an optimization of the mutation factors and cross factors of the differential evolution method. This proposed evaluation method also combines with the fuzzy clustering iterative method that is capable of evaluating the similarity of life loss in dam accidents. The effectiveness of the proposed method is verified by 16 dam-break case studies. (shrink)

A decentralized adaptive control based on human linguistic is investigated to learn human behaviors for multiple robotic manipulators. Many experts’ words or sentences can be transferred into the control actions by employing membership functions in robot systems, which can be synthesized fuzzy controller by employing reasoning mechanism. For the unknown model dynamical robot manipulators, one adjustable parameter that relates to the approximation accuracy of fuzzy logic systems is introduced at first, which be utilized to deal with the unknown (...) dynamics of robot manipulators. Switching fuzzy adaptive controller is designed to overcome the limitation of logic structure that the number of adaptive laws only focus on fuzzy rules in conventional fuzzy logic systems. Another advantage of this design method is that the control with human linguistic extend the semi-global stability to global stability. Finally, effectiveness of the developed control design scheme has been shown in simulation example. (shrink)

One of the main challenges in medicine is to guarantee an appropriate drug supply according to the real needs of patients. Closed-loop strategies have been widely used to develop automatic solutions based on feedback variables. However, when the variable of interest cannot be directly measured or there is a lack of knowledge behind the process, it turns into a difficult issue to solve. In this research, a novel algorithm to approach this problem is presented. The main objective of this study (...) is to provide a new general algorithm capable of determining the influence of a certain clinical variable in the decision making process for drug supply and then defining an automatic system able to guide the process considering this information. Thus, this new technique will provide a way to validate a given physiological signal as a feedback variable for drug titration. In addition, the result of the algorithm in terms of fuzzy rules and membership functions will define a fuzzy-based decision system for the drug delivery process. The method proposed is based on a Fuzzy Inference System whose structure is obtained through a decision tree algorithm. A four-step methodology is then developed: data collection, preprocessing, Fuzzy Inference System generation, and the validation of results. To test this methodology, the analgesia control scenario was analysed. Specifically, the viability of the Analgesia Nociception Index as a guiding variable for the analgesic process during surgical interventions was studied. Real data was obtained from fifteen patients undergoing cholecystectomy surgery. (shrink)

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 lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results; – interesting new concepts besides antitone and isotone ones (like, for instance, conjugated (...) pair), that were classically reducible to the first, gain independency in fuzzy setting. (shrink)

A logic is a doctrine of the logos, that is, of meaningful discourse; hence the first thing we expect from it is an account of what makes the logos meaningful — of what a meaning is. There is no single such doctrine or account: it is part of the immense richness of meaningful discourse that we can shift back and forth between several logics — several organized ways of reasoning, of providing reasons or grounds for our claims. Building on previous (...) work on Hegel's dialectical logic, the author here identifies three distinct logics simultaneously in play in our conversations. Analytic logic structures its organization of discourse around negation, contraries, and hence arguments forcing a conclusion to follow (under threat of inconsistency) from some premises. Dialectical logic's main tool is the construction of narratives, hence the attempted incorporation of interlocutors within one's own story. The third option, here labeled gradual logic, sees sorites (which are recalcitrant anomalies for the analytic approach) as ideal cases, since the bleeding of a predicate into an alleged contrary points the way to reaching an agreement among initially conflicting parties: to them eventually coming to regard themselves as stressing different aspects of one and the same thing. (shrink)

The dynamic nature and increasing complexity of the construction industry have led to increased conflicts in construction projects. An accurate prediction of the outcome of a dispute resolution in courts could effectively reduce the number of disputes that would otherwise conclude by spending more money through litigation. This study aims to introduce a two-layered fuzzy logic model for predicting court decisions in construction contract disputes. 100 cases of construction contract disputes are selected from the courts of Iran. A questionnaire (...) survey is then conducted to extract a set of fuzzy rules for identifying important decision parameters and expert knowledge. Accordingly, a two-layered fuzzy logic-based decision-making architecture is proposed for the prediction model. Furthermore, the fuzzy system is trained based on 10-fold cross-validation. Analysis of results indicates that 51 out of the 100 cases are filed after the dissolution and termination of the contract show a significant impact of these clauses as the root cause in construction contract disputes. Our results present a proposed hierarchical fuzzy system that can correctly predict nearly 60% of the test data. Also, we demonstrate a methodology of using argument before ML to establish interpretable AI models. Based on our findings, a fuzzy model with a hierarchical structure may be used as a simple and efficient method for predicting court decisions in construction contract disputes. (shrink)

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of \((\alpha,\beta)\)-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study \((\alpha,\beta)\)-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of \((\alpha,\beta)\)-hesitant fuzzy ideal generated by a hesitant fuzzy ideal (...) in a semigroup. In addition, we also introduce the concepts of \((\alpha,\beta)\)-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of \((\alpha,\beta)\)-hesitant fuzzy left ideals and \((\alpha,\beta)\)-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of \((\alpha,\beta)\)-hesitant ideals are given. (shrink)

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL-chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL-chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak (...) cancellation defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness. (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)

This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares of (...) opposition respectively. We clarify the differences between these two cubes, and discuss their gradual extensions, as well as the one of the hexagon when vertices are no longer two-valued. The second part of the paper is dedicated to the use of these structures of opposition for discussing the comparison of two items. Comparing two items usually involves a set of relevant attributes whose values are compared, and may be expressed in terms of different modalities such as identity, similarity, difference, opposition, analogy. Recently, J.-Y. Béziau has proposed an “analogical hexagon” that organizes the relations linking these modalities. Elementary comparisons may be a matter of degree, attributes may not have the same importance. The paper studies in which ways the structure of the hexagon may be preserved in such gradual extensions. As another illustration of the graded hexagon, we start with the hexagon of equality and inequality due to R. Blanché and extend it with fuzzy equality and fuzzy inequality. Besides, the cube induced by a tetra-partition can account for the comparison of two items in terms of preference, reversed preference, indifference and non-comparability even if these notions are a matter of degree. The other cube, which organizes the relations between the different weighted qualitative aggregation modes, is more relevant for the attribute-based comparison of items in terms of similarity. (shrink)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" (...) sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out. (shrink)

In this article, a new adaptive fuzzy wavelet neural network model is proposed for nonlinear function approximation problems. The AFWNN model is based on the traditional Takagi-Sugeno-Kang fuzzy system. Specifically, this model replaces the membership functions of fuzzy rules with wavelet basis functions, which are known to have time and frequency localization properties, i.e., they can approximate patterns both in the time and frequency domains. The structure of the AFWNN model is derived from that of the (...) adaptive neuro-fuzzy inference system. However, the AFWNN improves over the ANFIS by replacing Gaussian functions in the hidden layer with wavelet basis functions. The AFWNN model is trained using a gradient-based optimization algorithm. The AFWNN is then tested on three function approximation problems of time series prediction. For certain types of nonlinear time series, for instance fractal processes, the AFWNN is found to be substantially more accurate than alternative methods. (shrink)

In this essay, the author both reviews Scott Sowerby's book Making Toleration: The Repealers and the Glorious Revolution and makes a late contribution to, or comment on, the Common Knowledge symposium “Fuzzy Studies”. Sowerby opposes the “Whig interpretation” that James II was attempting to reinstate Stuart “popery and arbitrary government” and instead presents James II's policies as aimed at liberation of the Stuart monarchy from the borough, county, and clerical elites that had brought it back to power and regarded (...) restoration of the Church of England as their instrument and identity. The king thus had his own reasons for upholding the liberty of conscience, and so James II can be found using the language of a skeptical Enlightenment, while at the same time affirming the absoluteness of his authority and incurring the suspicion of popery. How “toleration” of Catholics and dissenters came about in Britain must be told by narrating the “hard” histories of various state structures, but there is a larger and “softer” history of Enlightenment to be extracted from that of the European ancien régime, in whose history and downfall “British history” has a part that can be narrated in both “hard” and “soft” terms. The recent revisionist accounts of James II — of which Sowerby's is said in this review to be among the best — offer the king a new role at that regime's beginnings. This review concludes by arguing that the pursuit of history as it has come to be practiced is among the “softest” modes of explanation — since it consists of the unending and unlimited pursuit of the contexts in which actions, words, and processes have been situated and need to be studied — and that the more there are of these, the more meanings the actions may bear and the fewer reasons there are for the use of Occam's razor. “The notion of ‘fuzziness’ ” does not disturb historians, as it does scholars in some other disciplines, since historians have at their disposal an established contextualist “means of navigating it.”. (shrink)

The Wiener index WI is one of the connectivity parameters used to know the biochemical and physicochemical properties of compounds depending upon their molecular structures. Intuitionistic fuzzy graphs IFG s are a convenient tool to represent the objects and relations between them with two types of information using truth membership degree and falsity membership degree. This research work presents the concept of WI under the structure IFG s, I F trees, and I F cycles. Some bounds on WI (...) are investigated. The relationship between WI and connectivity index CI is also studied. In the end of this study, an application of the WI in transport network flow is proposed. (shrink)

This meta-study of animal semantics is anchored in two claims, seemingly creating a fuzzy mismatch, that animal utterances generally appear to be simple in structure and content variation and that animals’ communicative understanding seems disproportionally more advanced. A set of excerpted, new studies is chosen as basis to discuss whether the semantics of animal uttering and understanding can be fused into one. Studies are prioritised due to their relatively complex designs, giving priority to dynamics between syntax, semantics, pragmatics, (...) and between utterers and receivers in context. A communicational framework based on utterance theory is applied as a lens for inspection of how these aspects relate to the assumed mismatch. Inspection and discussions of the studies bring several features to surface of which five are stressed in the following. Firstly, both syntactic structures and possible semantic content are seen as lean, although richer than earlier believed, and research continues to reveal new complexities in utterances. Secondly, there is a clear willingness to broaden the perception of animals’ semantic capacity to comprehend communication both by arguing theoretically and by generating empirical research in new contexts. Thirdly, the ambition to make sense of these tendencies is still often motivated by an evolutionary search for early building blocks for verbal language, with the pro et cons that such a position can have. Fourthly, the ‘allowed’ scientific frame for studying semantic capacity among animals is extended to new fields and contexts challenging the only-in-the-wild norm. Fifthly, the dilemma of integrating uttering and understanding as aspects of an after all functional communicational system, calls for new epistemological concepts to make sense of the claimed mismatch. Affordances, abduction, life-genre, and lifeworld are suggested. (shrink)

If beliefs are a map by which we steer, then, ceteris paribus, we should want a more accurate map. However, the world could be structured so as to punish learning with respect to certain topics—by learning new information, one’s situation could be worse than it otherwise would have been. We investigate whether the world is structured so as to punish learning specifically about moral nihilism. We ask, if an ordinary person had the option to learn the truth about moral nihilism, (...) ought she to take it? We argue, given plausible assumptions about ordinary human preferences, she should not. (shrink)

The proposed work describes an approach for the segmentation of abnormal lung CT scans of COVID-19. Lung diseases are the leading killer in both men and women. The pulmonary experts normally make attempts, such as early detection of patients by tomography tests before lung specialists treat patients who are tortured by lung disease. Moreover, lung specialists do their best to detect the presence of lung conditions. X rays or CT scan checks are performed for tomography tests. The finest approach for (...) medical diagnosis and a wide range of uses is computed tomography. This kind of imaging offers elaborate cross-sectional pictures of skinny slices of the organic structure. However, the preprocessing and denoising methods of Lung CT scans may mask some important image features. To address this challenge, we propose a novel framework involving an optimization technique algorithm to solve a multilevel thresholding problem based on information theory to segment abnormal lung CT scans. The proposed framework will evaluate a sample of CT scan images taken from a well-known benchmark database. The evaluation results will assess subjectively and objectively to demonstrate the effectiveness of the proposed framework. (shrink)

We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraïssé limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.

The theory of concept lattices is approached from the point of view of fuzzy logic. The notions of partial order, lattice order, and formal concept are generalized for fuzzy setting. Presented is a theorem characterizing the hierarchical structure of formal fuzzy concepts arising in a given formal fuzzy context. Also, as an application of the present approach, Dedekind–MacNeille completion of a partial fuzzy order is described. The approach and results provide foundations for formal concept (...) analysis of vague data—the propositions “object x has attribute y”, which form the input data to formal concept analysis, are now allowed to have also intermediate truth values, meeting reality better. (shrink)

A possible world structure consist of a set W of possible worlds and an accessibility relation R. We take a partial function r(·,·) to the unit interval [0, 1] instead of R and obtain a Kripke frame with graded accessibility r Intuitively, r(x, y) can be regarded as the reliability factor of y from x We deal with multimodal logics corresponding to Kripke frames with graded accessibility in a fairly general setting. This setting provides us with a framework for (...) fuzzy possible world semantics. The basic propositional multimodal logic gK (grated K) is defined syntactically. We prove that gK is sound and complete with respect to this semantics. We discuss some extensions of gK including logics of similarity relations and of fuzzy orderings. We present a modified filtration method and prove that gK and its extensions introduced here are decidable. (shrink)