Entropy-based algorithms have been suggested as robust estimators of electroencephalography (EEG) predictability or regularity. This study aimed to examine possible disturbances in EEG complexity as a means to elucidate the pathophysiological mechanisms in chronic stroke, before and after a brain computer interface (BCI)-motor observation intervention. Eleven chronic stroke subjects and nine unimpaired subjects were recruited to examine the differences in their EEG complexity. The BCI-motor observation intervention was designed to promote functional recovery of the hand in stroke subjects. (...) class='Hi'>Fuzzy approximate entropy (fApEn), a novel entropy-based algorithm designed to evaluate complexity in physiological systems, was applied to assess the EEG signals acquired from unimpaired subjects and stroke subjects, both before and after training. The results showed that stroke subjects had significantly lower EEG fApEn than unimpaired subjects (p < 0.05) in the motor cortex area of the brain (C3, C4, FC3, FC4, CP3, CP4) in both hemispheres before training. After training, motor function of the paretic upper limb, assessed by the Fugl-Meyer Assessment-Upper Limb (FMA-UL), Action Research Arm Test (ARAT), and Wolf Motor Function Test (WMFT) improved significantly (p < 0.05). Furthermore, the EEG fApEn in stroke subjects increased considerably in the central area of the contralesional hemisphere after training (p < 0.05). A significant correlation was noted between clinical scales (FMA-UL, ARAT, and WMFT) and EEG fApEn in C3/C4 in the contralesional hemisphere (p < 0.05). This finding suggests that the increase in EEG fApEn could be an estimator of the variance in upper limb motor function improvement. In summary, fApEn can be used to identify abnormal EEG complexity in chronic stroke, when used with BCI-motor observation training. Moreover, these findings based on the fApEn of EEG signals also expand the existing interpretation of training-induced functional improvement in stroke subjects. Entropy-based analysis might serve as a novel approach to understanding the abnormal cortical dynamics of stroke and the neurological changes induced by rehabilitation training. (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)

This is the first part of a two-part paper in which I conclude the process, initiated elsewhere, of tracking objective conditions of vagueness of representation from language to pictures, from philosophy to imaging science, from vagueness to approximation, from representation to reasoning, with a focus on the application of fuzzy set theory and its challenges.

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice (...) L. In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy n-c.e. sets which form the finite levels of this hierarchy. Intuitively, a fuzzy set is n-c.e. if its membership function can be approximated by changing monotonicity at most n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} times. We prove that the Fuzzy Ershov Hierarchy does not collapse; that, in analogy with the classical case, each fuzzy n-c.e. set can be represented as a Boolean combination of fuzzy c.e. sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does not exhaust the class of all Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} fuzzy sets. (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)

In the last decade, formal concept analysis in a fuzzy setting has received more attention for knowledge processing tasks in various fields. The hierarchical order visualisation of generated formal concepts is a major concern for the practical application of FCA. In this process, a major issue is the huge number of formal concepts generated from ‘a large context’, and another problem is their ‘storage’ complexity. To deal with these issues a method is proposed in this paper based on Shannon (...) entropy and Huffman coding. The proposed method is illustrated using crisply generated concepts such that the changes between obtained concepts can be measured using Levenshtein distance. The analysis derived from the proposed method is illustrated with an example for FCA in a fuzzy setting. (shrink)

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the (...) sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and (...) fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. (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)

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)

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some (...) theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (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 a supply chain system, the prices with which the suppliers supply its local commodity to the retailers should satisfy the requirements of the retailers and the consumers. The supply and demand scheme satisfying these requirements is reduced into fuzzy relation inequalities with min-product composition. Due to the difference between the min-product composition and the classical max-t-norm one, we first study the resolution of such min-product FRI system. For optimization management in the supply chain system, we further investigate a (...) maximin programming problem subject to the min-product FRIs. An algorithm is proposed to obtain the optimal solution based on the quasi-maximal matrix and corresponding index set. To illustrate the efficiency of our proposed algorithm, we provide a simple numerical example. The obtained optimal solution reflects an optimal pricing scheme, which maximizes the minimum prices of the commodity from the suppliers. (shrink)

This short paper about fuzzy set-based approximate reasoning first emphasizes the three main semantics for fuzzy sets: similarity, preference and uncertainty. The difference between truth-functional many-valued logics of vague or gradual propositions and non fully compositional calculi such as possibilistic logic or similarity logics is stressed. Then, potentials of fuzzy set-based reasoning methods are briefly outlined for various kinds of approximate reasoning: deductive reasoning about flexible constraints, reasoning under uncertainty and inconsistency, hypothetical reasoning, exception-tolerant plausible (...) reasoning using generic knowledge, interpolative reasoning, and abductive reasoning. Open problems are listed in the conclusion. (shrink)

The method of approximate reasoning using a fuzzy logic introduced by Baldwin (1978 a,b,c), is used to model human reasoning in the resolution of two well known paradoxes. It is shown how classical propositional logic fails to resolve the paradoxes, how multiple valued logic partially succeeds and that a satisfactory resolution is obtained with fuzzy logic. The problem of precise representation of vague concepts is considered in the light of the results obtained.

Since the curriculum is the core carrier to improve the level of talent cultivation in colleges and universities, strengthening the reform of course teaching and improving the quality of course teaching are fundamental to the survival and development of colleges and universities, and also an important part of higher education reform. In this study, a fuzzy analytic hierarchy process and an entropy method were used to determine the weight of the core evaluation indicators of undergraduate course quality improvement, (...) including four first-level indicators of the curriculum concept, curriculum resources, curriculum organization, and curriculum effectiveness, and 12 s-level evaluation indicators and weights. Then, based on a case study of the first-class undergraduate course “Management” of Anyang Normal University, the way to evaluate the course by the AHP and entropy method was explained. Finally, according to the evaluation results, the ideas of course construction were put forward, such as changing the course concept, enriching the course resources, paying attention to the course organization, and ensuring the course effectiveness, so as to improve the quality of undergraduate courses and also to improve the quality of undergraduate talent training with the improvement of course quality as the starting point. (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)

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)

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)

Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann's (1955) argument. I argue that Hemmo and Shenker's arguments fail due to several misunderstandings: about statistical-mechanical and thermodynamic domains of applicability, about the nature of mixed states, and about the role of approximations in physics. As a result, their arguments fail in all cases: in the single-particle case, the finite particles case, (...) and the infinite particles case. (shrink)

This work defines various stakeholder roles to overcome the barriers to implementing Education 4.0, which were recently identified in the domain literature. The stakeholder roles are evaluated against these barriers, and such evaluation is structured as a multicriteria sorting problem. To this end, an integrated entropy-based CRITIC-CODAS-SORT under a Fermatean fuzzy environment addresses epistemic uncertainties inherent in decision-making. The FF CRITIC assigns the priority weights of the barriers, while the FF CODAS-SORT determines the high-priority stakeholder roles. A case (...) of an HEI evaluating 57 possible roles of 5 stakeholders is demonstrated here. Findings suggest the lack of collaboration, apprehensive stakeholders, cybersecurity threats, health issues, and cost as crucial barriers to the HEI. The sorting process yields 13 high-priority roles, encompassing those within the influence of the government, university management, human resource function, and educators. Various managerial insights are offered as inputs to the design of initiatives in EDUC4 implementation. (shrink)

In this paper, an adaptive fuzzy containment condtrol is considered for nonlinear multiagent systems, in which it contains the unknown control coefficient and actuator fault. The uncertain nonlinear function has been approximated by fuzzy logic system. The unknown control coefficient and the remaining control rate of actuator fault can be solved by introducing a Nussbaum function. In order to avoid the repeated differentiations of the virtual controllers, first-order filters are added to the traditional backstepping control method. By designing (...) the maximum norm of ideal adaptive parameters, only one adaptive parameter needs to be adjusted online for each agent itself. An adaptive fuzzy containment controller is constructed through the backstepping control technique and compensating signals. It is demonstrated that all the signals in nonlinear multiagent systems are bounded by designing adaptive fuzzy containment controller, and all followers can converge to the convex hull built by the leaders. The simulation studies can further confirm the effectiveness of the proposed control method in this paper. (shrink)

De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also (...) established. (shrink)

In this paper, a special type of polysemantic words, that is, words with multiple meanings for the same part of speech, are analyzed under the name of neutrosophic words. These words represent the most dif cult cases for the disambiguation algorithms as they represent the most ambiguous natural language utterances. For approximate their meanings, we developed a semantic representation framework made by means of concepts from neutrosophic theory and entropy measure in which we incorporate sense related data. We (...) show the advantages of the proposed framework in a sentiment classification task. (shrink)

With reference to two specific modalities of sensation, the taste of saltiness of chloride salts, and the loudness of steady tones, it is shown that the laws of sensation (logarithmic and power laws) are expressions of the entropy per mole of the stimulus. That is, the laws of sensation are linear functions of molar entropy. In partial verification of this hypothesis, we are able to derive an approximate value for the gas constant, a fundamental physical constant, directly (...) from psychophysical measurements. The significance of our observation lies in the linking of the phenomenon of “sensation” directly to a physical measure. It suggests that if the laws of physics are universal, the laws of sensation and perception are similarly universal. It also connects the sensation of a simple, steady physical signal with the molecular structure of the signal: the greater the number of microstates or complexions of the stimulus signal, the greater the magnitude of the sensation (saltiness or loudness). The hypothesis is currently tested on two sensory modalities. (shrink)

We expect the laws of nature that describe the universe to be exact, but what if that isn't true? In this popular science article, I discuss the possibility that some candidate fundamental laws of nature, such as the Past Hypothesis, may be vague. This possibility is in conflict with the idea that the fundamental laws of nature can always and faithfully be described by classical mathematics. -/- [Bibliographic note: this article is featured on the magazine website under a different title (...) as "The fuzzy law that could break the idea of a mathematical universe" and on the magazine cover as "The Flaw at the Heart of Reality: Why precise mathematical laws can never fully explain the universe." It is a popular version of the article "Nomic Vagueness" that can be found on arXiv: 2006.05298.]. (shrink)

ABSTRACT The term fuzzy logic has two different meanings -broad and narrow. In Zadeh's opinion, fuzzy logic is an extension of many- valued logic but having a different agenda—as generalized modus ponens, max-min inference, linguistic quantifiers etc. The question we address in this paper is whether there is something in Zadeh's specific agenda which cannot be grasped by “classiceli”, “traditional” mathematical logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted (...) many-valued Pavelka- Lukasiewicz style rational quantification logic. This means that, besides the linguistic or approximation aspects, the logical aspect is present too and can be made explicit. (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)

Since Aristotle it is recognised that a valid syllogism cannot have two particular premises. However, that is not how a lay person sees it; at least as long as the premises read many, most etc, instead of a plain some. The lay people are right if one considers that these syllogisms do not have strict but approximate (Zadeh) validity. Typically there are only particular premises available in everyday life and one is dependent on such syllogisms. – Some rules on (...) the usage of particular premises are given below. (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)

. Prediction of crop yield is significant in order to accurately meet market requirements and proper administration of agricultural activities directed towards enhancement in yield. Several parameters such as weather, pests, biophysical and physio morphological features merit their consideration while determining the yield. However, these parameters are uncertain in their nature, thus making the determined amount of yield to be approximate. It is exactly here that the fuzzy logic comes into play. This paper elaborates an attempt to develop (...) fuzzy inference systems for crop yield prediction. Physio morphological features of Sorghum were considered. A huge database of physio morphological features such as days of 50 percent flowering, dead heart percentage, plant height, panicle length, panicle weight and number of primaries and the corresponding yield were considered for the development of the model. In order to find out the sensitivity of parameters, one-to-one, two-to-one and three-to-one combinations of input and output were considered. The results have clearly shown that panicle length contributes for the yield as the lone parameter with almost one-to-one matching between predicted yield and actual value while panicle length and panicle weight in combination seemed to play a decisive role in contributing for the yield with the prediction accuracy reflected by very low RMS value. (shrink)

In this introduction to Part 1 of the Common Knowledge symposium, “Fuzzy Studies,” the journal's editor discusses four essays from the 1980s by Richard Rorty, in which Rorty chose to associate himself with various neopragmatists, Continental thinkers, and “left-wing Kuhnians” under the rubric of the “new fuzziness.” The term had been introduced as an insult by a philosopher of science with positivist leanings, but Rorty took it up as an “endearing” compliment, arguing that “to be less fuzzy” was (...) also to be “less genial, tolerant, open-minded, and fallibilist.” He defined the “new fuzziness” as “an attempt to blur just those distinctions between the objective and subjective and between fact and value which the critical conception of rationality has developed.” This introduction also examines W. V. Quine's essay “Speaking of Objects” (1957), which describes objects as fuzzy “half-entities”; Clifford Geertz's essay “Blurred Genres” (1980), which advises social scientists that being “taxonomically upstanding” is futile; and Lofti Zadeh's article “The Concept of a Linguistic Variable and Its Application to Approximate Reasoning” (1975), which abandons “Aristotelian, bivalent logic” in favor of a “fuzzy logic” based on Zadeh's “fuzzy set theory.” This introductory piece relates these theoretical works of the past half-century to the sorites paradox and to classical issues of vagueness raised and still unresolved in Western philosophy. Returning then to Rorty, the author questions how Rorty expected his endorsement of the “new fuzziness” to be applied, as proposed, to theology and politics. Suggesting that such applications are the natural work of historians, the author, having asked the historian Natalie Zemon Davis for comment, then quotes her response—which associates fuzzy studies, “common knowledge,” and peacemaking—at length. (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)

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

The connection between similarity logic and the theory of closure operators is examined. Indeed one proves that the consequence relation defined in [14] can be obtained by composing two closure operators and that the resulting operator is still a closure operator. Also, we extend any similarity into a similarity which is compatible with the logical equivalence, and we prove that this gives the same consequence relation.

An adaptive fractional-order nonsingular terminal sliding mode controller for a microgyroscope is presented with uncertainties and external disturbances using a fuzzy neural network compensator based on a backstepping technique. First, the dynamic of the microgyroscope is transformed into an analogical cascade system to guarantee the application of a backstepping design. Then, a fractional-order nonsingular terminal sliding mode surface is designed which provides an additional degree of freedom, higher precision, and finite convergence without a singularity problem. The proposed control scheme (...) requires no prior knowledge of the unknown dynamics of the microgyroscope system since the fuzzy neural network is utilized to approximate the upper bound of the lumped uncertainties and adaptive algorithms are derived to allow online adjustment of the unknown system parameters. The chattering phenomenon can be reduced simultaneously by the fuzzy neural network compensator. The stability and finite time convergence of the system can be established by the Lyapunov stability theorem. Finally, simulation results verify the effectiveness of the proposed controller and the comparison of root mean square error between different fractional orders and integer order is given to signify the high precision tracking performance of the proposed control scheme. (shrink)

This paper aims to determine whether it is necessary to propose the extreme of putrefaction as the only unmistakable sign in diagnosing the death of the human organism, as David Oderberg does in a recent paper. To that end, we compare Oderberg’s claims to those of other authors who align with him in espousing the so-called theory of hylomorphism but who defend either a neurological or a circulatory-respiratory criterion for death. We then establish which interpretation of biological phenomena is the (...) most reasonable within the metaphysical framework of hylomorphism. In this regard, we hold that technology does not obscure the difference between life and death or confect metaphysically anomalous beings, such as living human bodies who are not organisms or animals of the human species who are informed by a vegetative soul, but instead demands a closer and more careful look at the “fuzzy area” between a healthy organism and a decaying corpse. In the light of hylomorphism, we conclude that neurological and circulatory-respiratory criteria are not good instruments for diagnosing death, since they can offer only probabilistic prognoses of death. Of the two, brain death is further away from the moment of death as it merely predicts cardiac arrest that will likely result in death. Putrefaction, the criterion that Oderberg proposes, is at the opposite end of the fuzzy area. This is undoubtedly a true diagnosis of death, but it is not necessary to wait for putrefaction proper—a relatively late stage of decomposition—to be sure that death has already occurred. Rather, early cadaveric phenomena demonstrate that the matter composing a body is subject to the basic forces governing all matter in its environment and has thus succumbed to the universal current of entropy, meaning that the entropy-resisting activity has ceased to constitute an organismal unity. When this unity is lost, there is no possibility of return. (shrink)

Robot manipulators have been extensively used in complex environments to complete diverse tasks. The teleoperation control based on human-like adaptivity in the robot manipulator is a growing and challenging field. This paper developed a disturbance-observer-based fuzzy control framework for a robot manipulator using an electromyography- driven neuromusculoskeletal model. The motion intention was estimated by the EMG-driven NMS model with EMG signals and joint angles from the user. The desired torque was transmitted into the desired velocity for the robot manipulator (...) system through an admittance filter. In the robot manipulator system, a fuzzy logic system, utilizing an integral Lyapunov function, was applied for robot manipulator systems subject to model uncertainties and external disturbances. To compensate for the external disturbances, fuzzy approximation errors, and nonlinear dynamics, a disturbance observer was integrated into the controller. The developed control algorithm was validated with a 2-DOFs robot manipulator in simulation. The results indicate the proposed control framework is effective and crucial for the applications in robot manipulator control. (shrink)

This paper presents a problem of observer-based adaptive fuzzy predefined performance control of a class of nonlinear pure-feedback systems with input delay and unknown control direction. Compared with the existing research, a novel predefined performance controller is proposed, which relaxes the assumption that the initial error is known. In addition, it is difficult to design the controllers due to input delay and nonaffine properties of the pure-feedback systems, which can be simplified by Pade approximation. Moreover, dynamic surface control and (...) Nussbaum functions are applied to overcome the calculation explosion caused by repeated differentiations and unknown control direction, respectively. Based on the above methods, an adaptive fuzzy predefined performance controller is proposed, and it is proved that all the signals of a closed-loop system are semiglobally uniformly ultimately bounded. The tracking errors converge within a predefined range, while the observer estimation errors converge within a small zero region. Finally, the simulation results demonstrate the effectiveness of the proposed control system. (shrink)

This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. In (...) a final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. (shrink)

This study focuses on the static output feedback control of nonlinear Markov jump singularly perturbed systems within the framework of Takagi–Sugeno fuzzy approximation. From a practical point of view, the phenomenon of asynchronous switching between the plant and the controller is considered and characterized by a finite piecewise-homogenous Markov process. Particularly, for facilitating the controller synthesis, the closed-loop system is transformed into a fuzzy Markov jump singularly perturbed descriptor system by adopting descriptor representation. In order to fully accommodate (...) the system features, an appropriate stochastic Lyapunov function is constructed. Afterwards, by combining Finsler’s lemma, the mean square exponential admissibility of the system is analyzed. The conditions ensuring the existence of the predesigned controller are given and further solved by designing a brief search algorithm. Finally, a typical circuit system is used to demonstrate the application potential of the developed control technology and the effectiveness of the control strategy. (shrink)

Clustering is one of the most fundamental and essential data analysis tasks with broad applications. It has been studied in various research fields: data mining, machine learning, pattern recognition and in engineering, economics and biomedical data analysis. Headache is not a disease that typically shortens one’s life, but it can be a serious social as well as a health problem. Approximately 27 billion euros per year are lost through reduced work productivity in the European community. This paper is focused on (...) a new strategy based on a hybrid model for combining fuzzy partition method and maximum likelihood estimation clustering algorithm for diagnosing primary headache disorder. The proposed hybrid system is tested on two data sets for diagnosing headache disorder collected from Clinical Centre of Vojvodina in Serbia. (shrink)