Comparison of fuzzy reasoning methods
TL;DR: This paper deals with the properties of their methods in the case of 'generalized modus tollens', and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1982-09-01. It has received 493 citations till now. The article focuses on the topics: Fuzzy logic & Fuzzy mathematics.
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31 Jul 1985
TL;DR: The book updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research.
Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.
7,877 citations
01 Apr 1990
TL;DR: The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined and several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated.
Abstract: For pt.I see ibid., vol.20, no.2, p.404-18, 1990. The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined. Several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated. Defuzzification strategies, are discussed. Some of the representative applications of the FLC, from laboratory level to industrial process control, are briefly reported. Some unsolved problems are described, and further challenges in this field are discussed. >
5,502 citations
Book•
01 Jan 1993
TL;DR: Fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic that can be found either as stand-alone control elements or as int ...
Abstract: Fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic. They can be found either as stand-alone control elements or as int ...
2,139 citations
Book•
14 Oct 2010
TL;DR: This paper presents a model for a Fuzzy Rule-Based System that automates the very labor-intensive and therefore time-heavy process of decision-making in the context of classical sets.
Abstract: Classical Sets and Fuzzy Sets.- Classical and Fuzzy Relations.- Membership Functions.- Defuzzification.- Fuzzy Rule-Based System.- Fuzzy Decision Making.- Applications of Fuzzy Logic.- Fuzzy Logic Projects with Matlab.
994 citations
Book•
01 Jan 1996TL;DR: This text is the first to combine the study of neural networks and fuzzy systems, their basics and their use, along with symbolic AI methods to build comprehensive artificial intelligence systems.
Abstract: From the Publisher:
"Covering the latest issues and achievements, this well documented, precisely presented text is timely and suitable for graduate and upper undergraduate students in knowledge engineering, intelligent systems, AI, neural networks, fuzzy systems, and related areas. The author's goal is to explain the principles of neural networks and fuzzy systems and to demonstrate how they can be applied to building knowledge-based systems for problem solving. Especially useful are the comparisons between different techniques (AI rule-based methods, fuzzy methods, connectionist methods, hybrid systems) used to solve the same or similar problems."
-- Anca Ralescu, Associate Professor of Computer Science, University of Cincinnati Neural networks and fuzzy systems are different approaches to introducing human-like reasoning into expert systems. This text is the first to combine the study of these two subjects, their basics and their use, along with symbolic AI methods to build comprehensive artificial intelligence systems.
In a clear and accessible style, Kasabov describes rule- based and connectionist techniques and then their combinations, with fuzzy logic included, showing the application of the different techniques to a set of simple prototype problems, which makes comparisons possible. A particularly strong feature of the text is that it is filled with applications in engineering, business, and finance. AI problems that cover most of the application-oriented research in the field (pattern recognition, speech and image processing, classification, planning, optimization, prediction, control, decision making, and game simulations) are discussed and illustrated with concrete examples.
Intended both as a text for advanced undergraduate and postgraduate students as well as a reference for researchers in the field of knowledge engineering, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering has chapters structured for various levels of teaching and includes original work by the author along with the classic material.
Data sets for the examples in the book as well as an integrated software environment that can be used to solve the problems and do the exercises at the end of each chapter are available free through anonymous ftp.
977 citations
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TL;DR: In this article, a fuzzy logic is used to synthesize linguistic control protocol of a skilled operator for industrial plants, which has been applied to pilot scale plants as well as in practical situations.
Abstract: This paper describes an application of fuzzy logic in designing controllers for industrial plants. A fuzzy logic is used to synthesize linguistic control protocol of a skilled operator. The method has been applied to pilot scale plants as well as in practical situations. The merits of this method and its usefulness to control engineering are discussed. An avenue for further work in this area is described where the need is to go beyond a purely descriptive approach, and means for implementing a prescriptive or a self-organizing system are explored.
2,011 citations
Book•
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01 Jan 1969
TL;DR: In Ch. IX of his treatise On Interpretation (De interpretatione), Aristotle discussed the truth-status of alternatives regarding future-contingent matters, whose occurrence is not yet determinable by us, and may indeed actually actually be undetermined as discussed by the authors.
Abstract: Throughout the orthodox mainsteam of the development of logic in the West, the prevailing view was that every proposition is either true or else false (although which of these is the case may well neither be necessary as regards the matter itself nor determinable as regards our knowledge of it). This thesis, commonly called the ‘law of bivalence’ — constituting one key articulation of the ‘law of the excluded middle’ — was, however, already questioned in antiquity. In Ch. IX of his treatise On Interpretation (De interpretatione), Aristotle discussed of the truth-status of alternatives regarding ‘future-contingent’ matters, whose occurrence — like that of the sea-battle tomorrow — is not yet determinable by us, and may indeed actually be undetermined. His views on the matter are still disputed, but many commentators, both in antiquity and later, held him to assert that propositions about future contingents, like that asserting the occurrence of the sea-battle, are neither actually true nor actually false, but potentially either, thus having — at least prior to the event — a third, indeterminate truth-status. The acceptance of the principle of bivalence was, in antiquity, closely bound up with the doctrine of determinism. The Epicureans, who were indeterminists, rejected the law of bivalence; the Stoics (and above all Chrysippus) who were rigid determinists, insisted upon it.1
683 citations
01 Aug 1996
TL;DR: The calculus of fuzzy restrictions is concerned with translation of propositions of various types into relational assignment equations, and the study of transformations of fuzzy Restrictions which are induced by linguistic modifiers, truth-functional modifiers, compositions, projections and other operations.
Abstract: A fuzzy restriction may be visualized as an elastic constraint on the values that may be assigned to a variable In terms of such restrictions, the meaning of a proposition of the form “x is P,” where x is the name of an object and P is a fuzzy set, may be expressed as a relational assignment equation of the form R(A(x)) = P, where A(x) is an implied attribute of x, R is a fuzzy restriction on x, and P is the unary fuzzy relation which is assigned to R For example, “Stella is young ,” where young is a fuzzy subset of the real line, translates into R(Age(Stella))= young The calculus of fuzzy restrictions is concerned, in the main, with (a) translation of propositions of various types into relational assignment equations, and (b) the study of transformations of fuzzy restrictions which are induced by linguistic modifiers, truth-functional modifiers, compositions, projections and other operations An important application of the calculus of fuzzy restrictions relates to what might be called approximate reasoning , that is, a type of reasoning which is neither very exact nor very inexact The main ideas behind this application are outlined and illustrated by examples
579 citations
TL;DR: The theory of fuzzy power sets is shown very naturally to require the use of a fuzzy implication operator and emphasis is placed on the dependence of the choice of operators upon the purposes the user has in hand.
462 citations
TL;DR: It is pointed out that the consequence inferred by the methods suggested does not always fit intuitions and improved methods are suggested which fit the authors' intuitions under several criteria.
171 citations