Book ChapterDOI
Calculus of fuzzy restrictions
Lotfi A. Zadeh
- pp 210-237
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TLDR
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 examplesread more
Citations
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Fuzzy sets as a basis for a theory of possibility
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
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Fuzzy logic = computing with words
TL;DR: The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa and, as an approximation, fuzzy logic may be equated to CW.
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An Introduction to Fuzzy Control
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 ...
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From computing with numbers to computing with words. From manipulation of measurements to manipulation of perceptions
TL;DR: The computational theory of perceptions (CTP) as mentioned in this paper is a methodology for reasoning and computing with perceptions rather than measurements, where words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in a natural language.
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Is there a need for fuzzy logic
TL;DR: In this paper, fuzzy logic is viewed in a nonstandard perspective and the cornerstones of fuzzy logic-and its principal distinguishing features-are: graduation, granulation, precisiation and the concept of a generalized constraint.
References
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The concept of a linguistic variable and its application to approximate reasoning—II☆
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
Journal ArticleDOI
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Journal ArticleDOI
Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.