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Business and Management
Artificial Intelligence
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Chapter
Expert Systems and Fuzzy Control
During the last two centuries the potential of electronic data processing (EDP) has been used to an increasing degree to support human decision making in different ways. In the sixties the management informati...
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Book
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Chapter
Decision Making in Fuzzy Environment
The term decision can have very many different meanings, depending on whether it is used by a lawyer, a businessman, a general, a psychologist, or a statistician. In one case it might be a legal construct, in ano...
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Chapter
Empirical Research in Fuzzy Set Theory
The terms model, theory, and law have been used with a variety of meanings, for a number of purposes, and in many different areas of our life. It is therefore necessary to defme more accurately what we mean by mo...
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Chapter
Fuzzy Sets—Basic Definitions
A classical (crisp) set is normally defined as a collection of elements or objects xεX which can be finite, countable, or overcountable. Each single element can either belong to or not belong to a set A, A⊆X. In ...
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Chapter
Fuzzy Measures and Measures of Fuzziness
In order to prevent confusion about fuzzy measures and measures of fuzziness, we shall first briefly describe the meaning and features of fuzzy measures. In the early 1970s, Sugeno defined a fuzzy measure as f...
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Chapter
Fuzzy Relations and Fuzzy Graphs
Fuzzy relations are fuzzy subsets of X × Y, that is, map**s from X → Y. They have been studied by a number of authors, in particular by Zadeh [1965, 1971], Kaufmann [1975], and Rosenfeld [1975]. Applications of...
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Chapter
Possibility Theory vs. Probability Theory
Since L. Zadeh proposed the concept of a fuzzy set in 1965 the relationships between probability theory and possibility theory have been discussed. Both theories seem to be similar in the sense that they both ...
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Chapter
Pattern Recognition
Pattern recognition is one of the oldest and most obvious application areas of fuzzy set theory. The termpattern recognition embraces a very large and diversified literature. It includes research in the area of a...
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Chapter
Fuzzy Set Models in Operations Research
The contents and scope of operations research has been described and defined in many different ways. Most of the people working in operations research will agree, however, that the modelling of problem situati...
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Chapter
Future Perspectives
In the first 9 chapters of this book we have covered the basic foundations of the theory of fuzzy sets, as they can be considered undisputed as of today. Many more concepts and theories could not be discussed ...
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Chapter
Introduction to Fuzzy Sets
Most of our traditional tools for formal modelling, reasoning, and computing are crisp, deterministic and precise in character. By crisp we mean dichotomous, that is, yes-or-no-type rather than more-or-less ty...
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Chapter
Extensions
In chapter 2 the basic definition of a fuzzy set was given and the original set theoretic operations were discussed. The membership space was assumed to be the space of real numbers, membership functions were ...
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Chapter
The Extension Principle and Applications
One of the most basic concepts of fuzzy set theory which can be used to generalize crisp mathematical concepts to fuzzy sets is the extension principle. In its elementary form it was already implied in Zadeh’s...
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Chapter
Fuzzy Analysis
A fuzzy function is a generalization of the concept of a classical function. A classical function f is a map** (correspondence) from the domain D of definition of the function into a space S; f(D)⊆S is called t...
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Chapter
Fuzzy Logic and Approximate Reasoning
“In retreating from precision in the face of overpowering complexity, it is natural to explore the use of what might be called linguistic variables, that is, variables whose values are not numbers but words or se...
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Book Series
International Series in Management Science/Operations Research
Volume 10 / 1987
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Chapter
Individual Decision Making in Fuzzy Environments
We shall consider two versions of a decision, the classical choice model of normative decision theory (definition 1.1) and the “evaluation model” described in the first part of chapter 1.
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Chapter
Fuzzy Mathematical Programming
Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively. The term fuzzy programming has been used in different ways in the past. Ostasiewicz [1982], Tanaka and Mizumoto...
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Chapter
Operators and Membership Functions in Decision Models
Many papers in the area of fuzzy sets start with statements such as “Given membership function µ A (x) and assuming that the minimum operator is an appropriate model for the intersec...
