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612-822-4611
Transforms of Undefined Sets, Undefined Structures, and Undefined β-Systems

Transforms of Undefined Sets, Undefined Structures, and Undefined β-Systems

Paperback

AlgebraGeneral Computers

ISBN13: 9798230306139
Publisher: Independent Publisher
Published: Jan 28 2025
Pages: 146
Weight: 0.78
Height: 0.31 Width: 8.50 Depth: 11.00
Language: English

The concept proposed by Zadeh.L.A.[82] defining a fuzzy subset A of a given universe X characterizing the membership of an element x of X belonging to A by means of a membership function A etc., in handling the imprecise real life situations mathematically. Now, several branches of fuzzy mathematics like fuzzy algebra, fuzzy topology, fuzzy control theory, fuzzy measure the- ory etc. have emerged. But in the decision making, the fuzzy theory takes care of membership of an element x only, that is the evidence of x belonging to A. It does not take care of the evidence against x belonging to A. It is felt by several decision makers and researchers that in proper decision making, the evidence of x belonging to A and evidence not belonging to A are both necessary, and how much x belongs to A or how much x does not belong to A are necessary. This is the problem with fuzzy sets. To counter this problem Gau.W.L. and Buehrer.D.J[28] introduced the concept of Vague Set Theory.

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