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Fuzzy mappings

Stanisław Heilpern — 1983

Mathematica Applicanda

Let X be the class of all fuzzy subsets of a metric space X. A fuzzy subset A is called an approximate value if A is a closed and convex fuzzy subset with supA(x)=1; the class of all such elements is denoted by W(X), and it is a metric space with the distance D(A,B)=sup dist(Aα,Bα), where Aα and Bα denote the α-level of A and B, respectively, and dist( , ) denotes the generalized Hausdorff distance [see, e.g., M. P. Chen and M. H. Shin , J. Math. Anal. Appl. 71 (1979), no. 2, 516–524; MR0548780]....

Selected problems in the theory of fuzzy sets

Stanisław Heilpern — 1980

Mathematica Applicanda

From the introduction: "This paper contains a review of fundamental concepts and theorems of some areas of fuzzy mathematics, and an example of their application to the theory of decision making. Elementary definitions and properties of fuzzy sets are introduced in Chapters 1 and 2 [see L. A. Zadeh, Informat. and Control 8 (1965), 338–353; MR0219427]. Chapter 3 contains rudiments of fuzzy topology as presented by C. L. Chang [J. Math. Anal. Appl. 24 (1968), 182–190; MR0236859] and C. K. Wong [ibid....

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