Fuzzy mappings

• Autorzy: Stanisław Heilpern
• Języki publikacji: EN

Abstrakty

EN

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]. The author is especially concerned with W(R). Algebraic operations in W(R) are defined and basic rules for arithmetic operations on approximate values are proved. Moreover, functions with values in W(R) are also investigated. Finally, a fixed point theorem for fuzzy mappings is stated and an example is given [for the proof see the author, ibid. 83 (1981), no. 2, 566–569; MR0641351].

PL

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Słowa kluczowe

EN

Fuzzy topology; Fuzzy set theory; Fixed-point and coincidence theorems

• Wydawca: Polish Mathematical Society
• Czasopismo: Mathematica Applicanda
• Rocznik: 1983
• Tom: 11
• Numer: 22

Daty

wydano

1983

online

2016-10-21

Twórcy

autor

Stanisław Heilpern

Identyfikatory

DOI

10.14708/ma.v11i22.1588