Geodesic
Fuzzy mappings
Mathematica Applicanda, Tome 11 (1983) no. 22, pp. 179-197.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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].
DOI : 10.14708/ma.v11i22.1588
Classification : 54A40 (03E72 54H25)
Mots-clés : Fuzzy topology, Fuzzy set theory, Fixed-point and coincidence theorems 
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Stanisław Heilpern. Fuzzy mappings. Mathematica Applicanda, Tome 11 (1983) no. 22, pp.  179-197. doi : 10.14708/ma.v11i22.1588. http://geodesic.mathdoc.fr/articles/10.14708/ma.v11i22.1588/

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