Fixed points of fuzzy functions

Rok, strany: 1997, 13 - 19

By a fuzzy function we understand a function $f$ defined on a metric space $(X, d)$, whose values are fuzzy numbers. We deal with fuzzy mappings of a complete metric space into itself. An $/varepsilon$-fixed point of $f$ is a point $x₀$ such that the value of the membership function which is the image of $x₀$ is greater or equal to $1$ – $/varepsilon$ in $x₀$. A Banach — type theorem on existence of such point is proved. It is also shown that the set of all $/varepsilon$-fixed points is closed and bounded in $(X, d)$. The second part of the paper deals with the fixed point of a fuzzy continuous function as it is defined in [M. Burgin, A. Šostak: Fuzzification of the theory of continuous functions, Fuzzy Sets and Systems 62 (1994), 71–81].

ISO 690:

Janiš, V. 1997. Fixed points of fuzzy functions. In Tatra Mountains Mathematical Publications, vol. 12, no.3, pp. 13-19. 1210-3195.

APA:

Janiš, V. (1997). Fixed points of fuzzy functions. Tatra Mountains Mathematical Publications, 12(3), 13-19. 1210-3195.