METRIC SPACE WITH DIFFERENT FUZZY COMPATIBILITIES

Pavol Kráľ

   Let a metric space (X,ρ) be given. We can try several attitudes to identify pairs of points at some level. One of them is fuzzy compatibility C studied by Janiš and Tepavčevič. They introduced a fuzzy metric ^ρ: X² → F(R) where F(R) is the system of all fuzzy subsets of a real line. Fuzzy compatibilities in the given metric space can be very diferent. They can be connected for example with equivalent metrics. In this paper we study the properties of fuzzy sets ^ρ(a, b) for given a, b ∈ X which are connected with such fuzzy compatibilities.

Keywords: fuzzy compatibility, metric space, fuzzy metric

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