Determining Fuzzy Distance Through Non-Self Fuzzy Contractions

Abstract

In the present work we solve the problem of finding the fuzzy distance between two subsets of a fuzzy metric space for which we use a non-self fuzzy contraction mapping from one set to the other. It is a fuzzy extension of the proximity point problem and, by its nature, is a problem of global optimization. The contraction is defined here with the help of two control functions. We define a geometric property of the fuzzy metric space. The main result is illustrated with an example. Our result extends a fuzzy version of the Banach contraction mapping principle.