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 which is by its nature a problem of global optimization. The contraction is defined here by 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.

Keywords

• fuzzy metric spaces
• global optimization
• proximity point
• non-self (ф-ψ)-proximal contraction
• optimal approximate solution
• fuzzy p-property