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Determining fuzzy distance through non-self fuzzy contractions

Saha Parbati (Indian Institute of Engineering Science and Technology, Department of Mathematics, Shibpur, Howrah, India)
Guria Shantanu (Indian Institute of Engineering Science and Technology, Department of Mathematics, Shibpur, Howrah, India)
Choudhury Binayak S. (Indian Institute of Engineering Science and Technology, Department of Mathematics, Shibpur, Howrah, India)

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