Determining fuzzy distance through non-self fuzzy contractions

Authors

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

DOI:

https://doi.org/10.2298/YJOR180515002S

Keywords:

Fuzzy metric spaces, global optimization, proximity point, non-self (Ф-Ψ)-proximal contraction, optimal approximate solution, fuzzy P-property

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.

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Published

2019-08-01

Issue

Vol. 29 No. 3 (2019)

Section

Research Articles

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