Open AccessDetermining fuzzy distance through non-self fuzzy contractions
Author(s) -
P. Saha,
Shantanu Guria,
S Binayak Choudhury
Publication year - 2019
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor180515002s
Subject(s) - mathematics , fuzzy number , fuzzy logic , fuzzy set operations , fuzzy classification , defuzzification , contraction (grammar) , contraction principle , fuzzy set , fuzzy subalgebra , type 2 fuzzy sets and systems , mathematical optimization , metric space , discrete mathematics , computer science , artificial intelligence , medicine
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.