Determining fuzzy distance via coupled pair of operators in fuzzy metric space

• Published in: Soft computing (Berlin, Germany) Vol. 24; no. 13; pp. 9403 - 9412
• Main Authors: Gopi, R., Pragadeeswarar, V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020; Springer Nature B.V
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Engineering; Foundations; Fuzzy sets; Global optimization; Mathematical Logic and Foundations; Mechatronics; Metric space; Operators (mathematics); Optimization; Ordinary differential equations; Robotics; Theorems; Coupled fixed point; Common coupled fixed point; Fuzzy metric space; Best proximity point; Fixed point
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-020-05001-8

In this present study, we introduce the new class of mappings called fuzzy proximally compatible mappings and we solve the common coupled global optimization problem of finding the fuzzy distance between two subsets of a fuzzy metric space for this class of non-self-fuzzy mappings. Further, we develop the notion CLRg property (CLR g common limit in the range of g ) for non-self-fuzzy mappings, and by having this idea, we derive common global minimal solution to the fuzzy coupled fixed point equations F ( x , y ) = g ( x ) = x and F ( y , x ) = g ( y ) = y , where the pair ( F ,  g ) is proximally fuzzy weakly compatible mappings, without the assumption of continuity on g . Finally, we find a relation between, our extended notions, proximal fuzzy E.A property and proximal fuzzy CLR g property, and we find a unique solution to the common global optimization problem with the assumption of proximal fuzzy E.A property.