Revision of Pseudo-Ultrametric Spaces Based on m-Polar T-Equivalences and Its Application in Decision Making

Azadeh Zahedi Khameneh, Adem Kilicman and Fadzilah Md Ali
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Azadeh Zahedi Khameneh: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia
Adem Kilicman: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia
Fadzilah Md Ali: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia

Mathematics, 2021, vol. 9, issue 11, 1-18

Abstract: In mathematics, distance and similarity are known as dual concepts. However, the concept of similarity is interpreted as fuzzy similarity or T -equivalence relation, where T is a triangular norm ( t -norm in brief), when we discuss a fuzzy environment. Dealing with multi-polarity in practical examples with fuzzy data leadsus to introduce a new concept called m -polar T -equivalence relations based on a finitely multivalued t -norm T , and to study the metric behavior of such relations. First, we study the new operators including the m -polar triangular norm T and conorm S as well as m -polar implication I and m -polar negation N , acting on the Cartesian product of [ 0 , 1 ] m -times.Then, using the m -polar negations N , we provide a method to construct a new type of metric spaces, called m -polar S -pseudo-ultrametric, from the m -polar T -equivalences, and reciprocally for constructing m -polar T -equivalences based on the m -polar S -pseudo-ultrametrics. Finally, the link between fuzzy graphs and m -polar S -pseudo-ultrametrics is considered. An algorithm is designed to plot a fuzzy graph based on the m -polar S L -pseudo-ultrametric, where S L is the m -polar Lukasiewicz t -conorm, and is illustrated by a numerical example which verifies our method.

Keywords: m -polar fuzzy relation; m -polar T -equivalence; m -polar S -pseudo-ultrametric; fuzzy graph; group decision making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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