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

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia)

  • Fadzilah Md Ali

    (Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia
    Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia)

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.

Suggested Citation

  • Azadeh Zahedi Khameneh & Adem Kilicman & Fadzilah Md Ali, 2021. "Revision of Pseudo-Ultrametric Spaces Based on m-Polar T-Equivalences and Its Application in Decision Making," Mathematics, MDPI, vol. 9(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1232-:d:564075
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    References listed on IDEAS

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    1. Arya Sebastian & John N Mordeson & Sunil Mathew, 2020. "Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking," Mathematics, MDPI, vol. 8(3), pages 1-21, March.
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