On Tripolar Fuzzy Soft Sets and Their Application in Ordered Semigroups

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DOI: https://doi.org/10.28924/2291-8639-24-2026-232
Published: Aug 3, 2026
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Sarapee Chairat, Somsak Lekkoksung, On Tripolar Fuzzy Soft Sets and Their Application in Ordered Semigroups, Int. J. Anal. Appl., 24 (2026), 232.

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Sarapee Chairat, Somsak Lekkoksung

Abstract

In this paper, we introduces and studies tripolar fuzzy soft sets in ordered semigroups. We define several key concepts, including tripolar fuzzy soft subsemigroups, left (right) ideals, quasi-ideals, and bi-ideals, and provide examples to clarify them. We analyze the structural properties of these ideals using a soft product operation. We show that the collection of all tripolar fuzzy soft sets forms a tripolar fuzzy soft ordered semigroup under this product. A main result of this study is the characterization of quasi-ideals: we prove that a tripolar fuzzy soft set is a quasi-ideal if and only if it is the intersection of a left ideal and a right ideal. Furthermore, we show that in regular ordered semigroups, the concepts of quasi-ideals and bi-ideals are identical.

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