Fuzzy $(m,n)$-Hyperideals and Regularity in Ordered Semihypergroups

Abstract

This paper introduces a novel framework for studying the structure of ordered semihypergroups through the lens of fuzzy set theory, focusing on the concept of fuzzy $(m,n)$-hyperideals. We define and characterize fuzzy left $n$-hyperideals and fuzzy right $m$-hyperideals, including their minimal and maximal forms. A key contribution is the introduction of $(m,n)$-intra-regular ordered semihypergroups, along with the exploration of their properties using fuzzy hyperideals. Additionally, we examine the interplay between fuzzy right $m$-hyperideals, fuzzy left $n$-hyperideals, and fuzzy $(m,n)$-quasi-hyperideals within the setting of $(m,n)$-regular ordered semihypergroups. This study offers new insights into the structural behavior of ordered semihypergroups and lays the groundwork for further investigations in fuzzy hyperstructure theory.

Keywords

• Ordered semihypergroup
• fuzzy left n-hyperideal
• fuzzy right m-hyperideal
• fuzzy (m,n) quasi hyperideal

Ethical Statement

It is declared that during the preparation process of this study, scientific and ethical principles were followed and all the studies benefited from are stated in the bibliography.

Thanks

The first and third authors would like to acknowledge Integral University, Lucknow, India, for providing the manuscript number IU/R&D/2025-MCN0003502

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