Exploring the Structure of Possibility Multi-Fuzzy Soft Ordered Semigroups Through Interior Ideals

Sana Habib, Kashif Habib, Violeta Leoreanu-Fotea () and Faiz Muhammad Khan
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Sana Habib: School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China
Kashif Habib: Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212000, China
Violeta Leoreanu-Fotea: Faculty of Mathematics, Al. I. Cuza University of Iasi, Bd Carol I, No. 11, 700506 Iasi, Romania
Faiz Muhammad Khan: Department of Mathematics and Statistics, University of Swat, Swat 19120, Pakistan

Mathematics, 2025, vol. 13, issue 2, 1-18

Abstract: This paper aims to introduce a novel idea of possibility multi-fuzzy soft ordered semigroups for ideals and interior ideals. Various results, formulated as theorems based on these concepts, are presented and further validated with suitable examples. This paper also explores the broad applicability of possibility multi-fuzzy soft ordered semigroups in solving modern decision-making problems. Furthermore, this paper explores various classes of ordered semigroups, such as simple, regular, and intra-regular, using this innovative method. Based on these concepts, some important conclusions are drawn with supporting examples. Moreover, it defines the possibility of multi-fuzzy soft ideals for semiprime ordered semigroups.

Keywords: multi-fuzzy soft sets; possibility multi-fuzzy soft ordered semigroup; possibility multi-fuzzy soft interior ideals; possibility multi-fuzzy soft simple; semiprime possibility multi-fuzzy soft ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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