Soft Intersection Bi-interior Ideals of Semigroups

Aslıhan Sezgin; Aleyna İlgin

doi:10.38088/jise.1638824

Soft Intersection Bi-interior Ideals of Semigroups

Abstract

Generalizing the ideals of an algebraic structure has shown to be both beneficial and interesting for mathematicians. In this context, the idea of the bi-interior ideal was introduced as a generalization of the bi-ideal and interior ideal of a semigroup. By introducing "soft intersection (₷-int) bi-interior (ᙝᏆ) ideals of semigroups", we introduce a framework integrating semigroup theory with soft set theory in this study. Finding the relationships between ₷-int ᙝᏆ-ideals and other specific kinds of ₷-int ideals of a semigroup is the main aim of this study. Our results show that an ₷-int ᙝᏆ-ideal is an ₷-int subsemigroup of a soft simple* semigroup, and that an ₷-int left (right/two-sided) ideal, bi-ideal, interior ideal and quasi-ideal is an ₷-int ᙝᏆ-ideal; in other words, the ₷-int ᙝᏆ-ideal is a generalization of the ₷-int left (right/two-sided) ideal, bi-ideal, interior ideal and quasi-ideal, however, we provide counterexamples demonstrating that the converses do not always hold. We demonstrate that the semigroup should be a soft simple* semigroup in order to satisfy the converses. Our key theorem, which states that if a nonempty subset of a semigroup is a ᙝᏆ-ideal, then its soft characteristic function is an ₷-int ᙝᏆ-ideal, and vice versa, enables us to bridge the gap between semigroup theory and soft set theory. Using this theorem, we show how this idea relates to the existing algebraic structures in classical semigroup theory. Furthermore, we present conceptual characterizations and analysis of the new concept in terms of soft set operations supporting our assertions with illuminating examples.

Keywords

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Aslıhan Sezgin ^*
0000-0002-1519-7294
Türkiye

Aleyna İlgin
0009-0001-5641-5462
Türkiye

Early Pub Date

September 15, 2025

Publication Date

December 15, 2025

Submission Date

February 12, 2025

Acceptance Date

May 23, 2025

Published in Issue

Year 2025 Volume: 9 Number: 2

DOI

https://doi.org/10.38088/jise.1638824

IZ

https://izlik.org/JA55SK25NA

Cite

RIS / Bibtex

APA

Sezgin, A., & İlgin, A. (2025). Soft Intersection Bi-interior Ideals of Semigroups. Journal of Innovative Science and Engineering, 9(2), 216-231. https://doi.org/10.38088/jise.1638824

AMA

1.Sezgin A, İlgin A. Soft Intersection Bi-interior Ideals of Semigroups. JISE. 2025;9(2):216-231. doi:10.38088/jise.1638824

Chicago

Sezgin, Aslıhan, and Aleyna İlgin. 2025. “Soft Intersection Bi-Interior Ideals of Semigroups”. Journal of Innovative Science and Engineering 9 (2): 216-31. https://doi.org/10.38088/jise.1638824.

EndNote

Sezgin A, İlgin A (December 1, 2025) Soft Intersection Bi-interior Ideals of Semigroups. Journal of Innovative Science and Engineering 9 2 216–231.

IEEE

[1]A. Sezgin and A. İlgin, “Soft Intersection Bi-interior Ideals of Semigroups”, JISE, vol. 9, no. 2, pp. 216–231, Dec. 2025, doi: 10.38088/jise.1638824.

ISNAD

Sezgin, Aslıhan - İlgin, Aleyna. “Soft Intersection Bi-Interior Ideals of Semigroups”. Journal of Innovative Science and Engineering 9/2 (December 1, 2025): 216-231. https://doi.org/10.38088/jise.1638824.

JAMA

1.Sezgin A, İlgin A. Soft Intersection Bi-interior Ideals of Semigroups. JISE. 2025;9:216–231.

MLA

Sezgin, Aslıhan, and Aleyna İlgin. “Soft Intersection Bi-Interior Ideals of Semigroups”. Journal of Innovative Science and Engineering, vol. 9, no. 2, Dec. 2025, pp. 216-31, doi:10.38088/jise.1638824.

Vancouver

1.Aslıhan Sezgin, Aleyna İlgin. Soft Intersection Bi-interior Ideals of Semigroups. JISE. 2025 Dec. 1;9(2):216-31. doi:10.38088/jise.1638824