T-Bipolar Soft Semigroups and Related Results

Tahir Mahmood; Muhammad Asif; Ubaid ur Rehman; Jabbar Ahmmad

doi:10.31181/smeor11202421

Authors

Tahir Mahmood Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan Author https://orcid.org/0000-0002-3871-3845
Muhammad Asif Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan Author https://orcid.org/0000-0002-5801-884X
Ubaid ur Rehman Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan Author https://orcid.org/0000-0001-5947-9827
Jabbar Ahmmad Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan Author https://orcid.org/0000-0002-1450-8484

DOI:

https://doi.org/10.31181/smeor11202421

Keywords:

T-bipolar soft set, Semigroup, AND product, OR product, Extended union, Extended intersection

Abstract

The role of semigroups (SGs) is to operate as the tool for the study and modeling of systems and phenomena in which inverse operation is not relevant or necessary. SGs are encountered in the subject of automata theory, coding theory, language theory, and the study of discrete dynamical systems. Moreover, T-bipolar soft set is closer to bipolarity as compared to other theories on bipolar soft sets. Based on the idea of T-bipolar soft sets, here we explore the notion and properties of the T-bipolar soft semigroup (T-BSSG). These properties include the AND and OR product, the Restricted Union (Res-Union) and Restricted Intersection (Res-Intersection), and the Extended Union (Ext-Union) and Extended Intersection (Ext-Intersection) on T-BSSG. Further, we also devise the related algebraic properties of T-BSSG.

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