Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups

Ideals play an essential part in studying ordered semigroups. There are several generalizations of ideals that are used to investigate ordered semigroups. It was known that (m, n)-ideals and n-interior ideals are an abstraction of bi-ideals and interior ideals, respectively. This paper introduces a generality of (m, n)-ideals and n-interior ideals, so-called (α, β)-fuzzy (m, n)-ideals and (α, β)-fuzzy n-interior ideals. Furthermore, we discuss our current notions with those that already exist. We examine connections between (m, n)- (resp., n-interior) ideals and (α, β)-fuzzy (m, n)- (resp., n-interior) ideals. A characterization of (α, β)-fuzzy (m, n)- (resp., n-interior) ideals, by a particular product, in ordered semigroups is provided. We demonstrate that our results generalize the known results through specific settings.

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Characterizations of generalized fuzzy ideals in ordered semigroups

Davvaz

Chinram

Lekkoksung

et al. 2023

IFS

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Partial Γ-Semimodules over Partial Γ-Semirings

Mala,

Rao,

Kumar

2024

Punjab Univ. j. math.

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The Theory of T-Bipolar Soft Modules

Mahmood,

Rehman

2024

Punjab Univ. j. math.

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Algebraic structures in mathematics and applications reveal an inherent duality or bipolarity that is seen in elements that have both positive and negative behaviors or properties. Integrating the already-known module theory concept with the capability of T-bipolar soft sets to handle such bipolar information can lead to discoveries and instruments that can be used to research and operate these algebraic structures. This integration of module theory and T-bipolar soft sets may result in new forms of analysis and methods of analysis. These new approaches could greatly improve the possibilities of studying, analyzing, and solving problems related to algebraic structures that are inherently bipolar. Thus, in this manuscript, we investigate the notion of a T-bipolar soft module. We also deduce the T-bipolar soft submodule, maximal T-bipolar soft submodule, and their associated results. Further, we investigate T-bipolar soft homomorphism, and T-bipolar soft isomorphism along with important results such as the First Isomorphism Theorem, Second Isomorphism Theorem, and Third Isomorphism Theorem in the structure of T-bipolar soft module. Additionally, we diagnose T-bipolar soft exactness and associated results.

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Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups

Cited by 3 publications

References 26 publications

Characterizations of generalized fuzzy ideals in ordered semigroups

Characterizations of generalized fuzzy ideals in ordered semigroups

Partial Γ-Semimodules over Partial Γ-Semirings

The Theory of T-Bipolar Soft Modules

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