Analysis of $$\Gamma $$-semigroups based on bipolar complex fuzzy sets

Mahmood, Tahir; Rehman, Ubaid ur; Albaity, Majed

doi:10.1007/s40314-023-02376-w

Cited by 2 publications

(1 citation statement)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Rehman et al [35] devised bipolar complex fuzzy (BCFS) semigroups. Mahmood et al [36] invented BCF G-semigroups. Yang et al [37] discussed BCF subgroups.…”

Section: Introductionmentioning

confidence: 99%

Bipolar complex fuzzy submodules

Alsuraiheed,

ur Rehman,

Khan

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

In this manuscript, we interpret the theory of bipolar complex fuzzy submodule (BCFSM) of a provided classical module over a ring by utilizing the well-known notion of bipolar complex fuzzy set (BCFS). We also devise the sum of two BCFS and investigate its related proposition for studying a few fundamental properties of the initiated BCFSM. Moreover, we investigate the cartesian product of two BCFS for developing properties of BCFSM. We also investigate that if a BCFS Ӈ_1 is a BCFSM of Ӎ_1, then image Ӻ(Ӈ) is a BCFSM of Ӎ_2 and the preimage Ӻ^(-1) (Ӈ) is a BCFSM of Ӎ_1, where, Ӎ_1 and Ӎ_2 are two modules and Ӻ:Ӎ_1→Ӎ_2 is a module homomorphism.

show abstract

“…Rehman et al [35] devised bipolar complex fuzzy (BCFS) semigroups. Mahmood et al [36] invented BCF G-semigroups. Yang et al [37] discussed BCF subgroups.…”

Section: Introductionmentioning

confidence: 99%

Bipolar complex fuzzy submodules

Alsuraiheed,

ur Rehman,

Khan

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Bipolar complex fuzzy near rings

Rehman,

Alnefaie,

Mahmood

2024

Phys. Scr.

View full text Add to dashboard Cite

In this article, we devise the novel concept of bipolar complex fuzzy (BCF) near rings (BCFNR), to fill a momentous research gap in connection of bipolar complex fuzzy sets with the theory of near rings in the existing literature. We expand the theory of near ring into the structure of BCF set (BCFS), offering a more suitable approach for the representation of algebraic systems with inherent ambiguity, bipolarity, and 2nd dimension information. Further, we introduce the concept of the bipolar complex fuzzy sub-near ring (BCFSNR), bipolar complex fuzzy left ideal (BCFLI), bipolar complex fuzzy right ideal (BCFRI), and bipolar complex fuzzy ideal (BCFI) in the near ring. After that, we prove the related theorem and results of these devised concepts. We also introduce theorems based on the homomorphism theory and Noetherian theory of near rings within the frame of bipolar complex fuzzy near rings. At the end of the manuscript, we reveal the application of BCFNRs in decision-making (DM) and illustrate it through an example.

show abstract

Analysis of $$\Gamma $$-semigroups based on bipolar complex fuzzy sets

Cited by 2 publications

References 38 publications

Bipolar complex fuzzy submodules

Bipolar complex fuzzy submodules

Bipolar complex fuzzy near rings

Contact Info

Product

Resources

About