Optimistic multigranulation roughness of fuzzy bipolar soft sets by soft binary relations and its applications

Mubarak, Asad; Mahmood, Waqas; Shabir, Muhammad

doi:10.1088/1402-4896/acd424

Cited by 4 publications

(2 citation statements)

References 40 publications

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“…In the future, we can extend these developed notions to the rough set theory [32,33], the theory of modules, and the ideals theory. Moreover, some more algebraic structures can be explored under the environment of delivered notions.…”

Section: Discussionmentioning

confidence: 99%

Classification of Data Mining Techniques under the Environment of T-Bipolar Soft Rings

Ahmmad,

Alsuraiheed,

Khan

et al. 2023

Symmetry

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Data mining evaluation is very critical in the sense that it determines how well a classification model performs and how well it can generate accurate predictions on brand-new, unexplored data. It is especially important for classification tasks. There are several methods for evaluating classification models, and the choice of evaluation strategies depends on the particular situation, the available data, and the desired outcomes. The notion of a T-bipolar soft set (TBSS) is a valuable parameterization tool and is closer to the concept of bipolarity. Moreover, algebraic structures like groups, rings, and modules, etc., are basic tools that can be helpful not only in mathematics but also in other scientific areas due to their symmetric properties. In this article, based on the novelty of TBSS and the characteristics of rings, we have generalized these two notions to deliver and introduce the notion of T-bipolar soft rings (TBSRs). Additionally, the concepts of AND product, OR product, extended union, extended intersection, restricted union, and restricted intersection for two TBSRs is introduced, and the related results are conferred. To support these proposed notions, we have delivered examples related to these ideas. For the applicability of the developed approach, an algorithm is defined based on the delivered approach. An illustrative example regarding the classification of data mining techniques is developed to show the applications of the introduced work. We can see that there are four alternatives, and their score values are, respectively, given by −4, 42, 0, and −32. Based on these results, we can evaluate the best data mining technique. So, the defined algorithm makes it easy for us to classify the data mining techniques. Further asymmetric data are frequently employed for selecting the best alternative in decision-making problems because the information regarding alternatives is not necessarily always symmetric. Therefore, asymmetric information can be discussed using these proposed concepts.

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Section: Discussionmentioning

confidence: 99%

Classification of Data Mining Techniques under the Environment of T-Bipolar Soft Rings

Ahmmad,

Alsuraiheed,

Khan

et al. 2023

Symmetry

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“…We want to do research on other algebraic BCFS-related structures in the future, including BCF vector spaces, BCF fields, BCF matrix spaces, and multigranulation roughness [38,39] etc…”

Section: Data Availability Statementmentioning

confidence: 99%

Bipolar complex fuzzy submodules

Alsuraiheed,

ur Rehman,

Khan

et al. 2024

Phys. Scr.

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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.

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Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

2023

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Optimistic multigranulation roughness of fuzzy bipolar soft sets by soft binary relations and its applications

Cited by 4 publications

References 40 publications

Classification of Data Mining Techniques under the Environment of T-Bipolar Soft Rings

Classification of Data Mining Techniques under the Environment of T-Bipolar Soft Rings

Bipolar complex fuzzy submodules

Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

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