Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications

Al-shami, Tareq M.

doi:10.1155/2021/6621854

Cited by 40 publications

(25 citation statements)

References 34 publications

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“…Shabir et al [61] initiated the idea of rough approximations of BSSs by soft relations and applied this idea in DM. Al-shami [9] came up with the concept of belong and nonbelong relations between a BSS and an ordinary point. Riaz and Tehrim [54] initiated the concept of bipolar fuzzy soft mappings and discuss their applications to bipolar disorders.…”

Section: A Literature Reviewmentioning

confidence: 99%

A Novel Approach Toward Roughness of Bipolar Soft Sets and Their Applications in MCGDM

et al. 2021

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The uncertainty in the data is an obstacle in decision-making (DM) problems. In order to solve problems with a variety of uncertainties a number of useful mathematical approaches together with fuzzy sets, rough sets, soft sets, bipolar soft sets have been developed. The rough set theory is an effective technique to study the uncertainty in data, while bipolar soft sets have the ability to handle the vagueness, as well as bipolarity of the data in a variety of situations. This study develops a new methodology, which we call the theory of dominance-based bipolar soft rough sets (DB-BSRSs), which will be used to propose a new technique to solve decision-making problems. The idea introduced in this study has never been discussed earlier. Furthermore, this concept has been explored by means of a detailed study of the structural properties. Moreover, some important measures like the accuracy measure, the measure of precision, and the measure of quality for DB-BSRSs are also provided. Finally, an application of the DB-BSRSs in multicriteria group decision-making (MCGDM) problem is presented and an algorithm for this application is proposed, supported by an example, which yields the best decision, as well as, the worst decision between some objects. In comparison with some existing results, we also present some advantages of our proposed method.

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Section: A Literature Reviewmentioning

confidence: 99%

A Novel Approach Toward Roughness of Bipolar Soft Sets and Their Applications in MCGDM

et al. 2021

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“…We will leave Questions 5. 16 Let M = {F, G, H, K, L, M }. Consider the STS (X, τ, A), where τ having M as a soft base.…”

Section: Relative Tss and Generated Stssmentioning

confidence: 99%

Soft Minimal Soft Sets and Soft Prehomogeneity in Soft Topological Spaces

Ghour¹

2021

IJFIS

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In this paper, we give characterizations for soft minimal soft open sets in terms of the soft closure operator, and we conclude that soft subsets of soft minimal soft open sets are soft preopen sets. In addition to these, we define soft minimal soft sets and soft minimal soft preopen sets as two new classes of soft sets in soft topological spaces, and we define soft prehomogeneity as a new soft topological property. We give several relationships regarding these new notions and related known soft topological notions. We show that soft minimal soft preopen sets are soft points, and we prove that soft minimal soft sets with non-null soft interiors are soft minimal soft open sets. Moreover, we show that soft prehomogeneous soft topological space that has a soft minimal soft set is soft locally indiscrete. Also, we give several characterizations of soft locally indiscrete soft topological space in terms of soft minimal soft open sets, soft minimal soft sets, soft preopen sets, and soft prehomogeneity. We deal with correspondence between our new soft topological notions and their analogs topological ones. Finally, we raise six open questions.

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“…Malik and Shabir [22] successfully applied rough fuzzy bipolar soft sets in decision-making problems. Many more authors have auspiciously adapted bipolar soft set theory in various fields (see , Zhang [27], Ali et al [28], Al-shami [29], Mahmood [30], Wang et al [31], Ali et al [32], Kamacı and Petchimuthu [33] and Lee and Hur [34]).…”

Section: Introductionmentioning

confidence: 99%

Bipolar Hypersoft Sets

Musa

Asaad

2021

Mathematics

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Hypersoft set theory is an extension of soft set theory and is a new mathematical tool for dealing with fuzzy problems; however, it still suffers from the parametric tools’ inadequacies. In order to boost decision-making accuracy even more, a new mixed mathematical model called the bipolar hypersoft set is created by merging hypersoft sets and bipolarity. It is characterized by two hypersoft sets, one of which provides positive information and the other provides negative information. Moreover, some fundamental properties relative to it such as subset, superset, equal set, complement, difference, relative (absolute) null set and relative (absolute) whole set are defined. Furthermore, some set-theoretic operations such as the extended intersection, the restricted union, intersection, union, AND-operation and OR-operation of two bipolar hypersoft sets with their properties are discussed and supported by examples. Finally, tabular representations for the purposes of storing bipolar hypersoft sets in computer memory are used.

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Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications

Cited by 40 publications

References 34 publications

A Novel Approach Toward Roughness of Bipolar Soft Sets and Their Applications in MCGDM

A Novel Approach Toward Roughness of Bipolar Soft Sets and Their Applications in MCGDM

Soft Minimal Soft Sets and Soft Prehomogeneity in Soft Topological Spaces

Bipolar Hypersoft Sets

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