On fuzzy bipolar soft sets, their algebraic structures and applications

Naz, Munazza; Shabir, Muhammad

doi:10.3233/ifs-130844

Cited by 83 publications

(53 citation statements)

References 16 publications

(10 reference statements)

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“…Wei et al [31] considered the qROF Heronian mean operators in multiattribute decision making and Shu et al [32] integrated the qROF continuous information. Keeping in view the importance of fuzzy sets, other generalizations of fuzzy sets had been introduced, such as rough sets [33], soft sets [34], bipolar-valued fuzzy sets [35] and bipolar soft sets [36][37][38].…”

Section: Figure 2 Evaluation Of Ranges Of Pfs Sfs and Tsfsmentioning

confidence: 99%

Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

et al. 2021

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Uncertainty is the unavoidable part of the life. In almost all circumstances, we regularly find ourselves in a state of uncertainty. Several reasons can lead to uncertainty, such as randomness, vagueness and rough knowledge. Fuzzy set (FS) theory deals with these kinds of information. Many generalizations had been made in the theory of FSs, such as intuitionistic FSs (IFSs), q-rung orthopair FSs (qROFSs), complex qROFSs (CqROFSs), spherical FSs (SFSs), T-spherical FSs (TSFSs), and complex TSFSs (CTSFSs). Among these generalizations of FSs, the CTSFSs are the most dominant generalization of the FSs. Although fuzzy relations (FRs), IF relations (IFRs) and complex FRs (CFRs) were defined in the literature, the concepts of relations have not yet been introduced in the CTSFSs. This paper unveils the novel concept of CTSF relations (CTSFRs), which provides the extensive generalizations of FRs. The proposed CTSFRs can give many generalized types of FRs, such as IFRs, CFRs, Pythagorean FRs, qROFRs, SFRs and TSFRs, etc. Additionally, some useful properties and results are obtained for CTSFRs. Moreover, a couple of applications demonstrate the usefulness of the proposed concepts. These CTSFRs can be used to depict the time-related interdependence of global market. Thus, we apply these CTSFRs to analyze the interdependence of the international trades among countries and compare the financial factors affecting business markets. Furthermore, the economic relationships with respect to time lag can be modeled by using the CTSFSs and the CTSFRs. Finally, a comparative analysis illuminates the supremacy of the proposed way in contrast with the existing ones.INDEX TERMS Fuzzy sets (FSs); T-spherical FSs (TSFSs); Complex TSFSs (CTSFSs); CTSF relations (CTSFRs); Cartesian product in CTSFSs; CTSF composite relation; Financial and economic relationships.

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Section: Figure 2 Evaluation Of Ranges Of Pfs Sfs and Tsfsmentioning

confidence: 99%

Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

et al. 2021

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“…Here, we state some definitions that are helpful in comprehending the content of the paper. For studying the applications of FBS set theory and further details, the readers may resort to [33]. An ordered semigroup ( , ⋅, ≤) is a set where ( , ⋅) is a semigroup and ( , ≤) is a partially ordered set (poset) such that the order relation "≤" is compatible with the binary operation of multiplication "⋅".…”

Section: Preliminariesmentioning

confidence: 99%

“…Let's recall that Naz and Shabir [33] presented the concept of fuzzy bipolar soft set which is a hybrid structure of fuzzy and soft set theories. Moreover, it possesses an intrinsic property of bipolarity.…”

Section: Preliminariesmentioning

confidence: 99%

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Fuzzy bipolar soft semiprime ideals in ordered semigroups

Aziz-ul-Hakim

Khan

Ahmad

et al. 2021

Heliyon

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FBS left ideal FBS right ideal FB ideal FBS semiprime ideal FBS prime idealIn this paper, we introduce fuzzy bipolar soft semiprimality in the structure of ordered semigroups and investigate some properties of the concept. Moreover, ordered semigroups and their some classes are characterized by means of fuzzy bipolar soft semiprimality. Finally, the Cartesian product of fuzzy bipolar soft semiprime (resp., prime) ideals over ordered semigroups is examined. Some of the ideas are supported by apt examples.

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“…But different from IFS, the value range of membership degree of the BFS is [-1, 1]. Naz and Shabir (2014) defined fuzzy bipolar soft sets and basic operations of union, intersection and complementation for fuzzy bipolar soft sets. Han et al (2015) discussed the relationship between bipolar-valued fuzzy set and fuzzy set with its extensions.…”

mentioning

confidence: 99%