Hesitant Bipolar-Valued Neutrosophic Set: Formulation, Theory and Application

Awang, Azzah; Ali, Mumtaz

doi:10.1109/access.2019.2946985

Cited by 11 publications

(11 citation statements)

References 25 publications

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“…(Awang et al 2019a , b ) Let X be a reference set and with a generic element in X denoted by . A hesitant bipolar-valued neutrosophic set in X is defined as: where and .…”

Section: Preliminariesmentioning

confidence: 99%

“…(Awang et al 2019a , b ) Let be a HBNE, then the score function is as below: where and are the number of elements in and , respectively. , , , , and .…”

Section: Preliminariesmentioning

confidence: 99%

“…Both of the bipolar and hesitancy concepts are important in achieving a realistic and precise decision. Awang et al ( 2019a ; b ) initiated to combine both BNS and HFS and introduced a hesitant bipolar-valued neutrosophic set (HBNS).…”

Section: Introductionmentioning

confidence: 99%

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A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision

Awang

Abdullah

Hashim

2021

J Ambient Intell Human Comput

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Bonferroni mean (BM) operators have been established as a powerful tool for handling the interrelationship between the input arguments under various decision-making information. However, the existing BM operators do not take into account the overall interaction among decision makers or criteria. To overcome this limitation, this study considers the Shapley fuzzy measure (SFM) with the normalized weighted BM (NWBM) operator under a neutrosophic environment. In addition, the current research ignores the bipolarity and hesitancy during decision elicitations, resulting in the imprecise decision results. In this paper, the hesitant bipolar-valued neutrosophic set (HBNS) which is the extension of hesitant fuzzy set and bipolar neutrosophic set is employed. The main focus of this paper is in the development of an aggregation operator for HBNS. Based on the literature review, we would like to fill in the gaps by developing a hesitant bipolar-valued neutrosophic Shapley NWBM (HBN-SNWBM) operator where the overall interaction among decision makers can be considered. Besides that, a three-phase decision making framework is also proposed to show the applicability of the proposed aggregation operator to the real-world decision problems. The HBN-SNWBM operator and the decision making framework are applied to two examples of investment selection where evaluations are implemented using the proposed aggregations that based upon hesitant bipolar-valued neutrosophic sets. In the first example, it is found that a weapon company is the best alternative for investment followed by a food company. Sensitivity of parameters of the aggregation operator is also analysed and it is found that the ranking results are consistent despite of different parameter values used. This verifies the insensitivity of p,q parameters in the developed aggregation operator. The proposed decision making framework and hesitant bipolar-valued neutrosophic sets would be a great significance for the practical implementation of the aggregation operators.

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“…(Awang et al 2019a , b ) Let X be a reference set and with a generic element in X denoted by . A hesitant bipolar-valued neutrosophic set in X is defined as: where and .…”

Section: Preliminariesmentioning

confidence: 99%

“…(Awang et al 2019a , b ) Let be a HBNE, then the score function is as below: where and are the number of elements in and , respectively. , , , , and .…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision

Awang

Abdullah

Hashim

2021

J Ambient Intell Human Comput

Self Cite

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show abstract

“…In 2020, Yiarayong 25 applied the theory of intervalvalued fuzzy soft sets (IVFSSs) to semigroups and introduced the notion of interval-valued fuzzy soft sets (IVFSSs), which is a generalization of fuzzy soft sets (FSSs). After fuzzy set theory, many set theories have been developed interval-valued fuzzy set theory and BFS theory, [26][27][28][29][30][31][32][33][34][35][36] and so forth.…”

Section: Introductionmentioning

confidence: 99%

A new approach of bipolar valued fuzzy set theory applied on semigroups

Yiarayong

2021

Int J Intell Syst

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In this paper, we generalize the concept of interval‐valued bipolar fuzzy sets (IVBFSs) and define interval‐valued bipolar fuzzy subsemigroups (IVBF‐subsemigroup) and interval‐valued bipolar fuzzy left (right, two‐sided) ideals (IVBF‐left [right, two‐sided] ideals) over semigroups, which is a generalization of the concept of an bipolar valued fuzzy set (BVFS) in a semigroup. The purpose of this paper is to deal with the algebraic structure of semigroups by applying IVBFS theory. We give characterizations of different classes of (intra‐regular, left [right] regular, regular, semisimple) semigroups by the properties of their IVBF‐ideals. We also characterize these classes in terms of IVBF‐left ideals, IVBF‐right ideals, and IVBF‐two‐sided ideals. In this respect, we prove that a semigroup is regular if and only if for every IVBF‐right ideal true A ˜ = )( true μ A P ˜ , true μ A N ˜ and every IVBF‐left ideal true B ˜ = )( true μ B P ˜ , true μ B N ˜ over S , we have true A ˜ ∩ true B ˜ = true A ˜ ⊙ true B ˜ . Further, we characterize intra‐regular and regular semigroups and prove that a semigroup is intra‐regular and regular if and only if for every IVBF‐left ideal true A ˜ = )( true μ A P ˜ , true μ A N ˜ and every IVBF‐right ideal true B ˜ = )( true μ B P ˜ , true μ B N ˜ over S we have true A ˜ ∩ true B ˜ 0.25em ≼ 0.25em true A ˜ ⊙ true B ˜ .

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“…A further study about a few aggregation operators for dual hesitant bipolar fuzzy information was discussed in [45]. Awang et al presented the perception of hesitant bipolarvalued neutrosophic sets and introduced an original decision-making method based on the novel model [46]. ose models were superior to other fuzzy mathematical tools in describing abilities because of considering the bipolarity and nonuniqueness of the membership degree of an element simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Hesitant Bipolar-Valued Fuzzy Soft Sets and Their Application in Decision Making

Wang

Liu

2020

Complexity

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As an extension of fuzzy sets, hesitant bipolar-valued fuzzy set is a new mathematical tool for dealing with fuzzy problems, but it still has the problem with the inadequacy of the parametric tools. In order to further improve the accuracy of decision making, a new mixed mathematical model, named hesitant bipolar-valued fuzzy soft set, is constructed by combining hesitant bipolar-valued fuzzy sets with soft sets. Firstly, some related theories of hesitant bipolar-valued fuzzy sets are discussed. Secondly, the concept of hesitant bipolar-valued fuzzy soft set is given, and the algorithms of complement, union, intersection, “AND,” and “OR” are defined. Based on the above algorithms, the corresponding results of operation are analyzed and the relevant properties are discussed. Finally, a multiattribute decision-making method of hesitant bipolar-valued fuzzy soft sets is proposed by using the idea of score function and level soft sets. The effectiveness of the proposed method is illustrated by an example.

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Hesitant Bipolar-Valued Neutrosophic Set: Formulation, Theory and Application

Cited by 11 publications

References 25 publications

A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision

A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision

A new approach of bipolar valued fuzzy set theory applied on semigroups

Hesitant Bipolar-Valued Fuzzy Soft Sets and Their Application in Decision Making

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