Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

Wang, Ping; Wang, Jie; Wei, Guiwu; Wei, Cun

doi:10.3390/math7040340

Cited by 143 publications

(97 citation statements)

References 57 publications

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“…Therefore, how to reasonably carry on the waste incineration plant scientific location is particularly important. Waste incineration plants location problem should be regarded as the corresponding MAGDM [45][46][47][48][49][50][51]. Thus, in this chapter we developed a case study concerning waste incineration plants location problem to demonstrate the approach presented in this essay.…”

Section: Numerical Casementioning

confidence: 99%

GRA Method for Probabilistic Linguistic Multiple Attribute Group Decision Making with Incomplete Weight Information and Its Application to Waste Incineration Plants Location Problem

Lei¹,

Wei²,

Lu³

et al. 2019

IJCIS

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Multiple attribute group decision making (MAGDM) Probabilistic linguistic term sets (PLTSs) GRA method Incomplete weight information Waste incineration plants A B S T R A C TIn this essay, we investigate the probabilistic linguistic multiple attribute group decision making (PL-MAGDM) with incomplete weight information. In this method, the linguistic representation developed recently is converted into probabilistic linguistic information. For deriving the weight information of the attribute, an optimization model is built on the basis of the fundamental idea of grey relational analysis (GRA), by which the attribute weights can be decided. Then, the optimal alternative is chosen through calculating largest relative relational degree from the probabilistic linguistic positive ideal solution (PLPIS) which considers both the largest grey relational coefficient (GRC) from the PLPIS and the smallest GRC form probabilistic linguistic negative ideal solution (PLNIS). In the end, a case study concerning waste incineration plants location problem is given to demonstrate the merits of the developed methods.

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Section: Numerical Casementioning

confidence: 99%

GRA Method for Probabilistic Linguistic Multiple Attribute Group Decision Making with Incomplete Weight Information and Its Application to Waste Incineration Plants Location Problem

Lei¹,

Wei²,

Lu³

et al. 2019

IJCIS

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show abstract

“…Li et al gave some methods for multiple attribute group decision‐making based on intuitionistic fuzzy Dombi Hamy mean operators. The IFS and their extensions have received more and more attention since its appearance . A new extension of IFS, namely, the Pythagorean fuzzy set (PFS), has been developed.…”

Section: Introductionmentioning

confidence: 99%

Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision‐making and their application to performance assessment of new rural construction

Tang

Wei

et al. 2019

Int J Intell Syst

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The dual hesitant Pythagorean fuzzy set (DHPFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain. It is very suitable to handle the situation that there are various possible values in membership and nonmembership degrees to depict the true circumstance. The bidirectional project method of DHPFS calculates method considered not only the bidirectional projection magnitudes and the distance but also includes angle between objects evaluated. Therefore, this paper proposes a bidirectional project method of DHPFS to handle the multiple attribute decision-making (MADM) problem under the dual hesitant Pythagorean fuzzy environment. Through the measure between each alternative decision matrix and the positive and negative ideal alternative matrix, the ranking order all alternatives can be used to select the best alternative. Furthermore, a model for MADM has been given. Finally, a numerical example for performance assessment of new rural construction has been given to demonstrate the application of bidirectional project method of DHPFS, and we used the dual hesitant Pythagorean weighted Bonferroni mean to compare its reasonable and effectiveness. K E Y W O R D Sbidirectional project method, dual hesitant Pythagorean fuzzy set, multiple attribute decision-making, new rural construction, performance assessment 1 | INTRODUCTION Atanassov 1,2 introduced the concept of intuitionistic fuzzy set (IFS) characterized by a membership function and a nonmembership function, which is a generalization of the concept of fuzzy set, 3 whose basic component is only a membership function. For the IFS, the sum of the membership and nonmembership degrees of each ordered pair is less than or equal to 1. Xu 4 developed the intuitionistic fuzzy weighted averaging (IFWA) operator, the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator, and the intuitionistic fuzzy hybrid aggregation (IFHA) operator. Xu 5 developed some geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator and gave an application of the IFHG operator to multiple attribute group decision-making with intuitionistic fuzzy information. Zhao and Wei 6 proposed some intuitionistic fuzzy Einstein hybrid aggregation operators for multiple attribute decision-making (MADM). Li et al 7 gave some methods for multiple attribute group decision-making based on intuitionistic fuzzy Dombi Hamy mean operators. The IFS and their extensions have received more and more attention since its appearance. A new extension of IFS, namely, the Pythagorean fuzzy set (PFS), 31,32 has been developed. The PFS is also characterized by the membership and nonmembership degrees. The difference between PFS and IFS is that the square sum of the membership and nonmembership de...

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“…Afterwards, more and more works about q-ROFS have been studied by numerous scholars [19][20][21][22][23][24][25]. However, the above-mentioned methods do not consider the human's hesitance.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, q-ROFS can be regarded as the extension of the IFS and PFS, when q = 1, the q-ROFS reduces to IFS, when q = 2, the q-ROFS reduces to PFS (see Figure 1). Afterwards, more and more works about q-ROFS have been studied by numerous scholars [19][20][21][22][23][24][25].…”

mentioning

confidence: 99%

Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Aggregation Operators and their Applications in Scheme Selection of Construction Project

et al. 2019

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The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment information and consider decision-maker's (DM's) hesitance. Thus, the concept of a dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) is developed in this paper. Then, based on Hamacher operation laws, weighting average (WA) operator and weighting geometric (WG) operator, some dual hesitant q-rung orthopair fuzzy Hamacher aggregation operators are developed, such as the dual hesitant q-rung orthopair fuzzy Hamacher weighting average (DHq-ROFHWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher weighting geometric (DHq-ROFHWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighted average (DHq-ROFHOWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighting geometric (DHq-ROFHOWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher hybrid average (DHq-ROFHHA) operator, and the dual hesitant q-rung orthopair fuzzy Hamacher hybrid geometric (DHq-ROFHHG) operator. The precious merits and some particular cases of above mentioned aggregation operators are briefly introduced. In the end, an actual application for scheme selection of construction project is provided to testify the proposed operators and deliver a comparative analysis.Keywords: multiple attribute decision-making (MADM) problems; Hamacher operation laws; dual hesitant q-rung orthopair fuzzy set (DHq-ROFS); the DHq-ROFHWA operator; the DHq-ROFHWG operator Symmetry 2019, 11, 771 2 of 26 of the membership degree µ and nonmembership degree v, which satisfies µ 2 + v 2 ≤ 1, so, it is obvious that the PFS can express more assessment information than the IFS. However, the scope of assessment information is still limited under Pythagorean fuzzy environment. For instance, given the evaluation value (0.7,0.9), we can easily find that 0.7 2 + 0.9 2 ≤ 1, which indicates that PFS cannot deal with such MADM problems. Then, to describe more evaluation information, Yager [18] further defined the q-rung orthopair fuzzy set (q-ROFS), q-ROFS is also consisted of the membership degree µ and nonmembership degree v which satisfies µ q + v q ≤ 1. Obviously, q-ROFS can be regarded as the extension of the IFS and PFS, when q = 1, the q-ROFS reduces to IFS, when q = 2, the q-ROFS reduces to PFS (see Figure 1). Afterwards, more and more works about q-ROFS have been studied by numerous scholars [19][20][21][22][23][24][25].

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Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

Cited by 143 publications

References 57 publications

GRA Method for Probabilistic Linguistic Multiple Attribute Group Decision Making with Incomplete Weight Information and Its Application to Waste Incineration Plants Location Problem

GRA Method for Probabilistic Linguistic Multiple Attribute Group Decision Making with Incomplete Weight Information and Its Application to Waste Incineration Plants Location Problem

Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision‐making and their application to performance assessment of new rural construction

Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Aggregation Operators and their Applications in Scheme Selection of Construction Project

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