Some q-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making

Xu, Yan; Shang, Xiaopu; Wang, Jun; Wen, Wang; Huang, Huiqun

doi:10.3390/sym10100472

Cited by 89 publications

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“…Liu et al [66] provided some Heronian mean operator to aggregate q-ROFNs. In this paper, according to the dual hesitant q-rung orthopair set defined by Xu et al [29], we shall propose some q-rung orthopair fuzzy Hamacher operation laws to fuse the q-rung orthopair fuzzy information. The goal of our paper is to develop some operators that can consider human's hesitance and the interrelationship between being fused arguments.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In accordance of the q-ROFSs and DHFSs [27,28], we further introduce the dual hesitant q-rung orthopair fuzzy sets (DHq-ROFSs) [29] as follows.…”

Section: Dual Hesitant Q-rung Orthopair Fuzzy Setmentioning

confidence: 99%

“…Definition 5 [29]. Assume that d = (h, g) is a DHq-ROFN, let s(d) = 1 2 1 + 1 #h α∈h α q − 1 #g β∈g β q be the score results of d = (h, g) and E(d) = 1 #h α∈h α q + 1 #g β∈g β q be the accuracy results of d = (h, g), where #h indicates the number of elements in set h and #g indicates the number of elements in set g, respectively, assume that d i = (h i , g i )(i = 1, 2) be any two DHq-ROFNs, then if s(d 1 ) > s(d 2 ), then d 1 d 2 ; if s(d 1 ) = s(d 2 ), then: (1) If E(d 1 ) = E(d 2 ), then d 1 = d 2 ; (2) If E(d 1 ) > E(d 2 ), then d 1 d 2 .…”

Section: Dual Hesitant Q-rung Orthopair Fuzzy Setmentioning

confidence: 99%

“…Definition 6 [29]. Let d 1 = (h 1 , g 1 ), d 2 = (h 2 , g 2 ), and d = (h, g) be three DHq-ROFNs, then, some new operations on the DHq-ROFNs are defined as…”

Section: Dual Hesitant Q-rung Orthopair Fuzzy Setmentioning

confidence: 99%

“…In order to overcome this limitation, the hesitant fuzzy sets (HFSs) [26] and dual hesitant fuzzy sets (DHFSs) [27,28] have been proposed to deal with MADM issues effectively. Combining the advantages of the two fuzzy sets, Xu et al [29] gave the concept of the dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) and presented some Heronian mean operators for MADM. Obviously, the dual hesitant q-rung orthopair fuzzy numbers (DHq-ROFNs) can express evaluation information more convenience in actual MADM applications.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Literature Reviewmentioning

confidence: 99%

“…In accordance of the q-ROFSs and DHFSs [27,28], we further introduce the dual hesitant q-rung orthopair fuzzy sets (DHq-ROFSs) [29] as follows.…”

Section: Dual Hesitant Q-rung Orthopair Fuzzy Setmentioning

confidence: 99%

Section: Dual Hesitant Q-rung Orthopair Fuzzy Setmentioning

confidence: 99%

“…Definition 6 [29]. Let d 1 = (h 1 , g 1 ), d 2 = (h 2 , g 2 ), and d = (h, g) be three DHq-ROFNs, then, some new operations on the DHq-ROFNs are defined as…”

Section: Dual Hesitant Q-rung Orthopair Fuzzy Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

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Generalized orthopair fuzzy weighted distance‐based approximation (WDBA) algorithm in emergency decision‐making

2019

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With the intensification of global warming trends, the frequent occurrence of natural disasters has brought severe challenges to the sustainable development of society. Emergency decision‐making (EDM) in natural disasters is playing an increasingly important role in improving disaster response capacity. In the case of EDM evaluation, the essential problem arises serious incompleteness, impreciseness, subjectivity, and incertitude. The q‐rung orthopair fuzzy set (q‐ROFS), disposing the indeterminacy portrayed by membership and nonmembership with the sum of qth power of them, is a more viable and effective means to seize indeterminacy. The aim of paper is to present a new score function of q‐rung orthopair fuzzy number (q‐ROFN) for solving the failure problems when comparing two q‐ROFNs. Firstly, we introduce some basic set operations for q‐ROFS. The properties of these operations are also discussed in detail. Later, we propose a q‐rung orthopair fuzzy decision‐making method based on weighted distance‐based approximation (WDBA), in which the weights of decision‐makers are obtained from a nonliner optimization model according to the deviation‐based method. Finally, some examples are investigated to illustrate the feasibility and validity of the proposed approach. The salient features of the proposed method, compared to the existing q‐rung orthopair fuzzy decision‐making methods, are as follows: (a) it can obtain the optimal alternative without counterintuitive phenomena and (b) it has a great power in distinguishing the optimal alternative.

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Some q‐rung interval‐valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making

et al. 2019

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In this paper, according to the Maclaurin symmetric mean (MSM) operator, the dual MSM (DMSM) operator and the q-rung interval-valued orthopair fuzzy set (q-RIVOFS), we develop some novel MSM operators under the q-rung interval-valued orthopair fuzzy environment, such as, the q-rung interval-valued orthopair fuzzy MSM operator, the q-rung interval-valued orthopair fuzzy weighted MSM (q-RIVOFWMSM) operator, the q-rung interval-valued orthopair fuzzy DMSM operator, and the q-rung interval-valued orthopair fuzzy weighted DMSM operator. In addition, some precious properties and numerical examples of these new operators are given in detail. These new operators have the advantages of considering the interrelationship of arguments and can deal with multiple attribute group decision-making problems with q-rung interval-valued orthopair fuzzy information. Finally, a reality example for green suppliers selection in green supply chain management is provided to demonstrate the proposed approach and to verify its rationality and scientific. green suppliers selection, multiple attribute group decision making (MAGDM), q-RIVOFWDMSM operator, q-RIVOFWMSM operator, q-rung interval-valued orthopair fuzzy sets (q-RIVOFSs) | INTRODUCTIONIn the study of fuzzy sets (FSs) 1 fields, finding the suitable way to express evaluation information is a hot topic. Although the intuitionistic FSs (IFSs) 2-7 and Pythagorean FSs (PFSs) [8][9][10][11][12][13][14][15][16] have emerged as useful tools to deal with actual decision-making problems, however, the scope of their assessment information remains limited. Thus, to overcome this limitation, the q-rung orthopair fuzzy set (q-ROFS), 17 which is characterized by the sum of q-th power of membership and nonmembership is less or equal to 1, was proposed for MADM problems. Since that, the q-ROFS has aroused the attention of a large number of scholars since its appearance. 18-21 Based on the weighted average (WA) operator and the weighted geometric (WG) operator, [22][23][24][25][26] Liu and Wang 27 developed two q-rung orthopair fuzzy aggregation operator to fuse q-rung orthopair fuzzy numbers. Combined q-rung orthopair fuzzy information and MSM operators, Wei, Wei, Wang, Gao, and Wei 28 proposed some new q-rung orthopair fuzzy aggregation operators and studied their applications to potential evaluation of emerging technology commercialization. Liu, Wang and Liu 29 proposed some q-rung orthopair fuzzy Heronian mean operators and q-rung orthopair fuzzy partitioned Heronian mean operators for MADM, and then some special cases about these operators were discussed. Based on the cosine similarity measure and cotangent similarity measure, Wang, Wang, Wei, and Wei 30 defined some novel q-rung orthopair fuzzy cosine and cotangent similarity measures. Bai, Zhu, Wang, and Zhang 31 defined some q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (MSM) operators for MADM. Xu, Shang, Wang, Wu, and Huang 32 combined the q-ROFS and the dual hesitant fuzzy set to propose the q-rung dual hesitant orthopair fuzz...

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Some q-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making

Cited by 89 publications

References 47 publications

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

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

Generalized orthopair fuzzy weighted distance‐based approximation (WDBA) algorithm in emergency decision‐making

Some q‐rung interval‐valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making

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