Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

Wang, Rui; Wang, Jie; Gao, Hui; Wei, Guiwu

doi:10.3390/sym11010006

Cited by 116 publications

(75 citation statements)

References 78 publications

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“…However, our developed methods can only deal with MADMs with dual hesitant Pythagorean fuzzy information, and it is clear that these operators cannot handle more complicated decision making problems, such as when the sum square of the membership and non-membership is more than 1. In the future, we shall continue studying MADM problems with the application and extension of the developed operators to other domains [67,68] and proposed more suitable methods [69][70][71][72][73][74][75].…”

Section: Discussionmentioning

confidence: 99%

Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Tang

Wang

et al. 2019

Mathematics

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On account of the indeterminacy and subjectivity of decision makers (DMs) in complexity decision-making environments, the evaluation information over alternatives presented by DMs is usually fuzzy and ambiguous. As the generalization of intuitionistic fuzzy sets (IFSs), the Pythagorean fuzzy set (PFS) is more useful in expressing fuzzy and ambiguous information. Meanwhile, in order to consider human hesitance, dual hesitant Pythagorean fuzzy sets (DHPFSs) are presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in DHPFSs more effectively, in this article, some dual hesitant Pythagorean fuzzy Heronian mean operators, which can consider the relationships between arguments being fused, are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some important properties of these Heronian mean (HM) operators are discussed. Subsequently, the defined aggregation operators are used in MADM with dual hesitant Pythagorean fuzzy numbers (DHPFNs), and the MADM model is developed. In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches. The method presented in this paper can effectively solve the MADM problems in which the decision-making information is expressed by DHPFNs and the attributes are interactive.

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Section: Discussionmentioning

confidence: 99%

Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Tang

Wang

et al. 2019

Mathematics

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“…Khalil et al [20] proposed some new operations on interval-valued PFSs. Wang et al [21] proposed Muirhead mean operators for PFSs. Wei [22] proposed a picture fuzzy Hamacher aggregation operator and used it to solve the MADM problem.…”

Section: Structure Characteristic Functions Restriction On Characterimentioning

confidence: 99%

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

et al. 2019

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The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches.

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“…the limitation of our approach is that the calculation formula is too complicated, thus, in future we will continue to study MADM problems and propose some simplified operators to other decision-making fields [69][70][71][72][73][74]. Furthermore, the application of the proposed methods in addressing practical MADM problems in other manufacturing environment, such as selection of an automated inspection system, selection of an industrial robot, selection of an additive manufacturing process and selection of a machine tool and will also be studied in our future work.…”

Section: Comparative Analysismentioning

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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Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

Cited by 116 publications

References 78 publications

Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

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

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