Some Hesitant Fuzzy Linguistic Muirhead Means with Their Application to Multiattribute Group Decision‐Making

Wang, Jun; Zhang, Runtong; Zhu, Xiaomin; Xing, Yuping; Buchmeister, Borut

doi:10.1155/2018/5087851

Cited by 17 publications

(15 citation statements)

References 46 publications

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“…In future works, we can apply the q ‐ROULNs to describe the linguistic information in other practical decision making problems. Meanwhile, we can expand the proposed power PHM operator into other fuzzy environments, such as hesitant fuzzy linguistic sets, interval‐valued fuzzy soft sets, and so on.…”

Section: Discussionmentioning

confidence: 99%

Power partitioned Heronian mean operators for q ‐rung orthopair uncertain linguistic sets with their application to multiattribute group decision making

et al. 2019

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In this paper, a new tool, called q-rung orthopair uncertain linguistic numbers (q-ROULNs), is developed and a new multiattribute group decision making (MAGDM) method for q-ROULNs is proposed. First, the concept of q-rung orthopair uncertain linguistic sets (q-ROULSs) is introduced, and some operational laws, expected function, accuracy function, and distance measure of q-ROULSs are defined. Further, to effectively aggregate q-ROULNs, we take advantage of partitioned Heronian mean operator and power average operator and propose the q-rung orthopair uncertain linguistic power partitioned Heronian mean operator and its weighted form. The proposed operators not only deal with this situations where attributes are divided into several parts and attributes in the same part are interrelated each other, whereas attributes in different parts have no relationship, but also reduce the negative influence of unreasonable attribute values provided by decision makers on final results. Some desirable properties and special cases of the proposed operators are also investigated. Finally, a MAGDM method based on the proposed operators is developed and a numerical instance as well as comparative analysis is conducted to illustrate the effectiveness and advantages of the proposed method. K E Y W O R D S multiattribute group decision making, power partitioned Heronian mean, q-rung orthopair uncertain linguistic power partitioned Heronian mean, q-rung orthopair uncertain linguistic set

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Section: Discussionmentioning

confidence: 99%

Power partitioned Heronian mean operators for q ‐rung orthopair uncertain linguistic sets with their application to multiattribute group decision making

et al. 2019

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“…Hence, we obtain the following results Step 3. Calculate T α k ij according to Equation (31). For convenience, we use the symbol T k to represent the values T α k ij (i, j = 1, 2, 3, 4; k = 1, 2, 3) Step 4.…”

Section: The Decision-making Processmentioning

confidence: 99%

“…The recently proposed Muirhead mean (MM) [30] has similar advantages as BM, HM, and MSM, as all of them can capture the interrelationship among attributes. However, MM is believed to be more flexible due to its skill of considering the interrelationship among arbitrary numbers of attributes [31][32][33][34]. Hence, it is very necessary to compound power average (PA) [35] with MM to integrate IVIF information and propose IVIF power MM (IVIFPMM) operators.…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach to Multi-Attribute Group Decision-Making based on Interval-Valued Intuitionistic Fuzzy Power Muirhead Mean

Shang

Wang

et al. 2019

Symmetry

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This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.

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“…For example, Liu and Li [45] developed an MM operator to aggregate hesitant fuzzy linguistic information. Wang J et al [46] developed a hesitant fuzzy linguistic MM operator. Hong and Rong [44] presented a hesitant fuzzy dual Muirhead mean operator.…”

Section: Introductionmentioning

confidence: 99%

A new multi-criteria decision-making method based on Pythagorean hesitant fuzzy Archimedean Muirhead mean operators1

Zhong

Guo

Gao

et al. 2019

IFS

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To describe the values of criteria and to generate a sort of alternatives are two important issues in multi-criteria decision-making (MCDM). A superior tool for the former issue is Pythagorean hesitant fuzzy number (PHFN) and an effective tool for the latter issue is aggregation operator. So far, a number of aggregation operators of PHFNs have been presented within the academia. Each aggregation operator has its own characteristics and can work well for its specific purpose. But there is not yet an aggregation operator of PHFNs that can provide satisfying generality and flexibility in aggregating the values of criteria and capturing the interactions of criteria. The Archimedean t-conorm and t-norm (ATT) are well-known for having the capability to generate versatile and flexible operational rules for fuzzy numbers, while the Muirhead mean (MM) operator is an all-in-one aggregation operator for capturing the interrelationships of the aggregated arguments. To this end, the MM operator and the ATT for PHFNs are combined to present a Pythagorean hesitant fuzzy Archimedean MM (PHFAMM) operator and a weighted PHFAMM operator and a new MCDM method based on the presented operators is proposed in this paper. Firstly, the generalised expressions of the presented operators are provided. The properties of the operators are explored and proved and their specific expressions based on Algebraic, Einstein, Hamacher, and Frank ATTs are then constructed. Based on these specific expressions, a new method for solving the MCDM problems based on PHFNs is developed. Finally, the developed MCDM method is demonstrated via an example, a set of experiments and qualitative and quantitative comparisons.

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Some Hesitant Fuzzy Linguistic Muirhead Means with Their Application to Multiattribute Group Decision‐Making

Cited by 17 publications

References 46 publications

Power partitioned Heronian mean operators for q ‐rung orthopair uncertain linguistic sets with their application to multiattribute group decision making

Power partitioned Heronian mean operators for q ‐rung orthopair uncertain linguistic sets with their application to multiattribute group decision making

A Novel Approach to Multi-Attribute Group Decision-Making based on Interval-Valued Intuitionistic Fuzzy Power Muirhead Mean

A new multi-criteria decision-making method based on Pythagorean hesitant fuzzy Archimedean Muirhead mean operators1

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