Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets

Mohagheghi, Vahid; Mousavi, Seyed Meysam; Vahdani, Behnam

doi:10.1016/j.asoc.2017.08.003

Cited by 98 publications

(65 citation statements)

References 32 publications

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“…The theory of Pythagorean fuzzy (PF) sets originally introduced by Yager is a useful tool for capturing the vagueness and uncertainty in real‐world decision situations . PF sets are related to the concept of the degrees of membership and nonmembership that fulfill a relaxed condition that the square sum of the two degrees is less than or equal to 1 .…”

Section: Introductionmentioning

confidence: 99%

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Chen

2018

Int J Intell Syst

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The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson‐like correlation‐based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval‐valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real‐life decision‐making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well‐known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson‐like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation‐based closeness coefficients to simultaneously measure the relative closeness to the positive‐ideal PF/IVPF solutions and the relative remoteness from the negative‐ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson‐like correlation‐based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.

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Section: Introductionmentioning

confidence: 99%

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Chen

2018

Int J Intell Syst

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“…Because the square sum of its membership and nonmembership degrees is equal to or less than 1, whereas the sum of membership and nonmembership degrees of IFSs is equal to or less than 1 . This fact undoubtedly indicates that PFSs permit larger space to describe agree, disagree, and hesitant information . More specifically, IFSs cannot handle some cases, for example, in which assume that

\frac{\sqrt{3}}{2}

and

\frac{\sqrt{3}}{2}

be the membership and nonmembership degrees of an alternative with respect to a criterion.…”

Section: Introductionmentioning

confidence: 99%

Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator

et al. 2018

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Pythagorean fuzzy sets are powerful techniques for modeling vagueness in practice. The aim of this article is to investigate an effective means to aggregate uncertain information and then employ it into settling multiple criteria decision making (MCDM) problems within the Pythagorean fuzzy circumstances. To capture the nature of the reality, some special cases should be comprehensively considered. First, though correlation commonly exist among criteria, a deep insight should also be provided into some realistic situations, in which not all the criteria are interrelated to others. Besides, it is more reasonable to take the importance of the input arguments into consideration. Effected by aforementioned point, this article explores a Pythagorean fuzzy partitioned normalized weighted Bonferroni mean (PFPNWBM) operator with the combination of partitioned Bonferroni mean (BM) and normalized weighted BM operators considering Shapley fuzzy measure. Subsequently, in the context of partially known weight information, models are established to identify the optimal Shapley fuzzy measure. Moreover, integrated the PFPNWBM operator with the optimal Shapley fuzzy measure identification model, a Pythagorean fuzzy MCDM approach is designed. Finally, an illustrative example and detailed analyses are performed to demonstrate its feasibility and reliability.

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“…Hence Pythagorean fuzzy set can model some situations that cannot be dealt with by intuitionistic fuzzy set. The Pythagorean fuzzy set has received broad attention and many useful methods have been developed …”

Section: Introductionmentioning

confidence: 99%

“…Zeng presented Pythagorean fuzzy probabilistic ordered weighted averaging (OWA) operator. Some multiple attribute decision‐making methods have been extended to accommodate Pythagorean fuzzy values . Zhang and Xu proposed an extended Pythagorean fuzzy TOPSIS (the technique for order preference by similarity to ideal solution) method.…”

Section: Introductionmentioning

confidence: 99%

“…Chen proposed remoteness index‐based Pythagorean fuzzy VIKOR (The VlseKriterijumska Optimizacija I Kompromisno Resenje, ie, multicriteria optimization and compromise solution) methods. Mohagheghi et al introduced a new index to rank alternatives, which can be used to estimate the utility degree of alternatives. Peng and Dai developed a Pythagorean decision‐making method based on the prospect theory and regret theory.…”

Section: Introductionmentioning

confidence: 99%

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Hesitant interval-valued Pythagorean fuzzy VIKOR method

Yang

Pang

2018

Int J Intell Syst

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In this article, we investigate multiple attribute decision‐making problems with hesitant interval‐valued Pythagorean fuzzy information. First, the concepts of hesitant interval‐valued Pythagorean fuzzy set are defined, and the operation laws, the score function, and accuracy function have been developed. Then several distance measures for hesitant interval‐valued Pythagorean fuzzy values have been presented including the Hamming distance, Euclidean distance, and generalized distance, and so on. Based on the operational laws, a series of aggregation operators have been developed including the hesitant interval‐valued Pythagorean fuzzy weighted averaging (HIVPFWA) operator, the hesitant interval‐valued Pythagorean fuzzy geometric weighted averaging (HIVPFGWA) operator, the hesitant interval‐valued Pythagorean fuzzy ordered weighed averaging (HIVPFOWA) operator, and hesitant interval‐valued Pythagorean fuzzy ordered weighed geometric averaging (HIVPFOWGA) operator. By using the generalized mean operator, we also develop the generalized hesitant interval‐valued Pythagorean fuzzy weighed averaging (GHIVPFWA) operator, the generalized hesitant interval‐valued Pythagorean fuzzy weighed geometric averaging (GHIVPFWGA) operator, the generalized hesitant interval‐valued Pythagorean fuzzy ordered weighted averaging (GHIVPFOWA) operator, and generalized hesitant interval‐valued Pythagorean fuzzy ordered weighted geometric averaging (GHIVPFOWGA) operator operator. We further develop several hybrid aggregation operators including the hesitant interval‐valued Pythagorean fuzzy hybrid averaging (HIVPFHA) operator and the generalized hesitant interval‐valued Pythagorean fuzzy hybrid averaging (GHIVPFHA) operator. Based on the distance measures and the aggregation operators, we propose a hesitant interval‐valued Pythagorean fuzzy VIKOR method to solve multiple attribute decision problems with multiple periods. Finally, an illustrative example for evaluating the metro project risk is given to demonstrate the feasibility and effectiveness of the proposed method.

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Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets

Cited by 98 publications

References 32 publications

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator

Hesitant interval-valued Pythagorean fuzzy VIKOR method

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