A Novel Method for Multiattribute Decision Making with Interval-Valued Pythagorean Fuzzy Linguistic Information

Du, Yuqin; Hou, Fujun; Zafar, Wasif; Qian, Yu; Zhai, Yubing

doi:10.1002/int.21881

Cited by 110 publications

(100 citation statements)

References 42 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 . PF sets have been created as a new and prospective class of nonstandard fuzzy sets because they can accommodate higher degrees of uncertainty than other nonstandard fuzzy models can .…”

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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“…If

0 \leq u_{\tilde{A}}^{U} (x) + v_{\tilde{A}}^{U} (x) \leq 1

, the interval‐valued Pythagorean uncertain linguistic number (IVPULN) degenerates to be an interval‐valued intuitionistic uncertain linguistic number . If

s_{θ (x)} = s_{τ (x)}

, the IVPULN retrogrades to be an interval‐valued Pythagorean fuzzy linguistic number …”

Section: Basic Conceptsmentioning

confidence: 99%

An integrated MCDM method for robot selection under interval‐valued Pythagorean uncertain linguistic environment

et al. 2018

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Robots have received considerable attention in many manufacturing companies due to their great capabilities and characteristics. Selecting an appropriate robot for a specific application can be regarded as a challenging multicriteria decision‐making problem. Furthermore, decision makers are inclined to represent their opinions by using linguistic terms owing to their ambiguous thinking. In this regard, we put forward a novel robot selection model by integrating quality function development (QFD) theory and qualitative flexible multiple criteria method (QUALIFLEX) under interval‐valued Pythagorean uncertain linguistic context. For the developed model, the evaluations given by decision makers are presented as interval‐valued Pythagorean uncertain linguistic sets for dealing with the uncertainty and vagueness of decision makers’ information. An extended QFD method is used for determining criteria weights from the perspective of customers. A modified QUALIFLEX technique based on closeness degree is utilized to generate the ranking order of alternative robots and determine the most suitable one. Finally, an empirical example of an auto manufacturing company is applied to clarify the effectiveness and accuracy of the proposed robot selection approach.

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“…However, in many practical decision process, due to insufficiency in available information, it is difficult for DMs to exactly express their opinions by a crisp number, but they can be represented by an interval number within [0,1] . Although q ‐rung orthopair fuzzy sets have attracted increasing attention recently, most of the existing related studies focus on the q‐ROFS itself, and ignore the extended information style of q‐ROFS.…”

Section: Introductionmentioning

confidence: 99%

Some interval‐valued q‐rung orthopair weighted averaging operators and their applications to multiple‐attribute decision making

Luo

et al. 2019

Int J Intell Syst

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Q‐rung orthopair fuzzy sets (q‐ROFSs), initially proposed by Yager, are a new way to reflect uncertain information. The existing intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets are special cases of the q‐ROFSs. However, due to insufficiency in available information, it is difficult for decision makers to exactly express the membership and nonmembership degrees by crisp numbers, and interval membership degree and interval nonmembership degree are good choices. In this paper, we propose the concept of interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) based on the ideas of q‐ROFSs and some operational laws of q‐rung orthopair fuzzy numbers (q‐ROFNs). Then, some interval‐valued q‐rung orthopair weighted averaging operators are presented based on the given operational laws of q‐ROFNs. Further, based on these operators, we develop a novel approach to solve multiple‐attribute decision making (MADM) problems under interval‐valued q‐rung orthopair fuzzy environment. Finally, a numerical example is provided to illustrate the application of the proposed method, and the sensitivity analysis is further carried out for the parameters.

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A Novel Method for Multiattribute Decision Making with Interval-Valued Pythagorean Fuzzy Linguistic Information

Cited by 110 publications

References 42 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

An integrated MCDM method for robot selection under interval‐valued Pythagorean uncertain linguistic environment

Some interval‐valued q‐rung orthopair weighted averaging operators and their applications to multiple‐attribute decision making

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