Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

By Xiaolu Zhang, Zeshui Xu. International Journal of Intelligent Systems, 2014

1,418 citations recorded by the source corpus.

Recently, a new model based on Pythagorean fuzzy set (PFS) has been presented to manage the uncertainty in real‐world decision‐making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision‐making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/8c38de170f470ac54409ca019cc1d092ed925c80

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Citations in the corpus

Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making (2016, methodology): “For convenience, Zhang and Xu 17 called p ( x i ) = ( μ P ( x i ) , ν P ( x i )) a PFN. Based on the above deﬁnition, Zhang and Xu 17 deﬁned the distance between p ( x i ) and p ( x j ) as follows: The main difference between PFNs and IFNs is their corresponding constraint conditions which are…”
Assessing occupational risks in pipeline construction using FMEA-based AHP-MOORA integrated approach under Pythagorean fuzzy environment (2019, methodology): “…on the proposed score functions of Pythagorean fuzzy numbers as demonstrated above, the following laws are defined to compare two Pythagorean fuzzy numbers (Garg 2018a; 2018b; 2017a; 2017b; Zhang and Xu 2014): iÞ If sðb1Þ<sðb2Þ; then b1 b2 iiÞ If sðb1Þ>sðb2Þ; then b1 b2 iiiÞ If sðb1Þ ¼ sðb2Þ; then…”
A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making (2016, background): “…μ P : X −→ [0 , 1] denotes the degree of membership and ν P : X −→ [0 , 1] denotes the degree of nonmembership of the element x ∈ X to the set P , respectively, with the condition that 0 (cid:2) For convenience, Zhang and Xu 15 called ( μ P ( x ) , ν P ( x )) a PFN denoted by P = ( μ P , ν P ).”
Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process (2017, methodology): “(cid:2) The degree of indeterminacy is given as: For convenience, Zhang and Xu 19 called (cid:4) μ P ( x ) , ν P ( x ) (cid:5) a PFN denoted by P = (cid:4) μ P , ν P (cid:5) .”
A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making (2016, background): “Recently, Zhang and Xu 13 provided the detailed mathematical expressions of PFSs and presented the concept of Pythagorean fuzzy number (PFN).”
Multiple-Attribute Decision-Making Based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers (2019, methodology): “Zhang and Xu [48] defined the distance measure based on PFNs and presented an extension of TOPSIS method for solving MADM problems.”
TOPSIS Method Based on Correlation Coefficient under Pythagorean Fuzzy Soft Environment and Its Application towards Green Supply Chain Management (2021, methodology): “Zhang and Xu [31] defined some operational laws for PFSs and developed a TOPSIS technique to solve MCDM problems under PFS environments.”
Spherical fuzzy sets and their applications in multi-attribute decision making problems (2018, positive): “According to Zhang and Xu [33], the ﬁrst step is to identify the Pythagorean fuzzy positive ideal solu-tion (PIS) and the Pythagorean fuzzy negative ideal solution (NIS) of the decision matrix, which are The decision matrix utilized in this paper are not be solve as this above technique because in…”
Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making (2018, methodology): “Zhang and Xu 28 deﬁned the distance measure to calculate the distances between each alternative based on PFNs and presented an extension of TOPSIS method for solving MADM problems.”
Spherical fuzzy sets and spherical fuzzy TOPSIS method (2018, positive): “Utilize Equations (34 and 35) to calculate the revised closeness ratio proposed by Zhang & Xu [42] given in Equation (36).”