A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making

By Harish Garg. International Journal of Intelligent Systems, 2016

634 citations recorded by the source corpus.

The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets (PFSs). The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging (PFEWA), Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA), generalized Pythagorean fuzzy Einstein weighted averaging (GPFEWA), and generalized Pythagorean fuzzy Einstein ordered weighted averaging (GPFEOWA), are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision‐making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3952be38d99803f8a6a74a74db500042b0b0bcba

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Citations in the corpus

Multiple-Attribute Decision-Making Based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers (2019, methodology): “[13] H. Garg, “Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process,” Int.”
A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem (2016, positive): “Peng and Yang [19] deﬁned the new operations such as division; subtraction and their corresponding properties on PFNs. Recently, Garg [14] proposed a new generalized Pythagorean fuzzy information aggregation operators using Einstein operations.”
Pythagorean Fuzzy Information Measures and Their Applications (2017, methodology): “Garg 28 proposed a new generalized Pythagorean fuzzy information aggregation using Einstein operations and applied it to decision making.”
Some q‐rung orthopair fuzzy Heronian mean operators in multiple attribute decision making (2018, neutral): “5) → [1, t] (30) Δ−1 ( si, α ) = i + α = β (31)”
Assessing occupational risks in pipeline construction using FMEA-based AHP-MOORA integrated approach under Pythagorean fuzzy environment (2019, neutral): “A Pythagorean fuzzy set P is an object having the form (Garg 2018a; 2018b; 2016a; 2016b; Zhang and Xu 2014): P ¼ <x; P lP xð Þ; vP xð Þð Þ>jx 2 X (1) where lPðxÞ : X 7!”
A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making Processes (2016, methodology): “Garg 21 presented a generalized aggregation operator using Einstein operations for aggregating different PFNs. Garg 22 proposed an improved accuracy function for interval-valued PFNs by overcoming the shortcoming of the existing functions.”
Pythagorean fuzzy set: state of the art and future directions (2017, background): “Definition 4.34 (Garg 2016a) Let pi = (μi , νi )(i = 1, 2, . . . , n) be a collection of PFNs, and w = (w1, w2, . . . , wn)T be the weight vector of pi , with wi ≥ 0,∑ni=1 wi = 1, λ > 0, then a generalized Pythagorean fuzzy Einstein weighted averaging (GPFEWA) operator is a mapping GPFEWA: Pn → P ,…”
TOPSIS Method Based on Correlation Coefficient under Pythagorean Fuzzy Soft Environment and Its Application towards Green Supply Chain Management (2021, methodology): “21727 ( ) > ( ) > ( ) > ( ) > ( ) Garg [35] PFEWA 0.”
Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making (2017, methodology): “Garg [6,23], further, presented a generalized averaging aggregation operator under the Pythagorean fuzzy set environment by utilizing the Einstein norm operations.”
Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems (2019, positive): “Garg [20–22] presented generalized Pythagorean fuzzy information aggregation using Einstein operations, Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm, accuracy function under interval-valued Pythagorean fuzzy environment and their…”
Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process (2017, background): “Peng and Yang 20 deﬁned the new operations such as division, subtraction, and their corresponding properties on PFNs. Garg 15 proposed a new generalized Pythagorean fuzzy information aggregation operators using Einstein operations for solving MCDM problems and studied some of their desirable propert”
Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making (2018, background): “Based on the operational laws of the q -ROFNs described in Equations (3)–(6), from Equation 29, we can get the aggregation result shown as Theorem 9.”
Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making (2018, background): “Garg 30 proposed some new generalized Pythagorean fuzzy information aggregation operators by combining Einstein operations and studied some of their desirable properties.”