Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process

By Harish Garg. International Journal of Intelligent Systems, 2017

363 citations recorded by the source corpus.

The objective of this paper is to present some series of geometric‐aggregated operators under Pythagorean fuzzy environment by relaxing 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 geometric, Pythagorean fuzzy Einstein ordered weighted geometric, generalized Pythagorean fuzzy Einstein weighted geometric, and generalized Pythagorean fuzzy Einstein ordered weighted geometric operators, are proposed in this paper. Some of its properties have also been investigated in details. Finally, an illustrative example for multicriteria decision‐making problems of alternatives is taken to demonstrate the effectiveness of the approach.

Subfields: Control and Systems Engineering, Management, Monitoring, Policy and Law, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ff392359fcbb253da543fb0cdab89e516c74e353

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Citations in the corpus

Assessing occupational risks in pipeline construction using FMEA-based AHP-MOORA integrated approach under Pythagorean fuzzy environment (2019, background): “…1 1 vb1 2 kq ; k>0 (6) Let b1 ¼ Pðlb1 ; vb1Þ and b2 ¼ Pðlb2 ; vb2Þ be two Pythagorean fuzzy numbers, a nature quasi-ordering on the Pythagorean fuzzy numbers is described below (Garg 2018a; 2018b; 2017a; 2017b; Zhang and Xu 2014): b1 b2 if and only if lb1 lb2 and vb1 vb2 To compare the…”
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.”
Pythagorean fuzzy set: state of the art and future directions (2017, background): “Definition 4.38 (Garg 2017a) 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 (i = 1, 2, . . . , n), with ∑ni=1 wi = 1, ηi be its corresponding confidence levels, then a confidence Pythagorean fuzzy weighted averaging (CPFWA)…”
Multiple-Attribute Decision-Making Based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers (2019, background): “Garg [12], [13] proposed some new Pythagorean fuzzy generalized AOs by combining Einstein operations and studied their some desirable properties.”
Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process (2018, methodology): “Garg 30,31 presented some generalized averaging and geometric aggregation operators based on the Einstein t-norm operations for PFNs. Ma and Xu 32 developed some symmetric PF weighted geometric and averaging operators under PF environment and investigated the relationships among these operators and…”
Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making (2018, methodology): “8843 Method by H. Garg 31 based on PFWG operator S (˜ r 1 ) = 0 .”
Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management (2021, methodology): “Keeping the supremacy of the elaborated laws, Garg (2017) explored the principle of generalized Pythagorean fuzzy geometric aggregation operators based on Einstein laws.”