Multi-attribute group decision making method based on Pythagorean fuzzy Einstein interactive power averaging approach for sustainable cement industry

Abstract

Pythagorean fuzzy numbers have been playing an essential role in decision-making problems. The existing operational rules (ORs) constructed based on Einstein t-norm and t-conorm operators in the Pythagorean fuzzy environment have some drawbacks. This type of t-norm and t-conorm operators need to consider the interaction between the membership degree and non-membership degree of Pythagorean fuzzy numbers and, consequently, produces some unreasonable results in some realistic decision-making problems. To eliminate such deficiencies, interactive operational rules have been formed, revising the existing operational rules. A new aggregation operator, namely, Pythagorean fuzzy Einstein interactive weighted averaging operator, has been presented in this article based on newly revised ORs, and some properties of this operator are discussed. At the same time to eliminate or reduce the effect of existing biases that occurred from the end of decision makers in the evaluation procedure of alternatives in multi-attribute group decision-making problem, we have presented the Pythagorean fuzzy Einstein interactive power weighted averaging operator. A novel multi-attribute group decision-making method for the best sustainable cement industry evaluation in India is presented based on Pythagorean fuzzy Einstein interactive power weighted averaging and Pythagorean fuzzy Einstein interactive weighted averaging operators. The validity of the method is tested by comparing some existing methods. At last, a comparative study with sensitivity analysis shows that the proposed method is superior to some considered existing methods.