The Pythagorean fuzzy Einstein Choquet integral operators and their application in group decision making

Abstract

Since Pythagorean fuzzy set is a powerful tool as it relaxing the condition that the sum of membership degrees is less than or equal to one with the square sum is less than or equal to one. Also Choquet integral is a very useful way of measuring the expected utility of an uncertain event. Therefore, in this paper we use the Choquet integral to develop Pythagorean fuzzy aggregation operators, namely Pythagorean fuzzy Einstein Choquet integral averaging operator and Pythagorean fuzzy Einstein Choquet integral geometric operator. The operators not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements or their ordered positions. It must be noted that several existing operators are the special cases of the developed operators. Further the properties such as boundedness, monotonicity and idempotency of the proposed operators have been studied in detail. Furthermore based on the developed operators a multi-criteria group decision-making method has been presented. Finally an illustrative example is presented to illustrate the validity and effectiveness of the proposed method.