Induced interval-valued intuitionistic fuzzy Einstein ordered weighted geometric operator and their application to multiple attribute decision making

Abstract

Interval-valued intuitionistic fuzzy information aggregation plays an important part in interval-valued intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on interval-valued intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop the induced interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (I-IVIFEOWG) operator. We also establish some desirable properties of this operator, such as commutativity, idempotency and monotonicity. Then, we apply the induced interval-valued intuitionistic fuzzy Einstein hybrid geometric (I-IVIFEHG) operator to deal with multiple attribute decision making under interval-valued intuitionistic fuzzy environments. Finally, an illustrative example for software quality evaluation is given to verify the developed approach and to demonstrate its practicality and effectiveness.