Cubic M-polar Fuzzy Hybrid Aggregation Operators with Dombi’s T-norm and T-conorm with Application

Abstract

A cubic m-polar fuzzy set (CmPFS) is a new hybrid extension of cubic set (CS) and m-polar fuzzy set (mPFS). A CS comprises two parts; one part consists of a fuzzy interval (may sometimes be a fuzzy number) acting as membership grade (MG), and the second part consists of a fuzzy number acting as non-membership grade (NMG). An mPFS assigns m number of MGs against each alternative in the universe of discourse. A CmPFS deals with single as well as multi-polar information in the cubic environment. In this article, we explore some new aspects and consequences of the CmPFS. We define score and accuracy functions to find the priorities of alternatives/objects in multi-criteria decision-making (MCDM). For this objective, some new operations, like addition, scalar/usual multiplication, and power, are defined under Dombi’s t-norm and t-conorm. We develop several new aggregation operators (AOs) using cubic m-polar fuzzy Dombi’s t-norm and t-conorm. We present certain properties of suggested operators like monotonicity, commutativity, idempotency, and boundedness. Additionally, to discuss the application of these AOs, we present an advanced superiority and inferiority ranking (SIR) technique to deal with the problem of conversion from a linear economy to a circular economy. Moreover, a comparison analysis of proposed methodology with some other existing methods is also given.