Interval-valued intuitionistic fuzzy aggregation methodology for decision making with a prioritization of criteria

Abstract

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.<br />The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.<br />Based on the ${L}$ukasiewicz triangular norm, we first propose a prioritized arithmetic mean to IVIF multi-criteria decision making (MCDM) problem where there is a linear ordering among the criteria.<br />The proposed aggregation operator overcomes the existing prioritized aggregation operator's shortcomings that it is not monotone with respect to the total order on interval-valued intuitionistic fuzzy values (IVIFVs).<br />We also prove that it is bounded and monotone with respect to the total order on IVIFVs, and therefore is a true generalization of such operations.<br />We finally propose an aggregation operators-based two-step procedure to IVIF MCDM in the situation that more than one criteria exist at some priority level.