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

Document Type : Research Paper


1 School of Economics and Management, Guangxi Normal University, Guilin 541004, China

2 Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564, USA


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.
The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.
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.
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).
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.
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.


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