Multi-criteria constrained interval type-2 fuzzy decision-making: A space analysis perspective

Abstract

Practical decision-making problems invariably involve inherent uncertainty in information, making it challenging to obtain precise evaluations. In this research, the utilization of constrained interval type-2 fuzzy sets (CIT2 FSs) enables the representation of complex uncertainty in decision information, and a space analysis approach, called CIT2 fuzzy multi-criteria acceptability analysis (CIT2FMAA), is proposed for conducting reliable decision-making. The CIT2FMAA introduces a novel paradigm for type-2 fuzzy decision-making, wherein CIT2 fuzzy evaluations are acknowledged as spaces of type-1 fuzzy evaluations and processed using type-1 fuzzy operations and methodologies. First, from a space analysis perspective, the type-2 fuzzy measures of logical rank expressions are formalized as CIT2 fuzzy rank acceptability indexes, and the CIT2 fuzzy rank acceptability analysis is developed to rank CIT2 fuzzy numbers. Second, the weighted average of the CIT2 fuzzy numbers is defined, and the CIT2FMAA is proposed to support uncertain multi-criteria decision-making. Subsequently, a sampling algorithm is designed for implementing CIT2 fuzzy rank acceptability analysis and CIT2FMAA. Finally, a linguistic disease diagnosis is performed to demonstrate the efficiency of CIT2FMAA. Compared to traditional type-2 fuzzy decision-making methods, CIT2FMAA is more efficient because it not only derives ranks of alternatives but also provides confidence degrees for those ranks.