Multiple criteria decision making for linguistic judgments with importance quantifier guided ordered weighted averaging operator

In this paper, an importance quantifier-guided Ordered Weighted Averaging (OWA) Operator for linguistic decision judgments is developed. To create a 'softer' decision aggregation task, the decision criteria are associated with the degree of importance in aggregation. The importance quantifier-guided OWA operator is extended from Yager's OWA using linguistic quantifiers. These interval type 2 fuzzy sets are used to map the linguistic quantifiers. The first stage of applying the importance quantifier-guided OWA operator is to rank a set of interval type 2 fuzzy sets. A new interval type 2 fuzzy set ranking methodology is proposed. Such ranking methodology is concerned with two newly defined type 2 fuzzy set characteristics, the extended level set (alpha-cut) and the parametric generalized graded mean integration representation. The partial ordering set properties of the ranking methodology are rigorously discussed. The framework of multiple criteria decision making with linguistic judgments is constructed using the importance quantifier-guided OWA operator. The optimal importance quantifier-guided OWA type 2 fuzzy weights for decision criteria, and the overall decision fuzzy rates for alternatives are obtained. The mixed integer linear programming models are created specifically for solving the optimal importance quantifier-guided type 2 fuzzy weights. The piecewise linear and the general non-linear quantifier models are developed. The overall procedure for interval type 2 fuzzy sets multiple criteria decision making with the optimal importance quantifier-guided OWA weights is formulated. A multiple criteria decision making problem, New Product Development Project Screening, is used to demonstrate the proposed methodology.