Abstract
There is always vagueness experienced by experts in practical decision making processes. Fuzzy sets are introduced for their ability to model objects and phenomena with a flexible degree. Then, it is more advisable to utilize fuzzy numbers to express the opinions of decision makers (DMs) for the purpose of reflecting the flexibility of DMs in a decision making process. Of much importance is how to quantify the flexibility degree of fuzzy numbers. In this article, a novel method for computing the flexibility degree of fuzzy numbers is generally presented by using the concept of \alpha-cut sets. In particular, some novel formulas are proposed to quantify the flexibility degrees of triangular and trapezoidal fuzzy numbers by equipping a bounded universe, respectively. The flexibility degree of a preference relation with triangular fuzzy numbers is computed by considering the effects of the applied scale and the reciprocal property. Furthermore, a new group decision making (GDM) model is formed when triangular fuzzy additive reciprocal preference relations (TFARPRs) are used to evaluate the judgments of DMs. A flexibility degree induced ordered weighted averaging operator is constructed to aggregate individual TFARPRs by offering more importance to that with less flexibility. Finally, some numerical results are reported to illustrate the new definitions and the proposed model. The sensitivity of confidence levels to the final decision reached by a group of experts is analyzed. The observations reveal that the flexibility degrees of DMs under various confidence levels are worth to be considered in the GDM problem with a dominant position, and the existing shortcomings are overcome.