Informatica

The purpose of this study is to develop a hesitant trapezoidal fuzzy TODIM (interactive and multi-criteria decision making) with a closeness index-based ranking method to handle hesitant qualitative group decision making problems. First, a novel closeness index-based ranking method is presented to compare the magnitude of hesitant trapezoidal fuzzy numbers (HTrFNs). Based on the developed ranking method, the dominance values of alternatives over others for each expert are calculated. Then, a nonlinear programming model is established to derive the dominance values of alternatives over others for the group and correspondingly the optimal ranking order of alternatives is obtained.

Interval-valued intuitionistic fuzzy numbers (IVIFNs) characterized by a membership function and a non-membership function with values that are intervals, have strong ability to handle imprecise and ambiguous information in real-world applications. This paper proposes an integrated maximizing consistency and multi-choice goal programming (MCGP) approach to handle hybrid multi-criteria group decision making problems based on IVIFNs. Firstly, the hybrid decision information (including crisp numbers, intervals, intuitionistic fuzzy numbers and linguistic variables) are normalized into the IVIFNs. Then, an ordinal consistency index and a cardinal consistency index are proposed to measure the consistency between the individual opinion and the group opinion, respectively. And an optimal model based on maximizing consistency is constructed to derive the weights of experts. Afterwards, the comprehensive ratings and the ranking values of alternatives are obtained by the hybrid weighted aggregation operator and the proposed ratio function of IVIFNs, respectively. Furthermore, a MCGP model based on the ranking values is constructed to identify the optimal alternatives and their optimum quantities. At length, an illustrative case is provided to verify the proposed approach.