An Approach to Determine Best Cutting-points in Group Decision Making Problems with Information Granules

In this paper, we propose a new approach to solve linguistic group decision making (GDM) problems through defining different linguistic terms for each expert and optimizing those terms. Information granules are often designed as the framework of linguistic terms and to vividly describe the approach, intervals are selected to express linguistic terms as large, medium, and small in the paper. Analytic Hierarchy Process (AHP) is set as the basic model and abstracted as linguistic reciprocal matrices. The abstraction process is carefully designed considering two strategies: each expert owns same linguistic terms (same distribution of cutting-points in an interval) and each expert owns different linguistic terms. As comparison, three methods of cutting-points allocation for the two strategies are realized with a synthetic example: optimizing allocation, uniform allocation and random allocation. The results coincide with theoretical analysis: each expert owns different linguistic terms reach the highest consensus.