Preference Order of Categorized Group Opinions Considering Grade of Decision Makers

Abstract

This paper proposes procedures for categorizing group opinions and making preference order of them, in circumstances of group decision-making. First, a fuzzy opinion matrix is constructed, in which each element is derived from the difference between two evaluation vectors. The difference of the two is well expressed by the symmetric evaluation method based on sigmoid function and tangent function. In fact, the conventional cosine method is not well balanced in expressing fuzzy similarity and dissimilarity simultaneously. To categorize opinions, the idea of fuzzy similarity relation is utilized. Then nature of the transitivity of opinion matrix plays an important role. Next, participants to the decision-making group are graded so that the total sum of each subgroup's dissatisfaction to the result is minimized. In this paper, using both the categorized group opinions and each grade of subgroups, final preference order is calculated. The significant feature of the proposed method appears in the combination of symmetric evaluation method, fuzzy similarity relation and optimized preference orders. By these techniques, the proposed method gives a reasonable decision-making in the context of logical treatment for various opinions due to diversified views or ideas.