Categorizing Group Opinions Through Fuzzy Similarity Relation

This paper proposes a procedure for categorizing human’s opinions in circumstances of group decision-making. Fuzzy similarity relation is utilized for categorizing opinion matrix whose each element is derived from the difference between two evaluation vectors. Those vectors are obtained from various opinions of decision-makers and the difference of the two is well expressed by the sigmoid function. Then, similar opinions in the group are clustered according to the nature of the fuzzy similarity relation. Especially, the transitive law plays an important role in the clustering. When the similarity relation is not existed in the opinion matrix and any negotiation is required among decision-makers, the final value of nth power of the opinion matrix is proposed as the consensus value. Furthermore, it is shown that the orthogonal condition of the opinion matrix is useful to derive order relations of opinions. Fuzzy opinion matrix enables one to investigate similarity of opinions of group members at a time and to make categories of similar opinions effectively. The proposed procedure gives decision-makers lead a reasonable group decision-making in the context of logical treatment for various opinions due to diversified views or ideas.