Elicitation of the Groups and Group Cognitive Structures: An Application of Ternary Fuzzy Relational Products

The aim of this thesis is to extend the fuzzy relational product calculations from binary to ternary relations, and apply the ternary fuzzy relational product calculations to processing of the URBS data. It is demonstrated that, by ternary fuzzy relational product calculations, the respondents with the similar cognitive structures can be clustered into groups and cognitive structures of those groups can be elicited by this approach. First, the concepts and formulas for ternary fuzzy relational products calculations were de ned and derived in this thesis. Second, in order to verify he applicability of those formulas empirically, new URBS data were collected. Third, the formulas were applied to both the new and the old data, forming cognitive structures of groups. Fourth, by analyzing the results, strong evidence was found that ternary fuzzy relational theory may have substantial potential practical applications but also demands further intensive theoretical studies. The main novel contribution of this thesis is its exploration of ternary fuzzy relational theory and the application. This thesis has paved the road to further studies. It raised a number of new practical and theoretical questions, which have to be examed by future studies. The author hopes that this work could stimulate the new developments in cognitive science and theory of fuzzy relations. 9 Chapter