The major contributions of this paper is the extention of the fuzzy relational product calculations from binary to ternary relations, and the application of the ternary fuzzy relational product calculations to processing of the URBS(Unbiased Research of Beings in Society) data in order to elicit the groups and group cognitive structures. First, the formulas for ternary fuzzy relational products calculations were defined and derived. Second, in order to verify the validity of those formulas, new URBS data were collected. Third, the formulas were applied to both the new and the old data by the computer program to elicit cognitive structures of groups. Fourth, by analyzing the results, strong evidences were found that ternary fuzzy relational products are valid tool in eliciting group cognitive structures.