1996 Volume 8 Issue 4 Pages 629-638
A transitive coupling problem discussed by Wakabayashi and Ouchi that arises in the embedding process of their method for fuzzy structural modeling. They also have considered the particular max and min solutions for the problem. The present paper aims at disclosing algebraic structure of the solution set for the problem based on a study of a generalized transitive coupling problem by the authors, whereby the followings are shown : ・the solution set is closed under scalar product, ・the solution set is closed under ∧-, ∨-operations, but not necessarily under ∨-, ∨-operations, ・if the solution set includes a solution which is different from the self-evident solution, the solution set has the carbinal number of continuum.Moreover, considering the relationship between the particular and the general solutions, the authors show that ・the min solutions decide whether the third inequality with α-product plays the role of a substaintial constrain or not, ・the min solutions are extremal in the solution set.
