Abstract
This paper deals with the structural modelling of a set whose elements have no transitivity of order relationship in their binary paired-comparison. When we connot give a linear order structure to the given set, i. e., when the set has a cycle, we need some new concepts to analyze and understand the structure of the set. Such concepts as the extended fundamental pattern, the pseudo-interval order and so forth have been proposed by the authors to represent the cycle systematically. The classification of the set can now be discussed by them.
This paper defines the generalized pseudo-interval order and states that the classification algorithm derived from it gives a finer classification of the set than that derived from the pseudo-interval order. The paper also states that we can obtain the two modelling methods: one is to obtain a transitive structural model derived from the pseudo-interval order and the other is to obtain a hierarchical structural model derived from the generalized pseudo-interval order.
