Connections between generalized fuzzy constraint interval representation and interactive fuzzy intervals

This article investigates the relationship between two representations of fuzzy intervals: interactive fuzzy intervals and generalized constraint fuzzy intervals. To this end, we construct a joint possibility distribution from generalized constraint representations of two or more fuzzy intervals. Using this joint distribution, we prove that, under certain weak conditions, the arithmetic of generalized constraint fuzzy intervals coincides with the sup- J extension principle of the corresponding arithmetic operation. Consequently, the two representation frameworks are shown to be closely related, allowing analytical results developed in one framework to be transferred to the other.