Qualitative fuzzy sets: Context based reasoning system in GrC

The category theory based model (8th GrC Model) has been proposed as the ldquofinalrdquo GrC Model. This paper is to discuss its specialization into the category of qualitative fuzzy sets. Here are the main points: 1) Let Col be the collection of real world fuzzy sets on U, where U is a crisp set. 2) Let V be the type I fuzzy sets of col. Namely, V, denoted by MF(U), is the set of all membership functions on U. 3) The map: Q; Col rarr 2^V defines a binary neighborhood system on V. Each Q(p), p rarr Col is a qualitative fuzzy set/ It is the mathematical model of the so-called elastic membership function. 4) The collection Q = {Q(p) | p ? Col}, by abuse of notation, is the universe of qualitative fuzzy sets. 5) The ldquounionrdquo and ldquointersectionrdquo of qualitative fuzzy sets are provided by the Boolean algebraic structure of Q. 6) Each membership function in Q(p) represents a state/context of p.