ORDERING, DISTANCE AND CLOSENESS OF FUZZY-SETS

In dense rule bases where the observation usually overlaps with severa l antecedents in the rule base, various algorithms are used for approx imate reasoning and control. If the antecedents are located sparsely, and the observation does not overlap as a rule with any of the anteced ents, function approximation techniques combined with the Resolution P rinciple lead to applicable conclusions. This kind of approximation is possible only if a new concept of ordering and distance, i.e. a metri c in the state space, and a partial ordering among convex and normal f uzzy sets (CNF sets) is introduced. So, the fuzzy distance of two CNF sets can be defined, and by this distance, closeness and similarity of CNF sets, as well.