Qualitative fuzzy sets: a comparison of three approaches

A real world fuzzy set should be able to tolerate "small amounts" of perturbations. There are three approaches. Thiele\´s (1999; 2000) approach, observing some weak points of Lin\´s earlier versions, proposed a refined approach based on Kripke style semantics; his results, but independently, are essentially applying Lin\´s (1996) view using Lin\´s (1998) new notion of neighborhood systems. A type II fuzzy set realizes the idea by representing each grade by a fuzzy number. Lin\´s approach represents a fuzzy set by a "fuzzy set" of membership functions. Lin did this in two ways; one by granulation and another by "physical" perturbation. In summary, Thiele\´s approach has a good Kripke style semantics. Type II fuzzifies the grade; its advantage is simplicity. Lin\´s approach fuzzifies the membership function; its advantage is to formalize the intuitive "physical" perturbation. The three approaches are not equivalent, but do have common intersection. Three results are discussed in different universes (categories)