Qualitative fuzzy sets: a comparison of three approaches
Tzu-Yu Lin · 2002
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).