Comparison of two fuzzy set-based logics: similarity logic and possibilistic logic

Fuzzy sets can be viewed as a convenient way for expressing a rank-ordering over a set of possible worlds, or equivalently, of possible interpretations. This use can be encountered in two fuzzy set-based logics, with different semantics, developed in the last past years; namely a logic of similarity or closeness introduced by Ruspini (1991), and a logic of preference, called possibilistic logic, previously proposed by the authors. The former accounts for some metrics on possible worlds while the latter distinguishes between more or less plausible interpretations. The basic principles underlying the two logics are restated and a comparative study of their semantics is provided. Links between Ruspini´s proposal and the idea of a fuzzy rough set (a rough set based on a fuzzy similarity relation rather than on a crisp equivalence relation) are also emphasized