Modeling Fuzzy Modifiers by Means of a Proximity Relation

Fuzzy modifiers are mappings that transform a fuzzy set into a modified fuzzy set without redefining the membership functions. In this paper, we propose an alternative approach for modeling fuzzy modifiers. The approach relies on a parameterized proximity relation. Given a fuzzy set F, we present two transformations that allow associating the set F with a nested pair of fuzzy sets. A new class of fuzzy modifiers can then be generated by such transformations. Due to the fuzzy set-based semantics underlying the proximity relation of interest, the new modifiers are not simply operators acting on the membership degrees but are endowed with a clear semantics. Last, we illustrate the practical interest of such modifiers in the context of flexible database querying