Filters in fuzzy class theory

摘要

A concept of filter is introduced in fuzzy class theory. Graded properties of filters, prime filters, and related constructions are investigated. In particular, the properties of filters relativized with respect to the three basic t-norms (Goedel, product, and Lukasiewicz) are studied. A naturally arising example of a graded filter is constructed and it is shown that the models of filters include well-known families of set functions.