Modifiers based on some t-norms in fuzzy logic

Abstract

Modifiers generated by n-placed functions are considered. The subject matter of modifiers are fuzzy sets, i.e. membership functions defined on the unit interval I = [0, 1]. Two sets of modifiers are considered as example cases. One of them is a set of modifiers generated by t-norms and t-conorms. Here different dual pairs of norms create modifiers of different grade of strength. These norms are examples of two-placed functions. Another case is to generate a series of modifiers using only one DeMorgan class of norms. Norms are generalized to be n-placed functions. The place number n takes effect to the strength of a modifier. Two different DeMorgan classes are taken into the consideration. The first steps to the direction of many-valued modifier logics are taken.