Characterizations on migrativity of continuous triangular conorms with respect to N-ordinal sum implications

Abstract

The migrative functional equations provide a very powerful tool for constructing and characterizing new fuzzy logic connectives by convex combination, and have particularly important applications in image processing. So far, the migrativity between conjunctive logic connectives has been extensively studied, the obtained results do not, however, work well for triangular conorms. This paper is devoted to an in-depth investigation on three types of migrativity for continuous triangular conorms S with respect to N-ordinal sum implications I, which have distinctive features from ordinary ordinal sum implications. We will provide first detailed characterizations on the (α,I)-migrativity of S for each case according to the position relation of α in the range of N, by giving the corresponding ordinal sum decompositions of the t-conorm and implication solutions. Then the (α,I)-migrativity is extended to internal and global cases, and their characterizations are given under some additional constraints.