Monotonicity in the construction of ordinal sums of fuzzy implications

Abstract

In this contribution we discus the problem of monotonicity of intervals in the ordinal sums of fuzzy implication constructions. As a result, new ways of constructing of ordinal sums of fuzzy implications are obtained. These methods allow to adapt the value of fuzzy implication to specific requirements. For our new methods of construction, several sufficient properties for obtaining a fuzzy implication as a result are presented. Moreover, preservation of some properties of the ordinal sums are examined. Among others neutrality property, identity property, and ordering property are considered.