New results on ordinal sum implications based on ordinal sum of overlap functions

Abstract

Recently, Baczyński et al. have introduced two new methods of constructing ordinal sums of fuzzy implications. These methods are based on a construction of ordinal sum of overlap functions and extend some type of algebraic structures. In this paper, we explore the family of ordinal sum implications constructed by one of the method presented in (M. Baczyński, P. Drygaś, A. Król, R. Mesiar (2017), [7]) and examine intersections of this new family of fuzzy implications with (S, N)-, (T, N)-, QL-, D-, R-, Yager's f- and g-implications, respectively. Concretely, this new family of fuzzy implications is shown to be different from the above mentioned implications. Moreover, the necessary and sufficient conditions under which these new ordinal sum implications are distributive over t-norms and t-conorms are given.