Distributivity of a class of ordinal sum implications over t-norms and t-conorms

摘要

Recently, Baczynski, Drygas, Krol and Mesiar have proposed two constructions of ordinal sums of fuzzy implications-based on the construction of ordinal sum of overlap functions. In this paper, we study the class of ordinal sum implications constructed using the first method, and show that this new class of fuzzy implications is different from the known (S, N)-, R-, QL-, f- and g-implications. Furthermore, we explore this new class of ordinal sum implications with respect to distributivity. (C) 2019 Elsevier B.V. All rights reserved.