Ordinal Sums of De Morgan Triples

Abstract

In this paper we consider the ordinal sum of the summands (a_i, b_i, T_i) ((a_i, b_i, S_i)), where (T_i)_{i\in I}$ $((S_i)_{i\in I}) are a family of t-(co)norms and $(]a_i, b_i[)_{i\in I}$ a family of nonempty, pairwise disjoint open subintervals of [0,1], and we characterize the ordinal sum of the summands (a_i, b_i, N_i) where (N_i)_{i\in I} are a family of fuzzy negations such that N_i\geq N_S and prove that the function N is a fuzzy negation. In addition, we prove if (T_i, S_i, N_i) is a De Morgan triple satisfy some specific conditions, then (T, S, N) is a semi De Morgan triple.