Ordinal Sums of De Morgan Triples - Mezzomo, Ivan; Bedregal, Benjamin (Trends in Computational and Applied Mathematics, 2018)
<!–StartFragment–>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)_iI ((S_i)_iI) are a family of t-(co)norms and (]a_i, b_i[)_iI 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)_iI are a family of fuzzy negations such that N_i≥ 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.<!–EndFragment–>