Open AccessOrdinal Sums of De Morgan Triples
Author(s) -
Ivan Mezzomo,
Benjamín Bedregal
Publication year - 2018
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2018.019.02.181
Subject(s) - mathematics , negation , disjoint sets , combinatorics , function (biology) , pairwise comparison , fuzzy logic , discrete mathematics , statistics , computer science , artificial intelligence , evolutionary biology , biology , programming language
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.