Ordinal Sums of De Morgan Triples

Ivan Mezzomo, Benjamin Bedregal

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.

Keywords


t-norm; t-conorm; fuzzy negation; De Morgan triples; ordinal sum

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DOI: https://doi.org/10.5540/tema.2018.019.02.181

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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