Ordinal Sums of De Morgan Triples

Authors

  • Ivan Mezzomo Centro de Ciência Exatas e Naturais Universidade Federal Rural do Semiarido
  • Benjamin Bedregal Departamento de Informática Matemática Aplicada Universidade Federal do Rio Grande do Norte

DOI:

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

Keywords:

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

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.

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Published

2018-09-12

How to Cite

Mezzomo, I., & Bedregal, B. (2018). Ordinal Sums of De Morgan Triples. Trends in Computational and Applied Mathematics, 19(2), 181. https://doi.org/10.5540/tema.2018.019.02.181

Issue

Vol. 19 No. 2 (2018)

Section

Original Article

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