Extension of fuzzy logic operators defined on bounded lattices via retractions

Authors:
E. S. Palmeira;B. C. Bedregal
Affiliations:
Department of Exact and Technological Sciences, State University of Santa Cruz, Campus Soane Nazaré de Andrade, Km 16 Rodovia Ilhéus-Itabuna, 45662-900 Ilhéus, Brazil;Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, CP 1524, 59072-970 Natal, Brazil
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

The primary goal of this paper is to present a method of extending t-norms, t-conorms and fuzzy negations from a sublattice M to the bounded lattice L by considering a more general version of the idea of the sublattice. In general terms, we consider M as a sublattice of the bounded lattice L, if M has the same lattice structure of the L equipped with the restriction of operations of L and is a subset of L. However, this latter condition may be relaxed without losing the essence of the usual definition of the sublattice. This is done through the use of retractions. Furthermore, the same idea is employed to extend t-subnorms and present some results related to extension and automorphism. Additionally, a formalization of a relaxed notion of De Morgan triple and its extension is provided.