On the extension of lattice-valued implications via retractions

Authors:
Eduardo S. Palmeira;Benjamin R. C. Bedregal;Javier Fernandez;Aranzazu Jurio
Affiliations:
Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual de Santa Cruz, Ilhéus, Brazil;Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal, Brazil;Departamento de Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain;Departamento de Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain
Venue:
Fuzzy Sets and Systems
Year:
2014

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Abstract

The main goal of this paper is to apply the method of extension of fuzzy connectives proposed in our previous work for fuzzy implications valued on a bounded lattice. Also we discuss about which properties of implications are preserved by this method and we prove some results involving extension and automorphisms. Finally, we investigate the behavior of the extensions of two special classes of fuzzy implications, namely (S,N)-implications and R-implications.