A new way to extend t-norms, t-conorms and negations

Authors:
Eduardo Palmeira;Benjamin Bedregal;Radko Mesiar;Javier Fernandez
Affiliations:
Department of Exact and Technological Sciences, State University of Santa Cruz, Ilhéus, Brazil;Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, Brazil;Slovak University of Technology, Bratislava, Slovakia and Centre of Excellence IT4Innovations, Division University of Ostrava - IRAFM, Czech Republic;Departamento de Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain
Venue:
Fuzzy Sets and Systems
Year:
2014

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Abstract

This work presents a method of extending t-norms, t-conorms and fuzzy negations to a lattice-valued setting by preserving the largest possible number of properties of these fuzzy connectives which are invariants under homomorphisms. Further, we also apply this method to extend De Morgan triples, automorphisms and n-dimensional t-norms.