Relating De Morgan triples with Atanassov's intuitionistic De Morgan triples via automorphisms

Authors:
Claudilene Gomes da Costa;Benjamín Callejas Bedregal;Adrião Duarte Dória Neto
Affiliations:
Department of Exact Science -- DCE, Federal University of Paraíba -- UFPB, Rua da Mangueira s/n, Rio Tinto-PB 58297-000, Brazil;Group of Logic, Language, Information, Theory and Applications -- LoLITA, Department of Informatics and Applied Mathematics -- DIMAp, Federal University of Rio Grande do Norte -- UFRN, Campus Univ ...;Department of Computing Engineering and Automation -- DCA, Federal University of Rio Grande do Norte -- UFRN, Campus Universitário s/n, Lagoa Nova, Natal-RN 59090-530, Brazil
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

In this paper the relation between De Morgan triples on the unit interval and Atanassov's intuitionistic De Morgan triples is presented, showing how to obtain, in a canonical way, Atanassov's intuitionistic De Morgan triples from De Morgan triples. Moreover, we also show that the automorphisms on the unit interval and on L* (the intuitionistic value lattice) are in one-to-one correspondence and how automorphisms on L* act on Atanassov's intuitionistic De Morgan triples. It is also proved that the action of automorphisms and the canonical construction of De Morgan triples on L* commutes.