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

• Published in: International journal of approximate reasoning Vol. 52; no. 4; pp. 473 - 487
• Main Authors: da Costa, Claudilene Gomes, Bedregal, Benjamín Callejas, Dória Neto, Adrião Duarte
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-06-2011; Elsevier
• Subjects: Applied sciences; Approximation; Atanassov’s intuitionistic fuzzy sets; Atanassov’s operators; Automorphism; Automorphisms; Computer science; control theory; systems; Construction; De Morgan triples; Exact sciences and technology; Intervals; Lattices; Logical, boolean and switching functions; Reasoning; Theoretical computing; Automorphism; Atanassov’s intuitionistic fuzzy sets; Atanassov’s operators; De Morgan triples; Commutativity; Fuzzy logic; Atanassov's operators; t Norm; Intuitionistic logic; Atanassov's intuitionistic fuzzy sets; Fuzzy set; Lattice
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2010.11.004

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.