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

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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.

Keywords

Atanassov’s intuitionistic fuzzy sets
De Morgan triples
Automorphism
Atanassov’s operators

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