Ovchinnikov's automorphisms revisited

Abstract

In [6] an approach to the representation of synonyms and antonyms via the automorphisms of the De Morgan Algebra [0,1] x was suggested. In [3], Ovchinnikov established a representation theorem for automorphisms of the function’s complete and completely distributive lattice [0,1] x with the pointwise extension of Min and max operations on [0,1]. Ovchinnikov’s results are now immediately generalized by using a positive t-norm T and its η-dual t-conorm T*. These results are applied to study the automorphism of [0,1] with different t-norms. Finally, the transformation by means of automorphisms of a given fuzzy on another given fuzzy set is studied.