Ovchinnikov's automorphisms revisited
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...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 1994 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2099/2437 |
| Acceso en línea: | https://hdl.handle.net/2099/2437 |
| Access Level: | acceso abierto |
| Palabra clave: | Automorphisms Ovchinnikov Fuzzy sets Sistemes difusos Automorfismes Reticles, Teoria de Classificació AMS::06 Order, lattices, ordered algebraic structures::06D Distributive lattices |
| Sumario: | 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. |
|---|