Geodesic
COMMENT ON AND A CHARACTERIZATION OF THE CONCEPT OF COMPLETE RESIDUATED LATTICE
ZEYADA , FATHEI M. 1 ; ABD-ALLAH, M. A. 2
1 Center of Mathematics and Theoretical Computer Sciences Assiut, Egypt
2 Department of Mathematics, Faculty of Science, Al Azhar University, Assiut, Egypt
Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 4, p. 203-205.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We prove that some properties of the definition of complete residuated lattice [2,4] can be derived from the other properties. Furthermore we prove that the concept of strictly two-sided commutative quantale [1,3] and the concept of complete residuated lattice are equivalent notions.
DOI : 10.22436/jnsa.001.04.01
Classification : 42A20, 42A32
Keywords: Complete residuated lattice, Quantale, Complete MV-algebra.

ZEYADA , FATHEI M.  1 ; ABD-ALLAH, M. A.  2

1 Center of Mathematics and Theoretical Computer Sciences Assiut, Egypt
2 Department of Mathematics, Faculty of Science, Al Azhar University, Assiut, Egypt 
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ZEYADA , FATHEI M. ; ABD-ALLAH, M. A. . COMMENT ON AND A CHARACTERIZATION OF THE CONCEPT OF COMPLETE RESIDUATED LATTICE. Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 4, p. 203-205. doi : 10.22436/jnsa.001.04.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.04.01/

[1] U. Höhle Characterization of L-topologies by L-valued neighborhoods, in: U. Höhle, S.E.Rodabaugh (Eds.), The Handbooks of Fuzzy Sets Series, Kluwer ACademic Publishers, Dordrecht, Volume 3 (1999), pp. 389-432 | DOI | Zbl

[2] Pavelka, J. On fuzzy logic II, Z. Math. Logic Gvundlagen Math., Volume 25 (1979), pp. 119-134 | Zbl | DOI

[3] Rosenthal, K. I. Quantales and their applications, Pitman Research Notes in Mathematics 234(Longman, Burnt Mill, Harlow )., , 1990

[4] Ying, M. S. Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets and Systems , Volume 56 (1993), pp. 337-373 | DOI | Zbl

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