Lattice-type fuzzy order is uniquely given by its 1-cut: Proof and consequences

Fuzzy Sets and Systems

Volumn 143, Issue 3, 2004, Pages 447-458

  Bělohlávek, Radim ^a,b  

^a PALACKÝ UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

Alpha cut; Fuzzy concept lattice; Fuzzy order; Lattice

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; THEOREM PROVING;

ALPHA CUT; FUZZY CONCEPT LATTICE; FUZZY ORDER; LATTICE;

FUZZY SETS;

EID: 19244375332     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(03)00239-2     Document Type: Article

References (15)

1. A. Arnauld, P. Nicole, La logique ou l'art de penser, 1662.
2. Bělohlávek R. Similarity relations in concept lattices. J. Logic Comput. 10(6):2000;823-845.
3. Bělohlávek R. Fuzzy closure operators. J. Math. Anal. Appl. 262:2001;473-489.
4. Bělohlávek R. Fuzzy Relational Systems, Foundations and Principles. 2002;Kluwer Academic/Plenum Press, New York.
5. R. Bělohlávek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic, to appear.
6. U. Bodenhofer, A similarity-based generalization of fuzzy orderings, Ph.D. Thesis, Vol. 26 of Schriftenreihe der Johannes-Kepler-Universität, Linz, Universitätsverlag Rudolf Trauner, 1999.
7. Goguen J.A. L-fuzzy sets. J. Math. Anal. Appl. 18:1967;145-174.
8. Goguen J.A. The logic of inexact concepts. Synthese. 18:1968-9;325-373.
9. Gottwald S. A Treatise on Many-Valued Logics. 2001;Research Studies Press, Baldock, Hertfordshire, England.
10. Hájek P. Metamathematics of Fuzzy Logic. 1998;Kluwer Academic Publishers, Dordrecht.
11. Höhle U. On the fundamentals of fuzzy set theory. J. Math. Anal. Appl. 201:1996;786-826.
12. Höhle U., Blanchard N. Partial ordering in L-underdeterminate sets. Inform. Sci. 35:1985;133-144.
13. Novák V., Perfilieva I., Močkoř J. Mathematical Principles of Fuzzy Logic. 1999;Kluwer, Boston.
14. Pavelka J. On fuzzy logic I, II, III. Z. Math. Logic Grundl. Math. 25:1979;45-52, 119-134, 447-464.
15. Zadeh L.A. Similarity relations and fuzzy orderings. Inform. Sci. 3:1971;159-176.