Fuzzy Ordering Relation and Fuzzy Poset
Connections between (weakly) reflexive, antisymmetric and transitive lattice-valued fuzzy relations on a nonempty set X (fuzzy ordering relations on X) and fuzzy subsets of a crisp poset on X (fuzzy posets) are established and various properties of cuts of such structures are proved.
A representation of fuzzy sets by cuts corresponding to atoms in atomically generated lattices has also been given.
AMS Mathematics Subject Classification (1991): 04A72.
Keywords and PhrasesLattice valued fuzzy ordering relation fuzzy weak ordering relation fuzzy poset cutworthy approach
- 1.Bělohlávek, R.: Fuzzy Relational Systems. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
- 6.Davey, B.A., Pristley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1992)Google Scholar
- 13.Šeselja, B.: Fuzzy Covering Relation and Ordering: An Abstract Approach, Computational Intelligence. In: Reusch, B. (ed.) Theory and Applications, pp. 295–300. Springer, Heidelberg (2006)Google Scholar