Lattice type fuzzy order and closure operators in fuzzy ordered sets

Author

Belohlavek, Radim

Author_Institution

Dept. of Comput. Sci., Palacky Univ., Olomouc

Volume

4

fYear

2001

fDate

25-28 July 2001

Firstpage

2281

Abstract

Complete lattices and closure operators in ordered sets are considered from the point of view of fuzzy logic. A typical example of a fuzzy order is the graded subsethood of fuzzy sets. Graded subsethood makes the set of all fuzzy sets in a given universe into a completely lattice fuzzy ordered set (i.e. a complete lattice in fuzzy setting). Another example of a completely lattice fuzzy ordered set is the set of all so-called fuzzy concepts in a given fuzzy context; the respective fuzzy order is the graded subconcept/superconcept relation. Conversely, each completely lattice fuzzy ordered set is isomorphic to some fuzzy ordered set of fuzzy concepts of a given fuzzy context. These natural examples motivate us to investigate some general properties of complete lattice-type fuzzy order. Particularly, the article focuses mainly on closure operators in fuzzy ordered sets

Keywords

equivalence classes; fuzzy logic; fuzzy set theory; closure operators; complete lattices; completely lattice fuzzy ordered set; fuzzy concepts; fuzzy context; fuzzy logic; fuzzy order; fuzzy sets; graded subconcept/superconcept relation; graded subsethood; lattice type fuzzy order operators; Boolean algebra; Computer science; Filters; Fuzzy logic; Fuzzy sets; Lattices; Mathematics;

fLanguage

English

Publisher

ieee

Conference_Titel

IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th

Conference_Location

Vancouver, BC

Print_ISBN

0-7803-7078-3

Type

conf

DOI

10.1109/NAFIPS.2001.944427

Filename

944427