Paper Info
Title
Cut approach to islands in rectangular fuzzy relations
Abstract
The paper investigates fuzzy relations on a finite domain in the cutworthy framework, dealing with a new property coming from the information theory. If the domain of a relation is considered to be a table, then a rectangular subset of the domain whose values under this relation are greater than the values of all neighboring fields is called an island. Consequently, the so called rectangular fuzzy relations are introduced; their cuts consist of rectangles as sub-relations of the corresponding characteristic functions. A characterization theorem for rectangular fuzzy relations is proved. We also prove that for every fuzzy relation on a finite domain, there is a rectangular fuzzy relation with the same islands, and an algorithm for a construction of such fuzzy relations is presented. In addition, using methods developed for fuzzy structures and their cuts, we prove that for every fuzzy relation there is a lattice and a lattice valued relation whose cuts are precisely the islands of this relation. A connection of the notion of an island with formal concept analysis is presented.
Year
DOI
Venue
2010
10.1016/j.fss.2010.04.019
Fuzzy Sets and Systems
Keywords
Field
DocType
cutworthy framework,. islands,rectangular subset,characterization theorem,information theory,rectangular fuzzy relation,finite domain,cut approach,fuzzy structure,islands,corresponding characteristic function,formal concept analysis,fuzzy relations.,fuzzy relations,fuzzy relation,characteristic function
Discrete mathematics,Defuzzification,Fuzzy classification,Fuzzy set operations,Fuzzy measure theory,Fuzzy mathematics,Fuzzy set,Fuzzy subalgebra,Fuzzy number,Mathematics
Journal
Volume
Issue
ISSN
161
24
Fuzzy Sets and Systems
Citations 
PageRank 
References 
2
0.39
9
Authors
3
Name
Order
Citations
PageRank
Eszter K. Horváth172.06
Branimir Šešelja217023.33
Andreja Tepavčević3847.83