Quotients with respect to similarity relations
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part 1
Similarity relations, fuzzy partitions, and fuzzy orderings
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
On an application of fuzzy relations in biogeography
Information Sciences: an International Journal
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Completion of ordered structures by cuts of fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Representing ordered structures by fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Representations and constructions of similarity-based fuzzy orderings
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
A compendium of fuzzy weak orders: Representations and constructions
Fuzzy Sets and Systems
The number of rectangular islands by means of distributive lattices
European Journal of Combinatorics
The minimum cardinality of maximal systems of rectangular islands
European Journal of Combinatorics
Elementary proof techniques for the maximum number of islands
European Journal of Combinatorics
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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.