The reduction of binary fuzzy relations and its applications

Authors:
Teimuraz Tsabadze
Affiliations:
Department of Applied Mathematics and Computer Science, The Tbilisi State University, 2 University Street, Tbilisi 0177, Georgia
Venue:
Information Sciences: an International Journal
Year:
2008

Citing 9
Cited 0

Special properties, closures and interiors of crisp and fuzzy relations

Fuzzy Sets and Systems
The cutting of compositions

Fuzzy Sets and Systems
On the existence and construction of T-transitive closures

Information Sciences: an International Journal
Toward a generalized theory of uncertainty (GTU): an outline

Information Sciences—Informatics and Computer Science: An International Journal
Additive decomposition of fuzzy pre-orders

Fuzzy Sets and Systems
Similarity relations and fuzzy orderings

Information Sciences: an International Journal
Fuzzy relational neural network

International Journal of Approximate Reasoning
General IF-sets with triangular norms and their applications to group decision making

Information Sciences: an International Journal
Fast solving method of fuzzy relational equation and its application to lossy image compression/reconstruction

IEEE Transactions on Fuzzy Systems

Quantified Score

Hi-index	0.07

Visualization

Abstract

This paper introduces the concept of T-reduction of binary fuzzy relations and establishes its properties. It presents an approach to providing the one-valued restoration of any boundary transitive and T-asymmetric binary fuzzy relation by its T-reduction. A theoretical basis for this approach is established, showing that T-reduction is the smallest fuzzy relation whose T-transitive closure coincides with the given binary fuzzy relation and where an (nxn) fuzzy relation on a finite universe with cardinality n can be represented by n-1 values. This approach opens up an original way for constructing the membership functions of certain binary fuzzy relations. Important examples for the application of this concept are given.