Traces of Fuzzy Relations Under Dual Operations

Hiroshi Hashimoto

doi:10.20965/jaciii.2005.p0563

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JACIII Vol.9 No.5 pp. 563-569

doi: 10.20965/jaciii.2005.p0563

(2005)

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Traces of Fuzzy Relations Under Dual Operations

Hiroshi Hashimoto

Faculty of Economics, Yamaguchi University, Yamaguchi 753-8514, Japan

Received:

February 14, 2003

Accepted:

April 11, 2005

Published:

September 20, 2005

Keywords:

fuzzy matrix, fuzzy matrix inequality, fuzzy relation, trace of a fuzzy relation

Abstract

We examined dual properties of traces of a fuzzy relation using fuzzy matrices. Traces of a fuzzy relation are reflexive and transitive fuzzy relations obtained from the given fuzzy relation. Under standard operations on fuzzy matrices, fuzzy matrix inequalities and equalities are deduced by applying the well-known equivalent transformation of a fuzzy matrix inequality. We present, in particular, propositions on the construction of transitive fuzzy relations.

Cite this article as:

H. Hashimoto, “Traces of Fuzzy Relations Under Dual Operations,” J. Adv. Comput. Intell. Intell. Inform., Vol.9 No.5, pp. 563-569, 2005.

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