Transitivity of generalized fuzzy matrices

Authors:
Hiroshi Hashimoto
Affiliations:
Faculty of Economics, Yamaguchi University, Yamaguchi City 753, Japan
Venue:
Fuzzy Sets and Systems
Year:
1985

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Abstract

Generalized fuzzy matrices are considered as matrices over a special type of semiring which is called a path algebra. Transitivity of generalized fuzzy matrices is defined and some properties of transitivity are shown. Especially properties of the composition of transitive fuzzy matrices representing transitive fuzzy relations are examined by introducing a third operation on the semiring with two operations. The transitivity is closely related to metrics, distances, ultrametrics, and so on.