Canonical form of a transitive fuzzy matrix

Authors:
Hiroshi Hashimoto
Affiliations:
-
Venue:
Fuzzy Sets and Systems
Year:
1983

Citing 4
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Abstract

Some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive matrix is given using the properties. As a special case an open problem concerning idempotent matrices of Kim and Roush is solved. In our results a nilpotent matrix and a symmetric matrix play an important role. We decompose a transitive matrix into the sum of a nilpotent matrix and a symmetric matrix. Then we obtain a canonical form of the transitive matrix.