Transitivity of generalized fuzzy matrices. (English) Zbl 0579.94033
Summary: 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.
MSC:
| 94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
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