| In this paper, we deal with theσ-decomposition of fuzzy relationsand the strongly transitive fuzzy matrices. We first investigate several propertiesof the binary operatorσand use them to characterize the fuzzy matrices, suchas re?exivity, anti-re?exivity and so on. Then we discuss theσ-decompositionof fuzzy relations, obtain its some properties. In the end, we consider the∧-∨multiplication of strongly transitive fuzzy matrices, show their some propertiesand prove that a strongly transitive fuzzy matrix oscillates with period 2.
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