In　this　paper,　generalized　fuzzy　matrices　are　considered　as　matrices　over　a　special　type　of　semiring　which　is　called　path　algebra.　Some　elementary　properties　and　characterizations　for　transitive　generalized　fuzzy　matrices　are　established　and　transitivity　of　powers　of　a　generalized　fuzzy　matrix　is　discussed.　Also,　the　transitive　closure　of　a　generalized　fuzzy　matrix　is　considered　and　some　properties　of　the　transitive　closures　are　obtained.　Partial　results　obtained　in　this　paper　generalize　the　corresponding　ones　on　nilpotent　matrices　and　on　matrices　with　periods.　©　2012　Elsevier　B.V.　All　rights　reserved.