Abstract
We establish concepts of weak commutativity of two types of fuzzy finite state machines, and investigate properties of weak commutativity of products of two types of fuzzy finite state machines. Firstly, we present the concept of weak commutativity of a fuzzy finite state machine, and study characterizations of weak commutativity of fuzzy finite state machines by utilizing semigroup and matrix. We then discuss properties of weak commutativity of products of fuzzy finite state machines. Afterwards, we define the notion of weak commutativity of a Mealy-type fuzzy finite state machine, and discuss characterizations of weak commutativity of Mealy-type fuzzy finite state machines. Moreover, we study weak commutativity of products of Mealy-type fuzzy finite state machines.
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