Mohammad Horry - Shahid Chamran University of Kerman, Kerman, Iran

In this paper, we define the concepts of a complex fuzzy subset and a complexfuzzy finite state automaton. Then we extend the notion of a complex fuzzy finitestate automaton and introduce the notion of a general complex fuzzy automaton.After that we define the concept of a max-min general complex fuzzy automaton andconstruct some equivalence relations and some congruence relations in a max-mingeneral complex fuzzy automaton and obtain different types of monoids in a max-min general complex fuzzy automaton and define a homomorphism between themThen we define the concepts of a general complex fuzzy transformation semi- group,a faithful general complex fuzzy transformation semigroup and a faithful generalcomplex fuzzy transformation semigroup associated with a max-min generalcomplex fuzzy automaton. Then we derive relationships between a max-min generalcomplex fuzzy automaton and a general complex fuzzy transformation semigroup.

Fuzzy Automata, Semigroup, Equivalence Relation, Congruence Relation