General Complex Fuzzy Transformation Semigroups in Automata

Abstract

<em>In this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. Then we extend the notion of a complex fuzzy finite state 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 and construct some equivalence relations and some congruence relations in a max-min general complex fuzzy automaton and obtain different types of monoids in a max-min general complex fuzzy automaton and define a homomorphism between them. Then we define the concepts of a general complex fuzzy transformation semi- group, a faithful general complex fuzzy transformation semigroup and a faithful general complex fuzzy transformation semigroup associated with a max-min general complex fuzzy automaton. Then we derive relationships between a max-min general complex fuzzy automaton and a general complex fuzzy transformation semigroup</em>.