Marzieh Shamsizadeh - Department of Mathematics, Faculty of Energy and Data Sciences , Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran
Khadijeh Abolpour - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
Mohammad Mehdi Zahedi - Department of Applied Mathematics, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran

In this paper, we present the notions of sub-general fuzzy automata, primary,transition generated, and homomorphisms for general fuzzy automata (GFA). Wedemonstrate how each GFA can be accurately represented by the sum of all of itsconstituent primaries. We prove that a transition generated is homomorphism andvice versa. Also, we prove that the primary is the maximal sub-GFA generated by asingle state. We also present some related theorems.

Subject Classification [۲۰۱۰]: ۰۳D۰۵, ۲۰M۳۵