Mohammad Mehdi Zahedi - Department of Applied Mathematics, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran
Mohammad Javad Agheli Goki - Department of Applied Mathematics, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran

In this paper, we de ne the weak homomorphism between two hesitant L-fuzzyautomata (HLFA) A۱ and A۲. Then, we use it in a theorem to show that if thereis a weak homomorphism from the HLFA A۱ to the HLFA A۲, then the language ofHLFA A۱ is a subset of the language of HLFA A۲, that is HLA۱ HLA۲ . Next, byintroducing the relationship between two HLFA, A۱ and A۲, we establish a relationshipbetween their languages and state the conditions under which their languages is equal,that is, HLA۱ = HLA۲ . For this purpose, while assuming that k is a non-negativeinteger, we introduce a k-behavior for the HLFA A, and denote it by HLkA. Weshow that HLA =S۱k=۰ HLkA. In addition, between two HLFA A۱ and A۲, weexpress concepts k-relation (A۱RkA۲) and completely relation (A۱RA۲). Finally, bya theorem, we show that if A۱RA۲, then HLA۱ = HLA۲ .

Hesitant set, Hesitant automata, Behavior, Complete lattice