Minimization of hesitant L-fuzzy automaton

In this paper, we study a new generalization for the notion of fuzzy automata, which we called hesitant L-fuzzy automaton (HLFA). We present the formulations of the mathematics framework for the theory of HLFA. Moreover, we present the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA. After that, for any hesitant L-fuzzy language we present a minimal complete accessible deterministic hesitant L-fuzzy automaton recognizing that. Finally, we present an algorithm, which determines states of the minimal hesitant L-fuzzy automaton and we present the time complexity of the algorithm.

Automated summary

In this paper, we study a new generalization for the notion of fuzzy automata, called hesitant L-fuzzy automaton (HLFA). The mathematics framework for the theory of HLFA is presented. Moreover, the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA are introduced. Additionally, a minimal complete accessible deterministic hesitant L-fuzzy automaton is presented for recognizing any hesitant L-fuzzy language, and an algorithm is proposed to determine the states of the minimal hesitant L-fuzzy automaton along with its time complexity.