Shamsizadeh, M., Zahedi, M. (2016). MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA. Iranian Journal of Fuzzy Systems, 13(7), 131-152. doi: 10.22111/ijfs.2016.2947

M. Shamsizadeh; M. M. Zahedi. "MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA". Iranian Journal of Fuzzy Systems, 13, 7, 2016, 131-152. doi: 10.22111/ijfs.2016.2947

Shamsizadeh, M., Zahedi, M. (2016). 'MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA', Iranian Journal of Fuzzy Systems, 13(7), pp. 131-152. doi: 10.22111/ijfs.2016.2947

Shamsizadeh, M., Zahedi, M. MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA. Iranian Journal of Fuzzy Systems, 2016; 13(7): 131-152. doi: 10.22111/ijfs.2016.2947

MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA

^{1}Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran

^{2}Department of Mathematics, Graduate University of Advanced Tech- nology, Kerman, Iran

Abstract

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(\alpha, \beta)$-language, we show that for any $(\alpha, \beta)$-language $\mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $\mathcal{L}$. We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(\alpha,\beta)$ to any $(\alpha, \beta)$-reduced max-min intuitionistic general L-fuzzy automaton. %Also, we prove that the minimal intuitionistic general L-fuzzy automaton is an $(\alpha, \beta)$-reduced. Also, we show that for any strong deterministic max-min intuitionistic general L-fuzzy automaton there exists a statewise $(\alpha, \beta)$-minimal intuitionistic general L-fuzzy automaton. In particular, a connection between the minimal and statewise $(\alpha, \beta)$-minimal intuitionistic general L-fuzzy automaton is presented. %We show if $\tilde{F}^*$ is an $(\alpha, \beta)$-complete $(\alpha, \beta)$-accessible deterministic max-min intuitionistic general L-fuzzy automaton and it is recognizing $(\alpha, \beta)$-language $\mathcal{L}$, then the minimal $\tilde{F}^*_{\mathcal{L}}$ is homomorphism with threshold $(\alpha, \beta)$ to statewise $(\alpha, \beta)$-minimal $\tilde{F}_{m}^*$, where $\tilde{F}_{m}^*$ is statewise $(\alpha, \beta)$-equivalent to $\tilde{F}^*$. Also, for a given intuitionistic general L-fuzzy automaton, we present two algorithms, which determines states of the minimal intuitionistic general L-fuzzy automaton and the statewise $(\alpha, \beta)$-minimal intuitionistic general L-fuzzy automaton. Finally, by giving some examples, we comparison minimal intuitionistic general L-fuzzy automaton and statewise $(\alpha, \beta)$-minimal intuitionistic general L-fuzzy automaton.

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