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MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 13، شماره 7، اسفند 2016، صفحه 131-152 اصل مقاله (780.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2947 | ||
| نویسندگان | ||
| M. Shamsizadeh* 1؛ M. M. Zahedi2 | ||
| 1Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran | ||
| 2Department of Mathematics, Graduate University of Advanced Tech- nology, Kerman, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Minimal automata؛ $(alpha؛ beta)$-language؛ Statewise minimal automata؛ Homomorphism with threshold $(alpha؛ beta)$ | ||
| مراجع | ||
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