MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA

Document Type : Research Paper

Authors

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.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 13, Issue 7
November and December 2016
Pages 131-152

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