Language of General Fuzzy Recognizer

Document Type : Research Paper

Authors

1 Department of Mathematics, Kazerun Branch, Islamic Azad Univer- sity, Kazerun, Iran

2 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this note first by considering the notion of general fuzzy automata (for simplicity GFA), we define the notions of direct product, restricted direct product and join of two GFA. Also, we introduce some operations on (Fuzzy) sets and then prove some related theorems. Finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given GFA. In particular, we define the notion of the language of a given general fuzzy  $\Sigma$-recognizer and we show that the language of direct product of two  $\Sigma$-recognizer is equal to direct product of their languages.

Keywords

References

\bibitem{[1].} M. A. Arbib, {\it From automata theory to brain theory}, Int. J. Man-Machine Stud., {\bf7(3)} (1975), 279-295.
\bibitem{[2].} A. W. Burks, {\it Logic, biology and automata -some historical reflections}, Int. J. Man- Machine Stud., {\bf7(3)} (1975), 297-312.
\bibitem{[3].} M. Doostfatemeh and S. C. Kremer, {\it New directions in fuzzy automata}, International Journal of Approximate Reasoning, {\bf38} (2005), 175-214.
\bibitem{[4].} M. Horry and M. M. Zahedi, {\it On general fuzzy recognizer}, Iranian Journal of Fuzzy Systems, {\bf8(3)} (2011), 125-135.
\bibitem{[5].} H. V. Kumbhojkar and S. R. Chaudhari, {\it Fuzzy recognizers and recognizable sets}, Fuzzy Sets and Systems, {\bf131} (2002), 381-392.
\bibitem{[6].} D. S. Malik and J. N. Mordeson, {\it Fuzzy discrete structures}, Physica-Verlag, New York, 2000.
\bibitem{[7].} M. L. Minsky, {\it Computation: finite and infinite machines}, Prentice-Hall, Englewood Cliffs, NJ, Chapter 3, (1967), 32-66.
\bibitem{[8].} J. N. Mordeson and D. S. Malik, {\it Fuzzy automata and languages, theory and applications}, Chapman and Hall/CRC, London/Boca Raton, FL, 2002.
\bibitem{[9].} W. Omlin, C. L. Giles and K. K. Thornber, {\it Equivalence in knowledge representation: automata, runs, and dynamical fuzzy systems}, Proc. IEEE, {\bf87(9)} (1999), 1623-1640.
\bibitem{[10].} W. G. Wee, {\it On generalization of adaptive algorithm and application of the fuzzy sets concept to pattern classification}, Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.
\bibitem{[11].} L .A. Zadeh, {\it Fuzzy sets}, Information and Control, {\bf8} (1965), 338-353.
\bibitem{[12].} M. M. Zahedi, M. Horry and K. Abolpour, {\it Bifuzzy (general) topology on max-min general fuzzy automata}, Advances in Fuzzy Mathematics, {\bf3(1)} (2008), 51-68.
Iranian Journal of Fuzzy Systems
Volume 11, Issue 1 - Serial Number 1
January and February 2014
Pages 113-134

Files

Share

How to cite

Statistics