Some (Fuzzy) Topologies on General\\ Fuzzy Automata

Document Type : Research Paper


1 Shahid Chamran University of Kerman, Kerman, Iran

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


In this paper, by presenting some notions and theorems, we obtain
different types of fuzzy topologies. In fact, we obtain some
Lowen-type  and Chang-type fuzzy topologies on general fuzzy
automata. To this end, first we define a Kuratowski fuzzy interior
operator which induces a  Lowen-type  fuzzy topology on the  set of
states of a max- min general   fuzzy automaton. Also by  proving
some theorems, we  can  define two  fuzzy closure (two fuzzy
interior) operators on the certain sets related to a  general fuzzy
automaton and then according to these notions we give some theorems
and obtain some different Chang-type fuzzy topologies.


bibitem{Arbib} M. A. Arbib,
{it From automata theory to brain theory},  International Journal of
Man-Machin Studies, {bf 7}textbf{(3)} (1975), 279-295.

bibitem{Ashby} W. R. Ashby, {it Design for a brain}, Chapman and Hall, London, 1954.

bibitem{AsWiWe} D. Ashlock, A. Wittrock and T. Wen, {it Training  finite  state
machines  to  improve  PCR  primer design} , In:  Proceedings of the
2002 Congress on  Evolutionary  Computation (CEC), {bf 20} (2002).

bibitem{CaFlMaVoSa} C. Cattaneo, P. Flocchini, G. Mauri, C. Q. Vogliotti and
N. Santoro, {it Cellular automata in fuzzy backgrounds}, Physica D,  {bf 105}
(1997), 105-120.

bibitem{Chang} C. L. Chang, {it Fuzzy topological spaces}, J. Math. Anal.
 Appl., {bf 24} (1968), 182-190.

bibitem{Das} P. Das, {it A  fuzzy topology associated with a fuzzy
 finite state machine}, Fuzzy Sets and Systems, {bf 105}
     (1999), 469-479.

bibitem{DoKr} M. Doostfatemeh and S.C. Kremer, {it New directions  in  fuzzy
automata}, International  Journal of Approximate Reasoning,  {bf
38} (2005), 175-214.

bibitem{GaKo} B. R. Gaines and L. J. Kohout, {it The logic of automata}, International
Journal of General Systems, {bf 2} (1976), 191-208.

bibitem{HoZa1} M. Horry and M. M. Zahedi, {it On general fuzzy recognizers}, Iranian Journal of
Fuzzy Systems, {bf 8}textbf{(3)} (2011), 125-135.

bibitem{HoZa2} M. Horry and M. M. Zahedi, {it  Hypergroups and general fuzzy automata},
Iranian Journal of Fuzzy Systems, {bf 6}textbf{(2)} (2009), 61-74.

bibitem{Kuratowski} K. Kuratowski, {it Topology}, Academic Presss, 1966.

bibitem{Lowen} R. Lowen, {it Fuzzy topological  spaces and  fuzzy
compactness}, Journal of  Mathematical Analysis and Applications, {bf 56} (1976), 621-633.

bibitem{MaSh1} R. Maclin and  J. Shavlik, {it Refing domain theories expressed as
finite-state automata}, In: L.B.G. Collins (ed.), Proceedings of the
8th International Workshop on Machine Learning (ML'91), Morgan
Kaufmann, San Mateo CA, 1991.

bibitem{MaSh2} R. Maclin and J. Shavlik, {it Refing algorithm with knowledge-based
neural networks: improving the choufasma algorithm for protein
folding}, In: S. Hanson, G. Drastal, R. Rivest (eds.), Computational
Learning Theory and Natural Learning Systems, MIT Press, Cambridge,
MA, 1992.

bibitem{MoMa} J. N. Mordeson and D. S. Malik, {it Fuzzy Automata and Languages}, Theory
and  Applications, Chapman and Hall/CRC, London/Boca Raton, FL,

bibitem{OmGiTh} W. Omlin, K. K. Giles and K. K. Thornber, {it Equivalence in knowledge
representation}: automata, rnns, and dynamical fuzzy systems,
Proceeding of  IEEE,  {bf 87}textbf{(9)} (1999), 1623-1640.

bibitem{OmThGi} W. Omlin, K. K. Thornber and K. K. Giles, {it Fuzzy finite-state
automata can be deterministically encoded into recurrent neural
networks}, IEEE Transactions on Fuzzy Systems, {bf 5}textbf{(1)} (1998),

bibitem{Tucker} B. Tucker (ed.), {it The computer science and engineering handbook},
CRC Press, Boca Raton, FL, 1997.

bibitem{ViZi} J. Virant and N. Zimic, {it Fuzzy automata with fuzzy relief}, IEEE
Transactions on Fuzzy Systems, {bf 3}textbf{(1)} (1995), 69-74.

bibitem{Wee} W. G. Wee, {it On generalization of adaptive algorithm and
application of the fuzzy sets concept to pattern classification},
Ph.D. dissertation, Purdue University, Lafayette, IN, 1967.

bibitem{Ying} M. Ying, {it A  formal  model of  computing  with  words}, IEEE
Transactions on Fuzzy Systems {bf 10}textbf{(5)} (2002), 640-652.

bibitem{Zadej} L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf 8} (1965), 338-353.

bibitem{ZaJpAb} M. M. Zahedi, M. Horry and K. Abolpor, {it Bifuzzy (General) topology
on max-min general fuzzy automata},  Advanced in Fuzzy Mathematics,
{bf 3}textbf{(1)} (2008), 51-68.vspace{.9cm}