Bipolar general fuzzy automata

Subject Areas : History and biography

M. Horry ¹ (Department of Mathematics Shahid Chamran University of Kerman, Kerman, Iran)

Received: 2015-12-27 Accepted : 2016-05-30 Published : 2016-08-01

Keywords: bipolar valued fuzzy set, closure, operator, Fuzzy automata,

Abstract :

In this paper, we define the notion of a bipolar general fuzzyautomaton, then we construct some closure operators on the set of states of a bipolar general fuzzy automaton. Also, we construct some topologies on the set of states of a bipolargeneral fuzzy automaton. Then we obtain some relationships between them.

References:

[1] M. A. Arbib, From automata theory to brain theory, International Journal of Man-Machin Studies, 7 (3) (1975), 279-295.

[2] W. R. Ashby, Design for a brain, Chapman and Hall, London, 1954.

[3] D. Ashlock, A. Wittrock and T. Wen, Training finite state machines to improve PCR primer design, in: Proceedings of the 2002 Congress on Evolutionary Computation (CEC) 20, 2002.

[4] M. Doostfatemeh, S. C. Kremer, New directions in fuzzy automata, International Journal of Approximate Reasoning, 38 (2005), 175-214.

[5] B. R. Gaines, L. J. Kohout, The logic of automata, International Journal of General Systems, 2 (1976), 191-208.

[6] M. Horry, M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of Fuzzy Systems, 6 (2) (2009), 61-74.

[7] K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technogies, Bangkok, Thailand (2002), 307-312.

[8] K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J. Fuzzy Logic Intelligent Systems 14 (2004), 125-129.

[9] J. N. Mordeson, D. S. Malik, Fuzzy Automata and Languages, Theory and Applications, Chapman and Hall/CRC, London/Boca Raton, FL, 2002.

[10] R. Maclin,J. Shavlik, 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.

[11] R. Maclin, J. Shavlik, 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.

[12] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: automata, rnns, and dynamical fuzzy systems, Proceeding of IEEE, 87 (9) (1999), 1623-1640.

[13] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks, IEEE Transactions on Fuzzy Systems, 5 (1) (1998), 76-89.

[14] B. Tucker (Ed.), The Computer Science and Engineering Handbook, CRC Press, Boca Raton, FL, 1997.

[15] J. Virant, N. Zimic, Fuzzy automata with fuzzy relief, IEEE Transactions on Fuzzy Systems, 3 (1) (1995), 69-74.

[16] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph.D. dissertation, Purdue University, Lafayette, IN, 1967.

[17] M. Ying, A formal model of computing with words, IEEE Transactions on Fuzzy Systems 10 (5) (2002), 640-652.

[18] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.