Abstract
In this note, we focus on behavior of BL-general fuzzy automata (for simplicity BL-GFA) and we obtain the free realization for a given behavior, that is, a BL-general fuzzy automaton whose behavior is given behavior. Then we find the realization with the minimum number of states. The minimization takes two steps: at first discard all superfluous states, and then we merge all pairs of states which have the same behavior. Moreover we prove some theorems. In particular, we show that the minimal reduction of the reachable part of an BL-GFA is the minimal realization of the behavior it. Finally we give some examples to clarify these notions.
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Abolpour, K., Zahedi, M.M., Golmohamadian, M.: Some hyper K-algebraic structures induced by max-min general fuzzy automata. Iran. J. Fuzzy Syst. 8(1) (2011)
Abolpour, K., Zahedi, M.M.: Isomorphism between two BL-general fuzzy automata. Inf. Sci. J. (submitted)
Adamek, J., Trnkova, V.: Automata and Algebras in Categories. Kluwer Academic, Dordrecht (1990)
Arbib, M.A.: From automata theory to brain theory. Int. J. Man-Mach. Stud. 7(3), 279–295 (1975)
Burks, A.W.: Logic, biology and automata—some historical reflections. Int. J. Man-Mach. Stud. 7(3), 297–312 (1975)
Doostfatemeh, M., Kremer, S.C.: New directions in fuzzy automata. Int. J. Approx. Reason. 38, 175–214 (2005)
Hajek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic, Dordrecht (1988)
Haveshki, M., Borumand Saeid, A., Eslami, E.: Some types of filters in BL algebras. Soft Comput. 10, 657–664 (2006)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation, 2nd edn. Addison–Wesley, Reading (2001)
Malik, D.S., Mordeson, J.N.: Fuzzy Discrete Structures. Physica-Verlag, New York (2000)
Minsky, M.L.: BL-general fuzzy automata and reachable realization. In: Computation: Finite and Infinite Machines, pp. 32–66. Prentice-Hall, Englewood Cliffs (1967), Chap. 3
Mordeson, J.N., Malik, D.S.: Fuzzy Automata and Languages, Theory and Applications. Chapman and Hall/CRC, London/Boca Raton (2002)
Turunen, E.: Boolean deductive systems of BL-algebras. Arch. Math. Log. 40, 467–473 (2001)
Zahedi, M.M., Horry, M., Abolpour, K.: Bifuzzy (general) topology on max-min general fuzzy automata. Adv. Fuzzy Math. 3(1), 51–68 (2008)
Omlin, W., Giles, C.L., Thornber, K.K.: Equivalence in knowledge representation: automata, RNNS, and dynamical fuzzy systems. Proc. IEEE 87(9), 1623–1640 (1999)
Omlin, W., Thornber, K.K., Giles, C.L.: Fuzzy finite-set automata can be deterministically encoded into recurrent neural networks. IEEE Trans. Fuzzy Syst. 5(1), 76–89 (1998)
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Abolpour, K., Zahedi, M.M. BL-general fuzzy automata and accept behavior. J. Appl. Math. Comput. 38, 103–118 (2012). https://doi.org/10.1007/s12190-010-0466-8
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DOI: https://doi.org/10.1007/s12190-010-0466-8