GENERAL FUZZY AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED

[1] K. Abolpour and M. M. Zahedi, Isomorphism between two BL-general fuzzy automata, Soft
Comput., 16 (2012), 729-736.
[2] M. A. Arbib, rom automata theory to brain theory, Int. J. Man-Machine Stud., 7 (1975),
279-295.
[3] M. A. Arbib and E. G. Manes, A categorist's view of automata and systems, in: E. G. Manes
(Ed.), Category Theory Applied to Computation and Control, Proc. First Internat. Symp.
Amherst MA, 1974, Lecture Notes in Computer Science, Springer, Berlin, 25 (1975), 62-78.
[4] M. A. Arbib and E. G. Manes, Basic concepts of category theory applicable to computation
and control, in: E. G. Manes (Ed.), Category Theory Applied to Computation and Control,
Proc. First Internat. Symp. Amherst MA, 1974, Lecture Notes in Computer Science, Springer,
Berlin, 25 (1975), 2-41.
[5] M. A. Arbib and E. G. Manes, Fuzzy machines in a category, Bull. Anstral. Math. Soc., 13
(1975), 169-210.
[6] M. A. Arbib and E. G. Manes, Machines in category: an expository introduction, SIAM Rev.,
16 (1974), 163-192.
[7] A. W. Burks, Logic, biology and automata -some historical re
ections, Int. J. Man- Machine
Stud. 7 (1975), 297-312.
[8] W. L. Deng and D. W. Qiu, Supervisory control of fuzzy discrete event systems for simulation
equivalence, IEEE Transactions on Fuzzy Systems, 23 (2015), 178-192.
[9] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
of Approximate Reasoning, 38 (2005), 175-214.
[10] J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145-174.
[11] Y. M. Li, A categorical approach to lattice-valued fuzzy automata, Fuzzy Sets and Systems,
156 (2006), 855-864.
[12] D. S. Malik and J. N. Mordeson, Fuzzy Discrete Structures, Physica-Verlag, Heidelberg, New
York, 2000.
[13] M. L. Minsky, Computation: nite and innite machines, Prentice-Hall, Englewood Clis,
NJ, Chapter 3, (1967), 32-66.
[14] J. Mockor, A category of fuzzy automata, Internat. J. General Systems, 20 (1991), 73-82.
[15] J. Mockor, Fuzzy and non-deterministic automata, Soft Comput., 3 (1999), 221-226.
[16] J. Mockor, Semigroup homomorphisms and fuzzy automata, Soft comput., 6 (2002), 423-427.
[17] J. N. Mordeson and D. S. Malik, Fuzzy Automata and languages: Theory and Applications,
Chapman & Hall, CRC, Boca Raton, London, 2002.
[18] W. Omlin, C. L. Giles and K. K. Thornber, Equivalence in knowledge representation: au-
tomata, rnns, and dynamical fuzzy systems, Proc. IEEE, 87 (1999), 1623-1640.
[19] D. W. Qiu, A note on Trillas CHC models, Artif. Intell., 171 (2007), 239-254.
[20] D. W. Qiu, Automata theory based on complete residuated latticed-valued logic (I), Sci. China
(Ser. F), 44 (2001), 419-429.
[21] D. W. Qiu, Automata theory based on complete residuated latticed-valued logic (II), Sci.
China (Ser. F), 45 (2002), 442-452.
[22] D. W. Qiu, Pumping lemma in automata theory based on complete residuated lattice-valued
logic: a note, Fuzzy Sets and Systems, 157 (2006), 2128-2138.
[23] D. W. Qiu, Supervisory control of fuzzy discrete event systems: a formal approach, IEEE
Transactions on Systems, Man and Cybernetics-Part B, 35 (2005), 72-88.
[24] D. W. Qiu and F. C. Liu, Fuzzy discrete event systems under fuzzy observability and a
test-algorithm, IEEE Transactions on Fuzzy Systems., 17(2009), 578-589.
[25] J. Tang, M. Luo and J. Tang, Results on the use of category theory for the study of lattice-
valued nite state machines, Information Sciences, 288 (2014), 279-289.
[26] S. P. Tiwari and A. K. Singh, On minimal realization of fuzzy behaviour and associated
categories, Journal of Applied Mathematics and Computing, 45 (2014), 223-234.

[27] S. P. Tiwari, K. Y. Vijay and A. K. Singh, Construction of a minimal realization and monoid
for a fuzzy language: a categorical approach, Journal of Applied Mathematics and Comput-
ing, 47 (2015), 401-416.
[28] V. Trnkova, Automata and categories, in: lecture notes computer science, Springer, Berlin,
32 (1975), 160-166.
[29] V. Trnkova, L-fuzzy functional automata, in: lecture notes computer science, Springer,
Berlin, 74 (1979), 463-473.
[30] V. Trnkova, Relational automata in a category and their languages, in: lecture notes com-
puter science, Springer, Berlin, 56 (1977), 340-355.
[31] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
to pattern classication, Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.
[32] L. H. Wu and D. Qiu, Automata theory based on complete residuated lattice-valued logic:
Reduction and minimization, Fuzzy Sets and Systems, 161 (2010), 1635-1656.
[33] L. H. Wu, D. Qiu and H. Xing, Automata theory based on complete residuated lattice-valued
logic: Turing machines, Fuzzy Sets and Systems, 208 (2012), 43-66.
[34] H. Xing and D. Qiu, Automata theory based on complete residuated lattice-valued logic: A
categorical approach, Fuzzy Sets and Systems, 160 (2009), 2416-2428.
[35] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
[36] M. M. Zahedi, M. Horry and K. Abolpour, Bifuzzy (general) topology on max-min general
fuzzy automata, Advances in Fuzzy Mathematics, 3(1) (2008), 51-68.