Document Type: Research Paper


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


In this paper, we de ne the concepts of compatibility between two
fuzzy subsets on Q, the set of states of a max- min general fuzzy automaton
and transitivity in a max-min general fuzzy automaton. We then construct a
uniform structure on Q, and de ne a topology on it. We also de ne the concept
of semi-uniform structures on a nonempty set X and construct a semi-uniform
structure on the set of states of a general fuzzy automaton. We then construct
a semi-uniform structure on , the set of all nite words on , the set of
input symbols of a general fuzzy automaton and, nally, using these semi-
uniform structures, we construct two topologies on Q and  and discuss their


[1] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
of Approximate Reasoning, 38 (2005), 175-214.
[2] I. M. Hanafy, A. M. Abd El-Aziz and T. M. Salman, Semi -compactness in Intuitionistic
Fuzzy Topological Spaces, Iranian Journal of Fuzzy Systems, 3(2) (2006), 53-62.
[3] K. D. Joshi, Introduction to general topology, New Age International Publisher, India, 1997.
[4] Y. B. Jun and H. S. Kim, Uniform structure in positive implicative algebras, International
Mathematical Journal, 2 (2002), 215-218.
[5] S. P. Li, Z. Fang and J. Zhao, P2-Connectedness in L-Topological Spaces, Iranian Journal of
Fuzzy Systems, 2(1) (2005), 29-36.
[6] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,
Cha-pman and Hall/CRC, London/Boca Raton, FL, 2002.
[7] D. S. Malik and J. N. Mordeson, Fuzzy discrete structures, Physica-Verlag, New York, 2000.
[8] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: au-
tomata, rnns, and dynamic fuzzy systems, Proc. IEEE, 87(9) (1999), 1623-1640.
[9] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy nite-state automata can be determinis-
tically encoded into recurrent neural networks, IEEE Trans. Fuzzy Syst. 5(1) (1998), 76-89.
[10] W. Page, Topological uniform structures, Dover Publication, Inc. New York, 1988.
[11] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
to pattern classif ication, Ph.D. dissertation Purdue University, IN, 1967.
[12] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
[13] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (General) topology on max-min general
fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 51-68.