Document Type : Research Paper


1 Department of Mathematics, Sri Sarada College for Women, Salem, Tamilnadu, India

2 Department of Mathematics, Sri Sarada College forWomen, Salem, Tamilnadu, India


In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.


[1] K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity,
J. Math. Anal. Appl., 82 (1981), 14{32.
[2] K. K. Azad, Fuzzy Hausdroff spaces and fuzzy perfect mappings, J. Math. Anal. Appl., 82
(1981), 297{305.
[3] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
[4] P. Das, A fuzzy topology associated with a fuzzy fi nite state machine, Fuzzy Sets and Systems,
105(3) (1999), 469{479.
[5] D. H. Foster, Fuzzy topological groups, J. Math. Anal. Appl., 67 (1979), 549{564.
[6] K. R. Gentry and H. B. Hoyle III, Somewhat continuous functions, Czech. Math. J., 21 (96)
(1971), 5{12.
[7] M. Ghorani and M. M. Zahedi, Characterizations of complete residuated lattice-valued fi nite
tree automata, Fuzzy Sets and Systems, 199 (2012) 28{46.
[8] E. Hewitt, A problem in set theoretic topology, Duke Math. J., 10 (1943), 309{333.
[9] J. Ignjatovic, M. Ciric and S. Bogdanovic, Determinization of fuzzy automata with member-
ship values in complete residuated lattices, Information Sciences, 178 (2008), 164{180.
[10] J. Ignjatovic, M. Ciric and V. Simovic, Fuzzy relation equations and subsystems of fuzzy
transition systems, Knowledge-Based Systems, 38 (2013), 48{61.
[11] Y. M. Li, A categorical approach to lattice-valued fuzzy automata, Fuzzy Sets and Systems,
157 (2006), 855{864.
[12] Y. M. Li, Finite automata theory with membership values in lattices, Information Sciences,
181 (2011), 1003{1017.
[13] P. Li and Y. M. Li, Algebraic properties of LA-languages, Information Sciences, 176 (2006),
[14] Z. H. Li, P. Li and Y. M. Li, The relationships among several types of fuzzy automata,
Information Sciences, 176 (2006), 2208{2226.
[15] D. S. Malik and J. N. Mordeson, Algebraic fuzzy automata theory, Arabian J. Sci, Eng., 25
(2000), 23{50.
[16] D. S. Malik, J. N. Mordeson and M. K. Sen, On subsystems of fuzzy fi nite state machines,
Fuzzy Sets and Systems, 68 (1994), 83{92.
[17] P. V. Ramakrishnan and V. Lakshmana Gomathi Nayagam, Nearly fuzzy Hausdor spaces,
Indian J. Pure Appl. Math., 31(5) (2000), 695{712.
[18] A. K. Srivastava and S. P. Tiwari, A topology for fuzzy automata, Proc. AFSS International
Conference on Fuzzy Systems, Lecture Notes in Artifi cial Intelligence, Springer-Verlag, 2275
(2002), 485{491.
[19] A. K. Srivastava and S. P. Tiwari, On relationships among fuzzy approximation operators,
fuzzy topology, and fuzzy automata, Fuzzy sets and systems, 138 (2003), 197{204.
[20] G. Thangaraj and G. Balasubramanian, On somewhat fuzzy continuous functions, J. Fuzzy
Math., 11(2) (2003), 725{736.
[21] S. P. Tiwari and S. Sharan, Fuzzy automata based on lattice-ordered monoids with algebraic
and topological aspects, Fuzzy Information and Engineering, 2 (2012), 155{164.
[22] S. P. Tiwari, A. K. Singh and S. Sharan, Fuzzy automata based on lattice-ordered monoid
and associated topology, Journal of Uncertain Systems, 6(1) (2012), 51{55.
[23] S. P. Tiwari, A. K. Singh, S. Sharan and V. K. Yadav, Bifuzzy core of fuzzy automata, Iranian
Journal of Fuzzy Systems, 12(2) (2015), 63{73.
[24] W. G.Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept
to pattern classifi cation , Ph. D. Thesis, Purdue University, 1967.
[25] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338{353.