Issue:On relationships among intuitionistic fuzzy approximation operators, intuitionistic fuzzy topology and intuitionistic fuzzy automata

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Title of paper: On relationships among intuitionistic fuzzy approximation operators, intuitionistic fuzzy topology and intuitionistic fuzzy automata Author(s): S. P. Tiwari Department of Applied Mathematics, Indian School of Mines University, Dhanbad-826 004, India sptiwarimaths@gmail.com Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 16 (2010) Number 1, pages 1—9 Download:  PDF (247  Kb, File info) Abstract: This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata. Keywords: Intuitionistic fuzzy set; Intuitionistic fuzzy approximation operator; Intuitionistic fuzzy topology; Fuzzy topology; Intuitionistic fuzzy automaton; Strong intuitionistic fuzzy subsystem. References: K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96. C.L. Chang, Fuzzy topological spaces, Jour. Math. Anal. Appl., 24 (1968) 182-189. D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997) 81-89. P. Das, A fuzzy topology associated with a fuzzy finite state machine, Fuzzy Sets and Systems, 105 (1999) 469-479. Y.B. Jun, Intuitionistic fuzzy finite state machines, Jour. Appl. Math. and Computing, 17 (2005) 109-120. R. Lowen, Fuzzy topological spaces and fuzzy compactness, Jour. Math. Anal. Appl., 56 (1976) 621-633. D.S. Malik, J.N. Mordeson and M.K. Sen, On subsystems of a fuzzy finite state machine, Fuzzy Sets and Systems, 68 (1994) 83-92. J.N. Mordeson, Algebraic properties of rough set theory, NAFIPS'99, 56-59. A.K. Srivastava and S.P. Tiwari, A topology for fuzzy automata, in: Proc. 2002 AFSS Internat. Conf. on Fuzzy Systems, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2275 (2002) 485-490. 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. A.K. Srivastava and S.P. Tiwari, IF-topologies and IF-automata, Soft Computing, DOI 10.1007/s00500-009-0427-z. Y.Y. Yao, Two views of the theory of rough sets infinite universes, Internat. Jour. of Approximate Reasoning, 15 (1996) 291{317. L. Zhou, W. Wu and W. Zhang, On intuitionistic fuzzy rough sets and their topological structures, International Journal of General Systems, DOI 10.1080/03081070802187723. Z. Zhou and W. Wu, On generalized intuitionistic fuzzy rough approximation operators, Information Sciences, 178 (2008) 2448{2465. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.