Fuzzy Idealization on \(gb\)-Continuity

V. Chitra, V. Indhumathi, C. Selvapriya


In this work, we introduce the notions of \(\emph{fgb}\)-\(I\)-closed sets, \(\emph{fgb}\)-\(I\)-continuous, \(\emph{fgb}\)-\(I\)-irresolute, \(\emph{fgb}\)-\(I\)-open functions and \(\emph{fgb}\)\(^*\)-\(I\)-open functions in fuzzy ideal topological spaces and investigate some of their characterizations and properties.


\(fgb\)-\(I\)-closed sets; \(fgb\)-\(I\)-neighbourhood; \(fgbq\)-\(I\)-neighbourhood; \(fgb\)-\(I\)-continuous functions; \(fgb\)-\(I\)-irresolute functions; \(fgb\)-\(I\)-closed functions; \(fgb\)\(^*\)-\(I\)-open functions; fuzzy \(gb\)-\(I\)-\(T_{1/2}\

Full Text:



G. Balasubramanian and P. Sundaram, On some generalization of fuzzy continuous, Fuzzy sets and Systems 86 (1997), 93–100.

S.S. Benchalli and J.J. Karnel, On fuzzy b-open sets in fuzzy topological spaces, J. Computer and Mathematical Sciences 1(2) (2010), 127–134.

S.S. Benchalli and J.J. Karnel, Fuzzy gb-continuous maps in fuzzy topological spaces, International Journal of Computer Applications 19(1) (2011), 24–29.

C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. (1968), 182–190.

M.K. Gupta and Rajneesh, Fuzzy-I-open sets and a new decompositions of fuzzy semi-I-continuity via fuzzy ideals, Int. J. Math. Anal. (Ruse) 3(28) (2009), 1349–1357.

K. Kuratowski, Topology, Vol. I (Transl.), Academic Press, New York (1966).

R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56 (1976), 621–633.

P.M. Pu and Y.M. Liu, Fuzzy topology-I, neighbourhood structure of fuzzy point and Moore-smith convergence, J. Math. Anal. Appl. 6 (1980), 571–599.

R.A. Mahmoud, Fuzzy ideals, fuzzy local functions and fuzzy topology, J. Fuzzy Math. Los Angelesn 5(1) (1997), 165–172.

A.A. Nasef and R.A. Mahmoud, Some topological applications via fuzzy ideals, Chaos, Solitons & Fractals 87 (2002), 117–123.

A.A. Nasef and E. Hatir, On fuzzy pre-I-open sets and a decomposition of fuzzy I-continuity, Chaos, Solitons & Fractals 40 (2009), 1185–1189.

N. Palaniappan, Fuzzy Topology, Narosa Publications (2002).

D. Sarkar, Fuzzy ideal theory, fuzzy local function and generated fuzzy topology, Fuzzy sets and Systems 87 (1997), 117–123.

R. Vaidyanathaswamy, Set Topology, Chelsea, New York (1960).

S. Yuksel, S. Kara and A. Acikgoz, On fuzzy b-I-continuous functions, Sdu Journal of Science (E-journal) 4(1) (2009), 87–98.

L.A. Zadeh, Fuzzy sets, Inform. Contr. 8 (1965), 338–353.

DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.1016

eISSN 0975-5748; pISSN 0974-875X