Abstract
In this treatise, we propose a new type of closed set in fuzzy topological spaces called \(g^*\) fuzzy closed set, which is lying in between the fuzzy closed set and the generalized fuzzy closed set. Also, we study another class of fuzzy sets called \(\theta \)-\(g^*\) fuzzy closed sets which is weaker than \(\theta \)- fuzzy closed sets but stronger than \(\theta \)-g fuzzy closed sets and an interrelationships among these newly defined fuzzy closed sets along with the existing generalized fuzzy closed sets are established. Furthermore, the idea of fuzzy \(g^*\)-connectedness is introduced in the light of \(g^*\)-fuzzy closed sets. Finally, we define \({T_{1/2}}^*\)-space, \(^*T_{1/2}\)-space, \({_\theta T_{1/2}}^*\)-space and \({^*}_\theta T_{1/2}\)-space and some applications of these newly defined spaces are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Balasubramanian, G., Sundaram, P.: On some generalizations of fuzzy continuous functions. Fuzzy Sets Syst. 86, 93–100 (1997)
Fatteh, U.V., Bassan, D.S.: Fuzzy connectedness and its stronger forms. J. Math. Anal. Appl. 111, 449–464 (1985)
Chang, C.L.: Fuzzy topological spaces. J. Math. Anal. Appl. 24, 182–190 (1968)
Veerakumar, M.K.R.S.: Between closed sets and \(g\)- closed sets. Mem. Fac. Sci. Kochi Univ. (Math.) 21, 1–19 (2000)
El-Shafei, M.E., Zakari, A.: \(\theta \)-generalized closed set in fuzzy topological spaces. Arab. J. Sci. Eng. 34(2A), 197–206 (2005)
Mukherjee, M.N., Sinha, S.P.: Fuzzy \(\theta \)-closure operator on fuzzy topological space internet. J. Math. Math. Sci. 14(2), 309–314 (1991)
Levine, N.: Generalized closed sets in topology. Rend. Circ. Math. Palermo 19, 89–96 (1970)
Zadeh, L.A.: Fuzzy Sets. Inf. Control 11, 341–356 (1965)
Dontchev, J., Maki, H.: On \(\theta \)-generalized closed sets. Int. J. Math. Math. Sci. 22, 239–249 (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Paul, G., Das, B., Bhattacharya, B. (2020). On \(g^*\)-Closed Sets in Fuzzy Topological Spaces. In: Castillo, O., Jana, D., Giri, D., Ahmed, A. (eds) Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019. Studies in Computational Intelligence, vol 863. Springer, Cham. https://doi.org/10.1007/978-3-030-34152-7_57
Download citation
DOI: https://doi.org/10.1007/978-3-030-34152-7_57
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34151-0
Online ISBN: 978-3-030-34152-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)