Nano Fuzzy Generalized α-closed Sets and Nano Fuzzy α-generalized Closed Sets and Application


Published: 2023-10-03

Page: 386-395

Purva Rajwade *

Department of Applied Mathematics, Institute of Engineering & Technology, DAVV, Indore (M. P.), India.

Rachna Navalakhe

Department of Applied Mathematics & Computational Science, Shri G. S. Institute of Technology & Science, Indore (M. P.), India.

*Author to whom correspondence should be addressed.


The presented article is a framework of research based on two main aims. The main objective of this paper is to introduce, provide definitions for, and conduct a comprehensive study of a novel category of sets known as Nano fuzzy generalized α-closed sets and Nano fuzzy α-generalized closed sets in Nano fuzzy topological spaces. These spaces are having applications in various fields. Within the context we have addressed a medical diagnosis problem by applying the principles of Nano fuzzy topological spaces.

Keywords: Nano fuzzy topological spaces, Nano fuzzy generalized α-closed sets, Nano fuzzy α-generalized closed sets

How to Cite

Rajwade , P., & Navalakhe , R. (2023). Nano Fuzzy Generalized α-closed Sets and Nano Fuzzy α-generalized Closed Sets and Application. Asian Journal of Pure and Applied Mathematics, 5(1), 386–395. Retrieved from


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Pawlak Z, Rough sets, International Journal of Computer & Information Sciences. 1982;11(5):341-356.

Thivagar L, Richard C. On Nano forms of weakly open set, International Journal of Mathematics and Statistics Invention. 2013;1(1):31-37.

Qays Hatem Imran, On Nano Semi Alpha Open Sets, Journal of Science and Arts. 2017;2(39):235-244.

Nasef AA, Aggour AI, Darwesh SM. On some classes of nearly open sets in nano topological spaces, Journal of the Egyptian Mathematical Society. 2016;24:585-589.

Nachiyar Thanga R, Bhuvaneswari K.. On Nano generalized α-closed sets and Nano α-generalized closed sets in Nano topological spaces, International Journal of Engineering Trends and Technology. 2014;13(6):257-260.

Zadeh LA. Fuzzy sets, Information and Control. 1965;8:338-353.

Chang CL. Fuzzy topological spaces, Journal of Mathematical Analysis and Applications. 1968;24:182-190.

Navalakhe R, Rajwade P. On Nano fuzzy topological spaces, International Review of Fuzzy Mathematics. 2019;14 (2):127-136.

Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems., 1990;17:191–208.

Rajwade P, Navalakhe R.. On Nano Fuzzy Forms of Weakly Fuzzy Open Sets, Journal of Northeastern University. 2022;25(4):3957-3964.

Rajwade P, Navalakhe R, Jain V. Nano Generalized Fuzzy Semi-open Sets and Nano Fuzzy β-Open Sets in Nano Fuzzy Topological Spaces, GANITA, Bhartiya Ganita Parishad. 2022;72(1):285-289.

Navalakhe R, Rajwade P. Nano Fuzzy b-open Sets in Nano fuzzy Topological Spaces, Annals of Pure and Applied Mathematics. 2022;25(1):55-61.

Thangammala R, Saraswathi M, Vadivel A, John Sundar C. Fuzzy nano Z-open sets in fuzzy nano topological spaces, Journal of Linear and Topological Algebra. 2022;11(01):27-38.

Andrijevic D. Semi-pre-open sets, Math. Vesnik. 1986;38:24-32.

Levin N. Semi-open sets and semi continuity in topological spaces, Amer. Math. Monthly. 1963;70:36-41.