On fuzzy γµ-open sets in generalized fuzzy topological spaces

• Das, Birojit ^[1] ; Chakraborty, Jayasree ^[1] ; Bhattacharya, Baby ^[1]
  1. [1] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 3, 2022, págs. 733-749
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4784
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we explore the existence of operation approach on open sets in a generalized fuzzy topological space. We introduce the concept of fuzzy γµ-open set and study some basic properties of it. We obtain an interesting result that the intersection of two fuzzy γµ-open sets may not be a fuzzy γµ-open set, but if the operation is regular then the intersection becomes a fuzzy γµ-open set. We also initiate the notions of fuzzy minimal γµ-open set and fuzzy γµ-locally finite space and establish various results related to these.

• Referencias bibliográficas
  • B. A. Asaad and N. Ahmed, “Operation on Semi Generalized Open Sets with Its Separation Axioms”, International Journal of Pure and Applied...
  • C. Carpintero, E. Roses, M. S. Brown, and J. Sanabiro, “Minimal Open Sets on Generalized Topological Spaces”, Proyecciones (Antofagasta),...
  • C. Carpintero, N. Rajesh, and E. Roses, “Operation Approaches on b-open Sets and Applications”, Boletim da Sociedade Paranaense de Matematica,...
  • G. P. Chetty, “Generalized Fuzzy Topology”, Italian Journal of Pure and Applied Mathematics, vol. 24, pp. 91-96, 2008.
  • B. Das, B. Bhattacharya, and A. K. Saha, “Some remarks on fuzzy infi topological spaces”, Proyecciones (Antofagasta), vol. 40, no. 2, pp....
  • B. Das, B. Bhattacharya, J. Chakaraborty, S. A. Ganapathiraju, and A. Paul, “A new type of generalized closed set via γ-open set in a fuzzy...
  • B. Das, J. Chakraborty, G. Paul, and B. Bhattacharya, “A new approach for some applications of generalized fuzzy closed sets”, Computational...
  • B. Das, B. Bhattacharya, J. Chakraborty, and B. C. Tripathy, “Generalized fuzzy closed sets in a fuzzy bitopological space via γ-open sets”,...
  • B. Das, B. C. Tripathy, P. Debnath, and B. Bhattacharya, “Study of Matrix Transformation of Uniformly Almost Surely Convergent Complex Uncertain...
  • B. Das, B. C. Tripathy, P. Debnath, and B. Bhattacharya, “Almost convergence of complex uncertain double sequences”, Filomat, vol. 35, no....
  • S. Hussain, “On Generalized Open Sets”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1438-1446, 2018.
  • Y. B. Jun, S. W. Jeong, H. J. Lee, and J. W. Lee, “Application of Preopen Sets”, Applied General Topology, vol. 9, no. 2, pp. 213-228, 2008.
  • S. Kasahara, “Operation-Compact Spaces”, Mathematica Japonica, vol. 24, pp. 97-105, 2007.
  • G. S. S. Krishnan, M. Ganster, and K. Balachandran, “Operation Approcahes on Semiopen Sets and Its Applications”, Kochi Journal of Mathematics,...
  • E. Nakaoda and N. Oda, “Some Applications of Minimal Open Sets”, International Journal of Mathematics and Mathematical Sciences, vol. 27,...
  • H. Ogata, “Operations on Topological Space and Associated Topologies”, Mathematica Japonica, vol. 36, pp. 175-184, 1991.
  • B. Roy, “Applications of Operations on Minimal Generalized Open Sets”, Afrika Mathematika, vol. 29, pp. 1097-1104, 2018.
  • S. Tahiliani, “Operation Approach to β-Open Sets and Applications”, Mathematical Communication, vol. 16, pp. 577-591, 2011.
  • B. C. Tripathy and S. Debnath, “γ-open sets and γ-continuous mappings in fuzzy bitopological spaces”, Journal of Intelligent and Fuzzy Systems,...
  • B. C. Tripathy and G. C. Ray, “Mixed fuzzy ideal topological spaces”, Applied Mathematics and Computations, vol. 220, pp. 602-607, 2013.
  • B. C. Tripathy and G. C. Ray, “Weakly continuous functions on mixed fuzzy topological spaces”, Acta Scientiarum. Technology, vol. 36, no....
  • T. Van An, D. X. Cuong, and H. Maki, “On Operation Preopen Sets in Topological Space”, Scientiae Mathematicae Japonicae, vol. 21, pp. 241-260,...