ScieXplore: International Journal of Research in Science

Open Access Open Access  Restricted Access Subscription Access

Intuitionistic Fuzzy Nano Topological Space: Theory and Applications


Affiliations
1 Department of Mathematics, Govt. Arts and Science College, Komarapalayam, Erode, India
2 Department of Mathematics, SVS College of Engineering, Coimbatore, India
 

We introduce the notion of intuitionistic fuzzy nano topological space, its properties and results. The topological characterizations of intuitionistic fuzzy nano continuous functions are derived, and the weak forms of intuitionistic fuzzy nano-open sets are obtained. The intuitionistic fuzzy Nano Upper approximation space in real life application is discussed.

Keywords

Intuitionistic Fuzzy Nano Forms of Weakly Open Sets, Intuitionistic Fuzzy Nano Topological Space, Multi Criterion Decision Making.
User
Notifications
Font Size


  • Atanassov KT. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems. 1986; 20(1): 87–96. https://doi.org/10.1016/S01650114(86)80034-3

  • Atanassov KT. Review and new result on IF Set, Mathematical foundation of artificial intelligence seminar, Sofia, Preprint I-88, 1988.

  • Atanassov KT. More on IF Sets. Fuzzy Sets and Systems. 1989; 33(1): 37–45. https://doi.org/10.1016/0165-0114(89)90215-7 4. Atanassov KT. New operations defined over the IF Sets.

  • Fuzzy Sets and Systems. 1994; 61: 137–142. https://doi.org/10.1016/0165-0114(94)90229-1

  • Coker D. An Introduction to IF Topological Spaces. Fuzzy Sets and Systems. 1997; 88: 81–9. https://doi.org/10.1016/S01650114(96)00076-0

  • Cornelis C, Cock MD, Kerre EE. IF rough sets: At the crossroads of imperfect knowledge, Expert Syst. 2003; 20: 260–70.https://doi.org/10.1111/1468-0394.00250

  • Hanafy IM, El A. Completely continuous functions in IF topological spaces. Czechoslovak Mathematical Journal. 2003; 53: 793–803. https://doi.org/10.1023/ B:CMAJ.0000024523.64828.31

  • Lellis Thivagar M, Richard C. On Nano Continuity. Mathematical Theory and Modelling. 2013; 3(7): 32–7.

  • Lellis Thivagar M, Richard C. On Nano Forms of Weakly Open Sets. International Journal of Mathematics and Statistics Invention. 2013; 1(1): 31–7.

  • Lin TY. Granular computing: Fuzzy logic and rough sets. In: Zadeh LA, Kacprzk, Editors . Computing with words in information/intelligent theories. Int. J. Information Comput. Sci. 1985; 11(5): 99–102.

  • Pawlak Z. Rough sets. International Journal of Computer and Information Sciences. 1982; 11: 341–56. https://doi.org/10.1007/BF01001956

  • Pawlak Z. Rough sets - Theoretical Aspects of Reasoning about data. Boston: Kluwer Academic Publishers; 1991.

  • Pawlak Z. Rough set theory and its applications. Journal of Telecommunications and Information Technology. 2002; 3: 7–10.

  • Pawlak Z., Zdzislaw. Rough set approach to knowledgebased decision support. European Journal of Operational Research. 1996; 99(1): 48–57. https://doi.org/10.1016/S03772217(96)00382-7

  • Pawlak Z., Zdzislaw. Rough set approach to Multi-attribute decision analysis. European Journal of Operational Research. 1997; 72(3): 443–53. https://doi.org/10.1016/03772217(94)90415-4

  • Tripathy BK. Rough sets on IF Approximation Spaces.In: Proceedings of 3rd International IEEE Conference on Intelligent Systems (IS06). p. 776–79. PMid:26029348 PMCid:PMC4444617

  • Wu, W-Z, Zhou L. On IF topologies based on IF reflexive and transitive relations. Soft Comput. 2011; 15: 1183–94. https:// doi.org/10.1007/s00500-010-0576-0

  • Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338–53. https://doi.org/10.1016/S0019-9958(65)90241-X


Abstract Views: 909

PDF Views: 510




  • Intuitionistic Fuzzy Nano Topological Space: Theory and Applications

Abstract Views: 909  |  PDF Views: 510

Authors

M. Ramachandran
Department of Mathematics, Govt. Arts and Science College, Komarapalayam, Erode, India
A. Stephan Antony Raj
Department of Mathematics, SVS College of Engineering, Coimbatore, India

Abstract


We introduce the notion of intuitionistic fuzzy nano topological space, its properties and results. The topological characterizations of intuitionistic fuzzy nano continuous functions are derived, and the weak forms of intuitionistic fuzzy nano-open sets are obtained. The intuitionistic fuzzy Nano Upper approximation space in real life application is discussed.

Keywords


Intuitionistic Fuzzy Nano Forms of Weakly Open Sets, Intuitionistic Fuzzy Nano Topological Space, Multi Criterion Decision Making.

References





DOI: https://doi.org/10.15613/sijrs%2F2017%2Fv4i1%2F172390