| Title of paper:
|
k-Intuitionistic fuzzy structures
|
| Author(s):
|
| P. Suseela
|
| Department of Mathematics, SBK College, Aruppukottai, 626 101 - India
|
| suceela93@gmail.com
|
| M. Shakthiganesan
|
| Department of Mathematics, SBK College, Aruppukottai, 626 101 - India
|
| shakthivedha23@gmail.com
|
| R. Vembu
|
| Department of Mathematics, SBK College, Aruppukottai, 626 101 - India
|
| msrvembu@yahoo.co.in
|
|
| Published in:
|
"Notes on IFS", Volume 22 (2016) Number 1, pages 13-26
|
| Download:
|
 PDF (209 Kb, Info)
|
| Abstract:
|
A more natural and necessary generalization of the intuitionistic fuzzy theory is developed and discussed in this paper. The generalization fits very nicely with almost all the intuitionistic fuzzy algebraic structures as well as with the intuitionistic fuzzy topological structures available in the literature. The higher dimensional intuitionistic fuzzy theory developed here helps us to define and discuss the concept of negation (complement) of a higher dimensional intuitionistic fuzzy set in a more natural way. In this paper we prove many theorems in the new context in both algebraic and topological points of view.
|
| Keywords:
|
Fuzzy sets, Intuitionistic fuzzy sets.
|
| AMS Classification:
|
03E72.
|
| References:
|
- Atanassov, K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
- Atanassov, K. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
- Atanassov, K., E. Szmidt & J. Kacprzyk. (2008) On intuitionistic fuzzy multi-dimensional sets, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 7, 1–6.
- Atanassov, K., E. Szmidt, J. Kacprzyk & P. Rangasamy. (2008) On intuitionistic fuzzy multi-dimensional sets - Part 2, Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Vol. I: Foundations, Academic Publishing House EXIT, Warszawa, 43–51.
- Atanassov, K., E. Szmidt & J. Kacprzyk. (2010) On intuitionistic fuzzy multi-dimensional sets – Part 3, Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Vol. I: Foundations. Warsaw, SRI Polish Academy of Sciences, 19–26.
- Atanassov, K., Szmidt, E. & Kacprzyk, J. (2011) On intuitionistic fuzzy multi-dimensional sets – Part 4, Notes on Intuitionistic Fuzzy Sets, 17(2), 1–7.
- Chang, C. L. (1968) Fuzzy Topological Spaces, J. Math. Anal. Appl., 24(1), 182–189.
- Chakraborty, A. B. & S. S. Khare. (1993) Fuzzy Homomorphisms and Algebraic Structures, Fuzzy Sets and Systems, 59(2), 211–221.
- Coker, D. (1997) An Introduction to Intuitionistic Fuzzy Topological Spaces, Fuzzy Sets and Systems, 88(1), 81–89.
- Goguen, J. A. (1967) L-Fuzzy Sets, J. Math. Anal.Appl., 18, 145–174.
- Herstein, I. N. (1999) Topics in Algebra, Wiley–India.
- Munkers, J. R. (2009) Topology, PHI learning, New Delhi.
- Kumar, R. (1992) Fuzzy Subgroups, Fuzzy Ideals, and Fuzzy Cosets: Some Properties, Fuzzy Sets and Systems, 48(2), 267–274.
- Kumar, R. (1992) Fuzzy Characteristic Subgroups of a Group, Fuzzy Sets and Systems, 48(3), 397–398.
- Liu,W-J. (1982) Fuzzy Invariant Subgroups and Fuzzy Ideals, Fuzzy Sets and Systems, 8(2), 133–139.
- Zadeh, L. A. (1965) Fuzzy Sets, Information and Control, 8, 338–353.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
