Title of paper:
|
Properties of interval-valued intuitionistic fuzzy vector spaces
|
Author(s):
|
R. Santhi
|
PG and Research Department of Mathematics, Nallamuthu Gounder Mahalingam College, Pollachi, Tamil Nadu, 642001 India
|
santhifuzzy@yahoo.co.in
|
N. Udhayarani
|
Department of Mathematics, Nallamuthu Gounder Mahalingam College, Pollachi, Tamil Nadu, 642001 India
|
udhayaranin@gmail.com
|
|
Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 1, pages 12–20
|
DOI:
|
https://doi.org/10.7546/nifs.2019.25.1.12-20
|
Download:
|
PDF (200 Kb, File info)
|
Abstract:
|
In this paper we introduced and studied the properties of interval-valued intuitionistic fuzzy vector spaces (in brief IVIF space) and its IVIF standard basis. We use the concept of
max-union and min-intersection algebra to define interval-valued ituitionistic fuzzy vector space.
|
Keywords:
|
Interval-valued intuitionistic fuzzy vector space, IVIF subspace, IVIF span, IVIF spanning set, dim(S), IVIF basis, IVIF standard basis.
|
AMS Classification:
|
46A40, 52A07.
|
References:
|
- Atanassov, K. T. Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
- Atanassov, K. T. & Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31, 343–349.
- Chiney, M. & Samanta, S. K. (2017). Intuitionistic fuzzy basis of an intuitionistic fuzzy vector space, Notes on Intuitionistic Fuzzy Sets, 23 (4), 62–74.
- Gehrke, M., Walker, C., & Walker, E., (2001). Some basic theory of interval-valued fuzzy sets, Transactions of the Joint IFSA World Congress and 20-th NAFIPS International Conference, July 25–28, 2001, Vancouver, British Columbia, 1332–1336.
- Hosseini, S. B., O’Regan, D. & Saadati, R. (2007). Some results on intuitionistic fuzzy spaces, Iranian Journal of Fuzzy Systems, 4 (1), 53–64.
- Huang, C. E. & Shi, F. G. (2012). On the fuzzy dimensions of fuzzy vector spaces, Iranian Journal of Fuzzy Systems, 9 (4), 141–150.
- Katsaras, A. K. & Liu, D. B. (1997). Fuzzy vector spaces and fuzzy topological vector spaces, Journal of Mathematical Analysis and Applications, 58, 135–146.
- Kumar, R. (1992). Fuzzy vector spaces and fuzzy cosets, Fuzzy Sets and Systems, 45, 109–116.
- Lubczonok, P. (1990). Fuzzy vector spaces, Fuzzy Sets and Systems, 38, 329–343.
- Malik, D.S. & Mordeson, J.N.(1991).Fuzzyvectorspaces, Inform.Sci., 55(1-3), 271–281.
- Mondal, S. (2012). Interval-valued fuzzy vector space, Annals of Pure and Applied Mathematics, 2 (1), 86–95.
- Mordeson, J. N. (1993). Bases of fuzzy vector spaces, Inform. Sci., 67 (1–2), 87–92.
- Pradhan, R., & Pal, M. (2012). Intuitionistic fuzzy linear transformations, Annals of Pure and Applied Mathematics, 1 (1), 57–68.
- Pradhan, R., & Pal, M. (2014). Solvability of system of intuitionistic fuzzy linear equations, International Journal of Fuzzy Logic Systems, 4 (3), 13–24.
- Shi, F. G. & Huang, C. E. (2010). Fuzzy bases and the fuzzy dimension of fuzzy vector space, Mathematical Communications, 15 (2), 303–310.
- 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.
|
|