Title of paper:
|
Multi-parameter temporal intuitionistic fuzzy sets
|
Author(s):
|
Rangasamy Parvathi
|
Department of Mathematics, Vellalar College for Women, Erode-638 012, Tamil Nadu, India
|
paarvathis@rediffmail.com
|
C. Radhamani
|
Kongu Arts and Science College, Erode-638 107, Tamil Nadu, India
|
palaniradhu@yahoo.co.in
|
|
Published in:
|
"Notes on Intuitionistic Fuzzy Sets", Volume 22 (2016) Number 1, pages 35-47
|
Download:
|
PDF (264 Kb, File info)
|
Abstract:
|
Fuzzy sets and intuitionistic fuzzy sets handle uncertainty and vagueness which Cantorian sets could not handle. Temporal intuitionistic fuzzy set with a time domain is an extension of intuitionistic fuzzy set and is useful in dealing with uncertainty and vagueness present in the time dependent real environment. In this paper, a new type of intuitionistic fuzzy set called multiparameter temporal intuitionistic fuzzy set is proposed and it’s operations are defined. Further, extended triangular membership and non-membership functions for temporal intuitionistic fuzzy sets and multi-parameter temporal intuitionistic fuzzy sets are defined. Geometric interpretation of a temporal intuitionistic fuzzy set is also dealt with a suitable example.
|
Keywords:
|
Temporal intuitionistic fuzzy sets, Multi-parameter temporal intuitionistic fuzzy sets, Extended triangular intuitionistic fuzzification functions.
|
AMS Classification:
|
11D79, 11H06.
|
References:
|
- Atanassov, K. T. (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia.
- Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96.
- Atanassov, K. T. (1999) Intuitionistic fuzzy sets: Theory and Applications, Physica-Verlag, Heidelberg.
- Atanassov, K. T. (2012) On Intuitionistic fuzzy sets theory, Springer, Berlin, Heidelberg.
- Atanassov, K. T., E. Szmidt & J. Kacprzyk. (2008) On intuitionistic fuzzy multi-dimensional sets, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 7, 1-6.
- Atanassov, K. T. , E. Szmidt, J. Kacprzyk & P. Rangasamy. (2008) On intuitionistic fuzzy multi-dimensional sets. Part 2. In: Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics.Vol.I: Foundations, Academic Publishing House EXIT, Warsaw, 43-51.
- K.T. Atanassov, E. Szmidt & J. Kacprzyk. (2010) On intuitionistic fuzzy multi-dimensional sets. Part 3. In: 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. T., E. Szmidt & J. Kacprzyk. (2011) On intuitionistic fuzzy multi-dimensional sets. Part 4. Notes on Intuitionistic Fuzzy Sets, 17(2), 1-7.
- Dubois, D. & H.Prade. (1980) Fuzzy sets and systems:Theory and Applications, Academic Press, New York.
- Pedrycz, W. (1994) Why triangular membership functions?, Fuzzy Sets and Systems, 64, 21-30.
- Shaw, A. K. & T. K. Roy. (2012) Some arithmetic operations on triangular intuitionistic fuzzy number and its application on reliability evaluation, International Journal of Fuzzy Mathematics and Systems, 2(4) , 363-382.
- 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.
|
|