CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

Estimation of Confidence Level ‘h’ in Fuzzy Linear Regression Analysis using Shape Preserving Operations

by B. Pushpa, R. Vasuki
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 68 - Number 17
Year of Publication: 2013
Authors: B. Pushpa, R. Vasuki
10.5120/11671-7279

B. Pushpa, R. Vasuki . Estimation of Confidence Level ‘h’ in Fuzzy Linear Regression Analysis using Shape Preserving Operations. International Journal of Computer Applications. 68, 17 ( April 2013), 19-25. DOI=10.5120/11671-7279

@article{ 10.5120/11671-7279,
author = { B. Pushpa, R. Vasuki },
title = { Estimation of Confidence Level ‘h’ in Fuzzy Linear Regression Analysis using Shape Preserving Operations },
journal = { International Journal of Computer Applications },
issue_date = { April 2013 },
volume = { 68 },
number = { 17 },
month = { April },
year = { 2013 },
issn = { 0975-8887 },
pages = { 19-25 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume68/number17/11671-7279/ },
doi = { 10.5120/11671-7279 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:28:07.661199+05:30
%A B. Pushpa
%A R. Vasuki
%T Estimation of Confidence Level ‘h’ in Fuzzy Linear Regression Analysis using Shape Preserving Operations
%J International Journal of Computer Applications
%@ 0975-8887
%V 68
%N 17
%P 19-25
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this discussion is to introduce a new fuzzy regression model, based on the distance between the outputs of the model in terms of its measurements along with the optimal confidence level 'h' using the shape preserving operations. Simple fuzzy regression models with fuzzy input- fuzzy outputs are also considered in which the coefficients of the models are themselves triangular fuzzy numbers. In the proposed method, the arithmetic operations are based on Tw norm, which preserves the shape during multiplication of two fuzzy numbers and it also satisfies the scale independent property. The numerical examples indicate that the proposed method has effective performance, especially when the data set includes some outliers.

References
  1. R. E. Bellman and L. A. Zadeh, "Decision making in a fuzzy environment", Manage. Sci. Vol. 17B, Pp. 141-164, 1970.
  2. H. Tanaka, S. Ueigma and K. Asai, "Linear regression analysis with fuzzy mode", IEEE Trans Systems, Man Cybernet. Vol. 12, Pp. 903-907, 1982.
  3. H. Tanaka, "Fuzzy data analysis by possibilistic linear models", Fuzzy Sets and Systems, Vol. 24, Pp. 363-375, 1987.
  4. H. Tanaka and J. Watada, "Possibilistic linear systems and their applications to the linear regression model", Fuzzy Sets and Systems, Vol. 27, Pp. 275-289, 1988.
  5. H. Tanaka, I. Hayashi and J. Watada, "Possibilistic linear regression analysis for fuzzy data", Eur. J. Opera. Res. Vol. 40, Pp. 389-396, 1980.
  6. D. T. Redden and W. H. Woodall, "Properties of certain fuzzy linear regression models", Fuzzy Sets and Systems, Vol. 44, Pp. 361-375, 1994.
  7. A. Celmins, "Least squares model fitting to fuzzy vector data", Fuzzy sets and systems, Vol. 22, Pp. 245-269, 1987.
  8. P. Diamond, "Fuzzy least squares", Inform. Sci. , Vol. 46, Pp. 141-157, 1988.
  9. D. H. Hong, S. Lee and D. Y. Do, "Fuzzy linear regression analysis for fuzzy input-output data using shape preserving operations", Fuzzy sets and Syst. Vol. 122, Pp. 513-526, 2001a.
  10. J. Mohammadi and S. M. Taheri, "Pedomodels fitting with fuzzy least squares regression", Iranian Journal Fuzzy Syst. , Vol. 1, Pp. 45- 61 2004.
  11. R. Coppi, P. D. Urso, P. Giordani and A. Santoro, "Least squares estimation of a linear regression model with LR fuzzy response", Comput. Stat. Data anal. Vol. 51, Pp. 267-286, 2006.
  12. A. R. Arabpour and M. Tata, "Estimating the parameters of a Fuzzy Linear Regression model", Iranian J. Fuzzy syst. Vol. 5, Pp. 1-20, 2008.
  13. H. K. Kim, J. H. Yoon and J. H. Li, "Asymptotic properties of least squares estimation with fuzzy observations", Infor. Sci. Vol. 178, Pp. 439-451, 2008.
  14. J. Lu and R. Wang, "An enhanced fuzzy linear regression model with more flexible spreads", Fuzzy sets and Syst. Vol. 160, Pp. 2505-2523, 2009.
  15. P. T. Chang and E. S. Lee, "Fuzzy least absolute deviations regression based on the ranking of fuzzy numbers", Proc. IEEE world congress on computational intelligence, Pp. 1365-1369, 1994.
  16. K. J. Kim, D. H. Kim and S. H. Choi, "Least absolute deviation estimator in fuzzy regression", J. Appl. Math. Comput. Vol. 18, Pp. 649-656, 2005.
  17. H. Torabi and J. Behboodian, " Fuzzy least absolutes estimates in linear regression models", Communi. Stat. – Theory methods, Vol. 36, Pp. 1935-1944, 2007.
  18. L. H. Chen and C. C. Hsueh, "A mathematical programming method for formuation a fuzzy regression model based on distance criterion", IEEE Trans. Syst. Man Cybernet. Vol. B 37, Pp. 705-712, 2007.
  19. S. H. Choi and J. J. Buckley, "Fuzzy regression using least absolute deviation estimators", Soft Comput. Vol. 12, Pp. 257-263, 2008.
  20. S. M. Taheri and M. Kelkinnama, "Least absolute regression", Proc. 4th international IEEE conference on intelligent systems, varna Bulgaria, Vol. 11, Pp. 55-58, 2008.
  21. S. M. Taheri, and M. Kelkinnama, "Fuzzy linear regression based on least absolute deviations", Iranian J. fuzzy system, Vol. 9, Pp. 121-140, 2012.
  22. C. H. Ling, "Representation of associative functions", Publicationes Mathematicae – Debrecen, Vol. 12, Pp. 189-212, 1965.
  23. L. A. Zadeh, "Fuzzy sets as a basis for a theory of possibility", Fuzzy sets and Syst. , Vol. 1, Pp. 3-28, 1988.
  24. D. H. Hong, "Shape preserving multiplication of fuzzy intervals", Fuzzy sets and Syst,. Vol. 123, Pp. 81-84, 2001.
  25. D. H. Hong, "On shape preserving addition of fuzzy intervals", Journal of Mathematical Analysis and applications, Vol. 267, Pp. 369-376, 2002.
  26. A. Kolsevera, "Additive preserving the linearity of fuzzy intervals", Tata mountains Math. Publi. Vol. 6, Pp. 75-81, 1994.
  27. R. Mesiar, "Shape preserving addition of fuzzy intervals", Fuzzy sets and Syst. , Vol. 86, Pp. 73-78, 1997.
  28. D. H. Hong and H. Y. Do, "Fuzzy system reliability analysis by the use TW (the weakest norm) on fuzzy arithmetic operations", Fuzzy Sets and Systems. , Vol. 90, Pp. 307-316, 1997.
  29. E. Modarres, E. Nasrabadi and M. M. Nasrabedi, "Fuzzy linear regression models with least square error", Applied mathematics and Computation, Vol. 163, Pp. 977-989, 2005.
  30. Y. S. Chen, "Outliers detection and confidence interval modification in fuzzy regression", Fuzzy sets and systems, Vol. 119, Pp. 252-279, 2001.
  31. C. H. Hsieh and S. H. Chen, "Similarity of generalized fuzzy numbers with graded mean integration representation", Proceedings of Eighth international fuzzy system association world congress, Taipei, Taiwan, Republic of China, Vol. 2, Pp. 551-555, 1999.
  32. M. M. Nasrabedi and E. Nasrabedi, "Mathematical programming approaches to fuzzy linear regression analysis", Appl. Math. Comput. , Vol. 155, Pp. 873-881, 2004.
  33. D. H. Hong, L. K. Song and H. Y. Do, "Fuzzy least square linear regression analysis using shape preserving operations", Inform. Sci. , Vol. 138, Pp. 185- 193, 2001b.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy linear regression Tw norm based arithmetic operations Fuzzy input and fuzzy output

Powered by PhDFocusTM