Development of a Tw-norm based Novel Fuzzy Regression Model

Authors

  • B. Pushpa 1. Research Scholar, Manonmaniam Sundaranar University. Tirunelveli, India. 2. Department of Mathematics, Panimalar Institute of Technology, Chennai, India.
  • S. Muruganandam Department of Mathematics, SRM-TRP Engineering College, Trichy, India

Keywords:

Weakest t-norm, Fuzzy regression, Symmetric difference

Abstract

The weakest t-norm (Tw-norm) based novel fuzzy regression model is developed using the concept of symmetric difference.  The proposed model will be useful in a realistic environment and improve upon the traditional fuzzy regression. The traditional system usually adopts alpha cut operations for its calculations.  Here the Tw- norm based operations are used, to reduce the width of the estimated responses which will give exact prediction. Fuzzy linear regression analysis can be seen as an optimization problem where the aim is to derive a model which fits the given dataset.  The proposed fuzzy regression analysis uses the extended objective function which is insensitive to the outlier data and the performance of the method is illustrated with different examples.

 

References

H. Tanaka, S. Uejima, and A. Asai, “Linear regression analysis with fuzzy model,†IEEE Transactions on Systems, Man and Cybernetics, vol. 12, pp. 903–907, 1982.

M. M. Nasrabadi and E. Nasrabadi, “A mathematical-programming approach to fuzzy linear regression analysisâ€, Applied Mathematics and Computation, vol. 55, no. 3, pp. 873–881, 2004.

P. Diamond, “Fuzzy least squaresâ€, Information Sciences, vol. 46, no. 3, pp. 141–157, 1988.

Wu B. & Tseng N. F, (2002) “A new approach to fuzzy regression models with application to business cycle analysisâ€, Fuzzy Sets and Systems, Vol. 130, pp. 33–42.

C. Kao and C.-L. Chyu, “A fuzzy linear regression model with better explanatory power,†Fuzzy Sets and Systems, vol. 126, no. 3, pp. 401–409, 2002.

C. Kao and C.-L. Chyu, “Least-squares estimates in fuzzy regression analysisâ€, European Journal of Operational Research, vol. 148, no. 2, pp. 426–435, 2003

B. Kim and R. R. Bishu, “Evaluation of fuzzy linear regression models by comparing membership functions,†Fuzzy Sets and Systems, vol. 100, no. 1-3, pp. 343–352, 1998

E. S. Lee and P.-T. Chang, “Fuzzy linear regression analysis with spread un- constrained in sign,†Computers and Mathematics with Applications, vol. 28, no. 4, pp. 61–70, 1994

Torabi H, & Behboodian J, (2007) “Fuzzy least absolutes estimates in linear regression modelsâ€, Communi. Stat. – Theory methods, Vol. 36, pp. 1935-1944L.-H.

Chen and C.-C. Hsueh, “A mathematical programming method for for- mulating a fuzzy regression model based on distance criterion,†IEEE Trans- actions on Systems, Man, and Cybernetics-part B: Cybernetics, vol. 37, no. 3, pp. 705–712, 2007.

Choi S. H. & Buckley J. J, (2008) “Fuzzy regression using least absolute deviation estimatorsâ€, Soft Comput. Vol. 12, pp. 257-263.

Taheri S. M. & Kelkinnama M, (2012) “Fuzzy linear regression based on least absolute deviationsâ€,Iranian J. fuzzy system Vol. 9, pp. 121-140.

Hong D.H., Lee S. & Do D.Y, (2001) “Fuzzy linear regression analysis for fuzzy input-output data using shape preserving operationsâ€, Fuzzy sets Syst. Vol.122, pp. 513-526.

L. A. Zadeh, “Fuzzy sets,†Information and Control, vol. 8, pp. 338–353, 1965.

D.Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic press, Newyork , 1980

D.H. Hong and H.Y Do, Fuzzy system reliability analysis by the use of (the weakest t-norm) on the fuzzy number arithmetic operations, Fuzzy sets and systems, 90(1997)307-316.

Hsieh C.H. & Chen. S.H, (1999) “Similarity of generalized fuzzy numbers with graded mean integration representationâ€, in Proceed. of 8th intn. fuzzy system association world congr., vol2, Taiwan, Republic of China, pp. 551-555.

Xu R. & Li C, (2001) “Multidimensional least- squares fitting with a fuzzy modelâ€, Fuzzy sets and systems, Vol. 119, pp. 215-223.

R.K. Singh, Himadri Ghosh, Possibility and necessity measure for fuzzy linear regression analysis: An Application, Journal of Indian Soc. Agricultural statistics, 62(1), 2008, pp. 19-25

Shih-Pin Chen, Jr-Fong Dang , “A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy, Information Sciences, 178 (2008) 3973–3988

L.-H. Chen and C.-C. Hsueh, “Fuzzy regression models using the least squares method based on the concept of distance,†IEEE Transations on Fuzzy Systems, vol. 17, no. 6, pp. 1259–1272, 2009.

H. Hassanpour, A Goal Programming Approach to Fuzzy Linear Regression. PhD thesis, Shahid Bahonar University of Kerman, Kerman, Iran, 2008.

H. Shakouri and R. Nadimi, “A novel fuzzy linear regression model based on a non-equality possibility index and optimum uncertainty,†Applied Soft Computing, vol. 9, no. 2, pp. 590–598, 2009

Hong D.H and C.Hwang, “Support vector Fuzzy regression machines, Fuzzy sets and systems, vol.138, No.2, pp.271-281, 2003.

A.Maleki , E.Pasha and T.Razzaghnia, “Possibility Linear regression analysis with Trapezoidal fuzzy dataâ€, World applied sciences Journal, 18,(1), pp. 37-42, 2012.

W.-L. Hung and M.-S. Yang, “An omission approach for detecting ouliers in fuzzy regression models,†Fuzzy Sets and Systems, vol. 157, pp. 3109–3122, 2006.

Y.-S. Chen, “Outliers detection and confidence interval modification in fuzzy regression,†Fuzzy Sets and Systems, vol. 119, pp. 252–279, 2001

M. Sakawa and H. Yano, Fuzzy linear regression and its applications, pp. 61–80.Fuzzy Regression Analysis, Heidelberg: Physica-Verlag, 1992.

M.Hojati, C.R.Bector and K.Smimou, A simple method for computation of fuzzy linear regression, European Journal of operational Research, Vol.166, No.1, pp. 172-185, 2005.

J.Lu and R. Wang, An enhanced Fuzzy linear regression model with more flexible spreads, Fuzzy sets and systems, Vol. 160, No.17, pp. 2505-2523, 2009.

M.S.Yang and T.S.Lin, Fuzzy least squres linear regression analysis for fuzzy input and fuzzy output data, Fuzzy sets and systems, Vol.126, No.3, pp.389-399, 2002.

Downloads

Published

2013-12-13

How to Cite

Pushpa, B., & Muruganandam, S. (2013). Development of a Tw-norm based Novel Fuzzy Regression Model. Asian Journal of Fuzzy and Applied Mathematics, 1(4). Retrieved from https://www.ajouronline.com/index.php/AJFAM/article/view/541

Issue

Vol. 1 No. 4 (2013): December 2013

Section

Articles

License

  • Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
  • It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
  • The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
  • The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
  • The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.