[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5391/JKIIS.2003.13.5.571

Fuzzy least squares polynomial regression analysis using shape preserving operations

Hong, Dug-Hun (Department of Mathematics, Myongji University)
Hwang, Chang-Ha (Department of Statistical Information, Catholic University of Daegu)
Do, Hae-Young (Department of Statistics, Kyungpook National University)

Publication Information

Journal of the Korean Institute of Intelligent Systems / v.13, no.5, 2003 , pp. 571-575 More about this Journal

Abstract

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input--output data using shape preserving operations for least-squares fitting. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using mixed nonlinear program.

Keywords

Polynomial fuzzy regression; shape-preserving operations; membership function; least-square fitting;

Citations & Related Records

Reference

1	R. Mesiar, Shape preserving additions of fuzzy intervals, Fuzzy Sets and Systems, vol. 86, pp. 73-78, 1997. DOI ScienceOn
2	H. Tanaka, S. Uejima and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Systems Man Cybernet. pp. 903-907, 1982.
3	A. Kolesarova, Additive preserving the linearity of fuzzy intervals, Tetra Mountains Math. Publ. vol. 6, pp. 75-81, 1995.
4	P. Diamond, Fuzzy least squares, Inform. Sci. vol. 46, pp. 141-157, 1998. DOI ScienceOn
5	D. H. Hong , S. Lee and H. Y. Do, Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations, Fuzzy Sets and Systems, vol. 122, pp. 157-170, 2001.
6	D. H. Hong, J. K. Song and D. H. Hong, Fuzzy least-squares linear regression analysis using shape preserving operations, Information Sciences, vol. 138, pp. 185-193, 2001. DOI ScienceOn
7	D. H. Hong and H. Y. Do, Fuzzy polynomial regression analysis using shape preserving operation, Korean J. of Comput. and App. Math., vol. 8, pp. 645-656, 2001.
8	A. Bardossy, R. Hagaman, L. Duckstein and I. Bogardi, Fuzzy least squares regression : Theory and application("Fuzzy Regression Analysis" J. Kacprzyk and M. Fedrizzi(eds), 1992 Omnitch Press, Warsaw and Physica-Verlag, Heidelberg, 181-193).
9	J. Kacprzyk and M. Fedrizzi, Fuzzy Regression Analysis(Physica-Verlag, Heidelberg, 1992).
10	D. H. Hong and H. Y. Do, Fuzzy system reliability analysis by the use of $T_{w}$ ( the weakest t-norm) on fuzzy number arithmetic operations, Fuzzy Sets and Systems, vol. 90, pp. 307-316, 1997. DOI ScienceOn
11	C. H. Ling, Representation of associative functions, Publ. Math. Debrecen, vol. 12, pp. 189-212, 1965.
12	A. Celmins, Apractical approach to nonlinear fuzzy regression, SIAM. J. Sci. Stat. Comput., vol. 12. No. 3. pp. 521-546, 1991. DOI
13	D. H. Hong, Shape preserving multiplication of fuzzy numbers, Fuzzy Sets and Systems vol.123, pp. 93-96, 2000.
14	P. Diamond and R. Korner, Extended fuzzy linear models and least square estimates, Computers Math. Applic. vol. 33, pp. 15-32, 1997.
15	L. A. Zadeh, Fuzzy sets, Inform. Control, vol. 8, pp.338-353, 1965. DOI
16	J. Buckley and T. Feuring, Linear and non-linear fuzzy regression: Evolutionary algorithm solutions, Fuzzy Sets and Systems, vol. 112, pp. 381-394, 2000. DOI ScienceOn