Utilizing Fuzzy Linear Regression in Medical Data Analysis: A Comparative Study of FLR and FLSLR Models for Enhancing Regional Health Planning

Sufian Munther Salih; Ghufran  Khalil Joad

Sufian Munther Salih Department of Management Economics Banking, College of Business Economics, Al-Nahrain University, Baghdad, Iraq
Ghufran Khalil Joad Department of Production and Metallurgy, University of Technology, Baghdad, Iraq

Keywords: Fuzzy Linear Regression, Least Squares, Regional Planning,Sustainable Development, Osteoporosis

Abstract

This research deals with the planning study in using fuzzy linear regression in the cases of fuzzy; non-fuzzy data, where the analysis was conducted using several methods, including fuzzy linear regression (FLR) and modified fuzzy linear regression, in counting up to the (FLR) method using least squares (FLSLR), in which linear programming (LP) was employed in the analysis process.The fuzzy parameters were estimated based on fuzzy and non-fuzzy data, and the regression idol was determined based on the concepts of fuzzy set theory. These methods were also applied in the medical field to accurate data on osteoporosis in a statistical study as part of the requirements for achieving regional planning, which is concerned with health population studies as an integral part of sustainable development, in which individual health is one of the most important variables affecting planning levels in general, where the researchers used this method, by measuring bone density using a DEXA device for thirty patients (10 males and 20 females). The study was conducted in the laboratories of the Department of Biomedical Engineering - College of Engineering - Al-Nahrain University.The results showed that the modified Tanaka model is more efficient than the FLR model, as it helps to elude the emergence of non-fuzzy given parameters. The FLSLR method also proved superior to FLR based on the degree of model affiliation, which enhances the accuracy and effectiveness of the estimation.

References

[1] B. Y. D. Al-Khayat, «Uncertainty through probability theory and the theory of fuzzy sets», Iraqi J. Stat. Sci. 631–184, 2004.
[2] R. F. Gunst and R. L. Mason, Regression Analysis and its Application. New York: Marcel Dekker, INC., 1980.
[3] D. T. Redden and W. H. Woodall, «Properties of Certain Fuzzy Linear Regression Methods», Fuzzy Sets Syst., т. 64, сс. 361–375, 1994.
[4] «Osteoporosis». 2002 year. http://www.chamclinic.com/edu/osteoporosis%20pre.doc
[5] W. L. Winston, Operations Research Applications of Algorithms. USA: Duxbury Press, 1994.
[6] A. A. S. Al-Muazawi, Operations Research. Beirut, Lebanon: Dar Al-Ulum Al-Hadithah, 1977.
[7] H. Moskowitz and K. Kim, «On assessing the H Value in Fuzzy Linear Regression», Fuzzy Sets Syst., . 58, . 303–327, 1993.
[8] P. B. McCauley and H. Wang, «Measurement of Cumulative Trauma Disorders Risks of Tasks Using Fuzzy linear regression», IEEE Trans. Syst. Man Cybern., . 29, . 1, 1–14, 1999.
[9] H. Tanaka, S. Uejima, and K. Asai, «Linear Regression Analysis with Fuzzy Model», IEEE Trans Syst. Man Cybernet, . 12,. 903–907, 1982.
[10] H.-F. Wang and R.-C. Tsaur, «Insight of a Fuzzy Regression Model», Fuzzy Sets Syst.,. 112, . 355–369, 2000.
[11] H. A. Ballout, «Health and Life. Osteoporosis». 2001 г.
[12] K. J. Kim, H. Moskowitz, and M. Koksalan, «Fuzzy Versus Statistical Linear Regression», Eur J Oper Res, . 92, . 417–434, 1996.
[13] H. T. Lee and S. H. Chen, «Fuzzy Regression Model with Fuzzy Input and Output Data for Manpower Forecasting», Fuzzy Sets Syst., . 119, . 205–213, 2001.
[14] Y.-H. Chang and B. M. Ayyub, «Fuzzy Regression Methods A Comparative Assessment», Fuzzy Sets Syst., . 119, . 187–203, 2001.
[15] A. Kandel, Fuzzy Mathematical Techniques with Applications. England: Addison-Wesley Publishing Company, 1986.
[16] P.-T. Chang and E. S. Lee, «Fuzzy Linear Regression with Spreads Unrestricted in Sign», Comput Math Appl, . 28, . 61–70, 1994.
[17] B. Heshmaty and A. Kandel, «Fuzzy Linear Regression and Its Applications to Forecasting in Uncertain Environment», Fuzzy Sets Syst., . 15, . 159–191, 1985.
[18] H. Tanaka, «Fuzzy Data Analysis by Possibilistic Linear Models», Fuzzy Sets Syst., 24, . 363–375, 1987.
[19] D. A. Savic and W. Pedrycz, «Evaluation of Fuzzy Linear Regression Models», Fuzzy Sets Syst., 39, . 51–63, 1991.
[20] C. Haslett, E. R. Chilver, J. A. A. Hunter, and N. A. Boon, Davidson’s Principles and Practice of Medicine. U.K.: Harcourt Brace and Company, 1999.
[21] M. Hojati, C. R. Bector, and K. Smimou, «A Simple Method for Computation of Fuzzy Linear Regression», Eur. J. Oper. Res., 2005.
[22] M. M. Nasrabadi and E. Nasrabadi, «A Mathematical Programming Approach to Fuzzy Linear Regression Analysis», Appl. Math. Comput., . 155, 3, . 873–881, 2004.