A study on fuzzy linear regression

Abstract

The fuzzy set theory was first proposed by Zadeh in 1965. The fuzzy linear regression was proposed by Tanaka et al in 1982. Many different fuzzy regression approaches have been proposed by different researchers. Since then this subject has drawn much attention from more and more people concerned. There are two approaches in fuzzy regression analysis, one is linear programming based method and another one is fuzzy least square method. The first method is based on minimizing fuzziness as an optimal criterion and the second method is fuzzy least square method, which is based on the notion of the distance between the predicted fuzzy outputs and the observed fuzzy outputs and the goodness-of-fit. In this work, we have used the Tanaka s possibilistic fuzzy linear regression. We have considered a symmetric triangular fuzzy number and have incorporated the concept of fuzzy linear system into the fuzzy linear regression. The fuzzy coefficients involved in the regression line are determined using normalized equations and the fuzzy lines are determined. A numerical example is solved to illustrate the efficiency of the proposed method. Next the fuzzy linear regression equation is applied for the waste water treatment to identify the chemical factors. Iv An algorithm for the newly formulated fuzzy linear regression is developed. Data of oral cancer patients have been collected and used in the algorithm to identify the risk factors involved in oral cancer. The classical correlation is converted into fuzzy correlation model. The fuzzy lines of y on x and x on y are obtained. The collected oral cancer data are utilized to identify the risk factors of oral cancer. The data employed in fuzzy linear regression, algorithm and fuzzy correlation methods have given reasonably good results in the prediction of risk factors involved in the oral cancer. These methods can serve as a powerful mathematical tool to predict the risk factors involved in the chronic diseases in medical domain.