Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several alpha-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.
Fuzzy regression models are developed to construct the relationship between explanatory variables and responses in a fuzzy environment. In order to increase the explanatory performance of the model, the least-squares method is applied to determine the numeric coefficients based on the concept of distance. Unlike most existing approaches, the numeric coefficients in the proposed model can have negative values. The proposed model minimizes total estimation error in terms of the sum of the average squared distance between the observed and estimated responses based on a few α-cuts. The proposed approach is not limited to triangular fuzzy numbers; it can be used to carry out a large number of fuzzy observations efficiently because the model is based on traditional statistical methods. Comparisons with existing methods show that based on the total estimation error using the mean squared error and Kim and Bishu's criterion, the explanatory performance of the proposed model is satisfactory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.