A new approach for fuzzy multiple regression with fuzzy output

In regression analysis, in order to achieve the consistent estimations and predictions, certain statistical assumptions have to be provided. When faced with problems such as insufficient observations, non-normality of error term, autocorrelation and heteroscedasticity, the specific techniques are applied to resolve them. If the mentioned problems are not solved by statistical techniques, either data set are changed or the certain observations are discarded. However, changing data set or elimination of certain observations causes loss of knowledge for decision makers. In such a situation, fuzzy regression is a useful alternative vs. the least squares method (LSM) and the classic probabilistic methods. Nevertheless, there are some deficiencies in fuzzy regression approaches, such as selecting h-cut level, finding efficient solutions and using excess constraint. In this study, to overcome problem of h-cut level, to achieve the efficient solutions and to integrate both the central tendency of LSM and the possibilistic property of fuzzy regression, a new constrained non-linear programming approach is proposed. In application part, the proposed models are compared with LSM, linear and quadratic models of Tanaka et al. and quadratic approach of Donoso et al. by means of two different data set.