Multi-objective fuzzy regression:: a general framework

Previous research has shown that in some cases fuzzy regression may perform better than statistical regression. On the other hand, fuzzy regression has also been criticized because it does not allow all data points to influence the estimated parameters, it is sensitive to data outliers, and the prediction intervals become wider as more data are collected. Here, several multi-objective fuzzy regression (MOFR) techniques are developed to overcome these problems by enabling the decision maker to select a non-dominated solution based on the tradeoff between data outliers and prediction vagueness. It is shown that MOFR models provide superior results to existing fuzzy regression techniques; furthermore the existing fuzzy regression approaches and classical least-squares regression are specific cases of the MOFR framework. The methodology is illustrated with rainfall-runoff modeling examples; more specifically, fuzzy linear conceptual rainfall-runoff relationships, which are essential components of hydrologic system models, are analyzed here. Scope and purpose The purpose of this paper is to develop a multi-objective fuzzy regression (MOFR) tool to overcome the shortcomings of existing fuzzy regression approaches while keeping their good characteristics, and to study systems with uncertain elements, using the example of rainfall-runoff processes to illustrate the approach. Previous research has shown that fuzzy regression might perform better than statistical regression in the following cases: when the data set is insufficient to support statistical regression analysis, when statistical distributional assumptions cannot be justified, if the aptness of the regression model is poor, when human judgements are involved (Bardossy. Fuzzy Sets and Systems 1990;37:65-75; Tanaka et al. IEEE Transactions on Systems, Man and Cyberneties, 1982;12 (6):903-7). On the other hand, fuzzy regression has also been criticized because it does not allow all data points to influence the estimated parameters, it is sensitive to data outliers, and the prediction intervals become wider as more data are collected (Redden and Woodall. Fuzzy Sets and Systems 1994;64:361-75, 1996;79:203-11). Here, several MOFR techniques are developed to overcome these problems by enabling the decision maker to select a non-dominated solution based on the tradeoff between data outliers and prediction vagueness. The methodology is illustrated with rainfall-runoff modeling examples; more specifically, fuzzy linear conceptual rainfall-runoff relationships, which are essential components of hydrologic system models, are analyzed here. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.