A New Algorithm for Fuzzy Linear Regression with Crisp Inputs and Fuzzy Output

Abstract: In this work, the parameters of fuzzy linear regression based on the least squares approach is computed by ST-decomposition method. This method is not an iterative technique, however, it is a powerful method for nonsingular coefficient matrices. Numerical examples are at the end of this paper to illustrate the performance of the new method

A Flexible Fuzzy Regression Method for Addressing Nonlinear Uncertainty on Aesthetic Quality Assessments

Development of new products or services requires knowledge and understanding of aesthetic qualities that correlate to perceptual pleasure. As it is not practical to develop a survey to assess aesthetic quality for all objective features of a new product or service, it is necessary to develop a model to predict aesthetic qualities. In this paper, a fuzzy regression method is proposed to predict aesthetic quality from a given set of objective features and to account for uncertainty in human assessment. The proposed method overcomes the shortcoming of statistical regression, which can predict only quality magnitudes but cannot predict quality uncertainty. The proposed method also attempts to improve traditional fuzzy regressions, which simulate a single characteristic with which the estimated uncertainty can only increase with the increasing magnitudes of objective features. The proposed fuzzy regression method uses genetic programming to develop nonlinear structures of the models, and model coefficients are determined by optimizing the fuzzy criteria. Hence, the developed model can be used to fit the nonlinearities of sample magnitudes and uncertainties. The effectiveness and the performance of the proposed method are evaluated by the case study of perceptual images, which are involved with different sampling natures and with different amounts of samples. This case study attempts to address different characteristics of human assessments. The outcomes demonstrate that more robust models can be developed by the proposed fuzzy regression method compared with the recently developed fuzzy regression methods, when the model characteristics and fuzzy criteria are taken into account