Optimization of multiple responses in the Taguchi method using fuzzy regression

Abstract

AbstractIn reality, the behavior of processes is sometimes vague and the observed data is irregular. This research proposes an approach for optimizing fuzzy multiple responses using fuzzy regression. In this approach, each response repetition is transformed into a signal to noise ratio then modeled using statistical multiple regression. A trapezoidal fuzzy regression model is formulated for each response utilizing the statistical regression coefficients. The most desirable response values and the deviation function are determined for each response. Finally, four optimization models are formulated for the trapezoidal membership fuzzy number to obtain the optimal factor level at each number. Two case studies are adopted for illustration, where excluding response fuzziness will result in misleading optimal factor settings if solved by the traditional optimization techniques. In conclusion, the proposed approach based on fuzzy regression approach can successfully optimize fuzzy multiple responses in a wide range of manufacturing applications on the Taguchi's method. Moreover, compared to other approaches, such as data envelopment analysis and grey relational analysis, the proposed approach has the distinct advantage of being able to generate models using only a small number of experimental data sets and minimizing inherent variations.