MODELING AND OPTIMIZATION OF MULTI-RESPONSE SURFACE PROBLEMS WITH FUZZY APPROACH

Abstract

The most widely used approach for solving multi response surface problems is response surface methodology. It is thought to be that the response surface methodology is inadequate for evaluation of unexplained vagueness in real world problems. Therefore in the study, fuzzy approach is proposed as an alternative to solve the multi response surface problems. The main aim of this study is to represent the applicability of the fuzzy approach for solving of the multi-response problems in which the probability distributions of the response variables cannot be determined. At the modeling stage, the fuzzy least squares regression analysis, based on Diamond's distance metric, is used. In the optimization stage, the problem is considered as a fuzzy multi-objective optimization problem. Nondominated Sorting Genetic Algorithm-II (NSGA-II), defined in the literature, is adapted by using centroid index fuzzy ranking approach then called Fuzzy NSGA-II (FNSGA-II). Fuzzy Pareto solution set is obtained by optimizing the problem, which is composed of fuzzy objective functions, with FNSGA-II. The proposed fuzzy solution approaches are applied on a data set defined in the literature. Thus, it is seen that an obtained fuzzy Pareto solution is a set of acceptable different response values for the performed multi-response experiments at the defined levels of input variables.