Fuzzy Development of Multiple Response Optimization

Abstract

This paper proposes a developed approach to Multiple Response Optimization (MRO) in two categories; responses without replicates and with some replicates based on fuzzy concepts. At first, the problem without any replicate in responses is investigated, and a fuzzy Decision Support System (DSS) is proposed based on Fuzzy Inference System (FIS) for MRO. The proposed methodology provides a fuzzy approach considering uncertainty in decision making environment. After calculating desirability of each response, total desirability of each experiment is measured by using values of each response desirability, applying membership function and fuzzy rules expressed by experts. Then Response Surface Methodology (RSM) is applied to fit a regression model between total desirability and controllable factors and optimize them. Next, a methodology is proposed for MRO with some replicates in responses which optimizes mean and variance simultaneously by applying fuzzy concepts. After introducing Deviation function based on robustness concept and using desirability function, a two objective problem is constituted. At last, a fuzzy programming is expressed to solve the problem applying degree of satisfaction from each objective. Then the problem is converted to a single objective model with the goals of increasing desirability and robustness simultaneously. The obtained optimum factor levels are fuzzy numbers so that a bigger satisfactory region could be provided. Finally, two numerical examples are expressed to illustrate the proposed methodologies for multiple responses without replicates and with some replicates.