In considering an engineer’s opinion in optimizing a multiresponse problem, attention must be paid to vagueness and hesitancy in revealing his or her perceptions of a fuzzy concept such as “importance” or “excellence.” Recently, the notion of intuitionistic fuzzy sets has been found to be more effective than that of fuzzy sets for dealing with vagueness and hesitancy. However, little research has been done on optimizing multiresponse problems using intuitionistic fuzzy sets. This article focuses on state systems and explores optimization of multiresponse problems with intuitionistic fuzzy sets, in which the importance of each response is given by an engineer as intuitionistic fuzzy set. A novel optimization procedure is proposed that is based on a measure of similarity between intuitionistic fuzzy sets. To demonstrate the efficiency and effectiveness of the proposed method, two case studies are provided–one of plasma-enhanced chemical vapor deposition and the other the copper chemical mechanical polishing.
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