The Taguchi method is a powerful method of solving quality problems in various fields of engineering. However, this method was developed to optimize single-response processes. In many multi-response optimization problems, the important response is determined subjectively, based on knowledge or experience. However, using only exact numbers to represent this importance is problematic, because there is uncertainty and vagueness. The concept of intuitionistic fuzzy sets (IFSs) is a powerful method for characterization, using a membership function and a non-membership function. This paper proposes an efficient VIKOR method that optimizes multi-response problems in intuitionistic fuzzy environments. The importance weights of various responses are evaluated in terms of IFSs. In the proposed method, the similarity measure between IFSs is used to determine the crisp weights of the responses. This scheme eliminates the need for complicated intuitionistic fuzzy arithmetic operations and increases efficiency in solving multi-response optimization problems in intuitionistic fuzzy environments. Two case studies: plasma-enhanced chemical vapor deposition and a double-sided surface mount technology electronic assembly operation are used to demonstrate the effectiveness of the proposed method.

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.