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.

After total knee replacement, the model-based Roentgen stereophotogrammetric analysis (RSA) technique has been used to monitor the status of prosthetic wear, misalignment, and even failure. However, the overlap of the prosthetic outlines inevitably increases errors in the estimation of prosthetic poses due to the limited amount of available outlines. In the literature, quite a few studies have investigated the problems induced by the overlapped outlines, and manual adjustment is still the mainstream. This study proposes two methods to automate the image processing of overlapped outlines prior to the pose registration of prosthetic models. The outline-separated method defines the intersected points and segments the overlapped outlines. The feature-recognized method uses the point and line features of the remaining outlines to initiate registration. Overlap percentage is defined as the ratio of overlapped to non-overlapped outlines. The simulated images with five overlapping percentages are used to evaluate the robustness and accuracy of the proposed methods. Compared with non-overlapped images, overlapped images reduce the number of outlines available for model-based RSA calculation. The maximum and root mean square errors for a prosthetic outline are 0.35 and 0.04 mm, respectively. The mean translation and rotation errors are 0.11 mm and 0.18°, respectively. The errors of the model-based RSA results are increased when the overlap percentage is beyond about 9%. In conclusion, both outline-separated and feature-recognized methods can be seamlessly integrated to automate the calculation of rough registration. This can significantly increase the clinical practicability of the model-based RSA technique.