Analyzing KANSEI from facial expressions with fuzzy quantification theory II

There is no direct translation for Kansei into English, however the creator of the Kansei engineering methodology describes Kansei as "the consumer\´s psychological feeling" towards a product. Here we describe an application where a picture presentation system was applied to define the properties of facial expressions. Instead of analyzing facial expressions of an individual to determine his emotional state, proposed system introduces fuzzy quantification theory II to build a membership function that describes the emotions induced in a subject after the presentation of small set of facial expressions. Using type-II fuzzy quantification theory, the relationship between induced emotions and facial features is linearized by solving a dense generalized eigenvalue problem. As the matrices are ill-conditioned and indefinite, the theory describing the possible solutions of the eigenvalue problem gets complicated. After a generalization of Fix and Heiberger\´s algorithm is adapted to tackle the problem, facial expressions are sorted on the real number axis and membership functions of two subjects are analyzed.