Fuzzy Clustering with Viewpoints

In this study, we introduce a certain knowledgeguided scheme of fuzzy clustering in which domain knowledge is represented in the form of so-called viewpoints. Viewpoints capture a way in which the user introduces his/her point of view at the data by identifying some representatives, which, being treated as externally introduced prototypes, have to be included in the clustering process. More formally, the viewpoints (views) augment the original, data-based objective function by including the term that expresses distances between data and the viewpoints. Depending upon the nature of domain knowledge, the viewpoints are represented either in a plain numeric format (considering that there is a high level of specificity with regard to how one establishes perspective from which the data need to be analyzed) or through some information granules (which reflect a more relaxed way in which the views at the data are being expressed). The detailed optimization schemes are presented, and the performance of the method is illustrated through some numeric examples. We also elaborate on a way in which the clustering with viewpoints enhances fuzzy models and mechanisms of decision making in the sense that the resulting constructs reflect the preferences and requirement that are present in the modeling environment.