Convex hull approach to fuzzy regression analysis and its application to oral age model

Fuzzy multivariate analyses, including linear regression analysis, fuzzy time-series analysis, fuzzy possibilistic linear models, etc., are formulated in terms of the extension principle. One objective of a fuzzy linear regression model is to build a model using fuzzy numbers which represent the possibilities included in the system. In this paper, in order to overcome this issue, we propose an effective method to drastically reduce the number of samples in terms of the convex hull method. Stress is placed on the fact that (1) only those vertex points obtained by the convex hull are constraints on linear programming, that (2) the convex hull approach works efficiently in real-time data gathering, and that (3) the number of vertices obtained by the convex hull will not increase much. Using a numerical example, we show the difference between the convex hull approach and the conventional approach to reduce the number of samples in building the model. We also illustrate and build an oral age model using real data on patients´ ages and their number of sound teeth, based on the convex hull method