66 Fuzzy Clustering Regression Model and a Satisfying Solution for an LP Problem
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This work will employ methods from fuzzy regression models to build a fuzzy clustering regression model that can be used in statistical process control. Suppose that a subset D of Rn is a set of sampling points that represents n quality characteristics of K objects and a set S represents a fuzzy score space that provides ratings by experts on the characteristics of the K objects. The fuzzy ratings given by the experts can be described as a mapping f: D → S. Suppose further that a clustering can be preformed on D to generate q classes based upon the experts' ratings. Let C be the set of centers of the q clustering classes. Using a special method this work will generate a core mapping f0 from C to S based on the mapping f.Then extend the mapping f0 to a complete mapping f*: F → S. The extension mapping is the fuzzy clustering regression model. This work will give the details of the special mapping and the extension mapping evaluations. In particular, formulation of the special mapping f0 that involves finding a satisfying solution for a special kind of linear programming problem will be presented.