A new fuzzy clustering validity criterion and its application to color image segmentation

A new strategy for the determination of the degree of validity of a fuzzy partition is introduced. The strategy is mathematically justified via its relation to hard partition validity measures. The relationship between this fuzzy validity function and the most general, and well defined, hard clustering validity function (the separation index of J.C. Dunn (1974)) for which the condition of uniqueness has already been established is derived. Using this relationship, the existence of a unique fuzzy c-partition produced by the fuzzy validity function is also proved. Examples of applications to segmentation of color image for IC defects give encouraging results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>