A fuzzy scheme for the ranking of multivariate data and its application

This paper presents a generic fuzzy scheme for the ranking of multivariate data. The scheme is based on a comparison function of two numbers. The comparison function values are fused by a T-norm for all components of two vectors, giving the comparison values. For each vector in a set of vectors, the smallest value of its comparison values with all other elements of the set is assigned to this vector as its ranking value. Then, all further processing is based on the ranking values alone. As a suitable comparison function, bounded division is identified. The application of the scheme to define a color morphology and an evolutionary multiobjective optimization algorithm is demonstrated.