On the Generalization of Grey Relational Analysis

Abstract

In this paper we developed new grey relational analysis by expanding a range of treatable value. The classical GRA procedure deals with almost whitened values, reference vectors (or sequences), inspected vectors and grey relational grades. The classical GRA is called White-In-White-Out (WIWO) GRA in this paper. We developed two kinds of GRA algorithm based on the topological-based GRA, after defined several new operations of the interval grey number. On the one hand, GRA which provides the grey relational grade a whitened value finally is named Grey-In-White-Out (GIWO) GRA. On the other hand, GRA which provides the grey relational grade the interval grey number is named Grey-In-Grey-Out (GIGO) GRA. Both new GRA procedures deal with the reference vector and inspected vectors as the interval grey number. Three examples are given in this paper; the properties of the grey relational grade given by the proposals are discussed.