New Grey Relational Analysis for Finding the Invariable Structure and Its Applications

Grey relational analysis is a useful method in many fields as well known, and is presented variously, since the distinguish coefficient is fixed on using. This paper proposes a new approach for grey relational analysis that is based on topological background, and this proposal method has 3 features: (1) Grey relational matrix is always symmetric, (2) Order relation of with given samples is followed grey relational grade, (3) Distinguish coefficient is able to find an invariable structure of given data set. Two simulation examples are given, such as IRIS data set and WINE data set. This proposal method is compared with traditional grey relational analysis, about metric calculation and grey relational characteristic. In addition, it has obtained the order of given samples more clearly. And three examples are also given to show how to use the proposal method and distinguish coefficient in pattern recognition, information retrieval, and kansei engineering.