The information measure index and its property of interval grey number

Purpose In order to express the intrinsic information of interval grey number reasonably, this paper discusses the information measure index and its property of interval grey number. Design/methodology/approach Firstly, based on the generalized greyness and generalized whiteness of interval grey number, the definitions of the generalized grey information quantity, the generalized white information quantity and total information quantity of interval grey number are given, and the basic properties of the information quantity of interval grey number are analyzed. After that, in order to express the information dynamics of interval grey number, the concepts of generalized grey information density, generalized white information density and background information density of interval grey number are given, and the internal relationship between them is analyzed. Then, according to the principle of difference information, the definition of information difference quantity of interval grey numbers is given, and its property and the relationship between information difference quantity and greyness (whiteness) distance are analyzed, and a grey pattern recognition model based on grey information difference quantity is presented. Finally, the grey pattern recognition model is applied to the decision-making of artillery weapon procurement. Findings The results show that the generalized grey (white) information quantity of interval grey number is relative, normative, connected, gradual change, opposites, unity and justice, and is conserved. The generalized grey information density and generalized white information density of an interval grey number can better reflect the information dynamics of an interval grey number. The effect of the grey (white) information difference quantity is equivalent to that of the greyness (whiteness) distance. The grey pattern recognition model based on generalized grey information can make full use of the intrinsic information of interval grey numbers, and the application examples show that it is feasible and effective. Practical implications The concepts and properties of the generalized grey (white) information quantity, generalized grey (white) information density and information difference quantity proposed in this paper not only provide a theoretical basis for the dialectical analysis of grey and white information evolution for interval grey numbers, but also provide a new thinking for the study of methods such as grey relational analysis, grey decision-making, grey pattern recognition and grey forecast from the perspective of information. Originality/value The paper succeeds in revealing some basic properties of the information quantity of interval grey number, such as the principle of information conservation and the relationship between information densities and so on, and gives a grey pattern recognition model based on grey information difference quantity, which provide a theoretical basis for the rational use of the information contained in interval grey number.