The ordinary variable weight principle and multi-objective decision-making

Having introduced the tentative idea of compromise variable weight in document, we firstly present the generalized definition of compromise variable weight in this paper, being followed by discussing relations among various variable weights. It is one of the important points of our work to study the nature of variable weight induced by the family of impellent utility function for revealing the relation between variable weight analysis and utility theory. As a result of this study, some types of impellent utility function family fitting to variable weight analysis is given in this paper. Finally, the compatibility principle of variable weight is stated for structuring some particularly operatable variable weight to restrict the parameter in application, and the method of variable weight for multi-objective decision-making is given as an example.