Multiple-Attribute Decision Making with Complete-Imperfect Substitution between Attributes

Abstract

Multiple-attribute decision making in the presence of independence between attributes, the shortage of value of one attribute can be compensated with the other attributes and the substitution rate is 100%. However, this violates the law of diminishing marginal rate of substitution and destroys the additive of attributes. So, the valuations of alternatives based on weighed aggregation operator are failure. In this paper, four styles of attribute substitution are proposed, named by, complete-perfect, complete-imperfect, incomplete-perfect and incomplete-imperfect. We focus on the complete-imperfect substitution. Firstly, based on the law of diminishing marginal rate of substitution, the value of attributes is divided into many intervals with different levels. On the same level, the substitution rate is 100% and the additive of different attributes is effective. Secondly, the multiple-attribute decision making is transformed into single-attribute decision making and the valuations of alternatives are calculated based on single attribute with different levels, Thirdly, the comprehensive value of each alternative are calculated through by accumulating value of different levels and all alternatives are ranked by the comprehensive value of alternative.