A statistical approach to multiple-attribute decision-making with interval numbers

Abstract

In multiple-attribute decision-making, the overall values of alternatives would be interval numbers due to the inherent uncertain property of the problems in the ambiguous decision domain. Bryson and Mobolurin proposed the use of linear programming models to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, transforming the overall values of the alternatives from intervals to points may result in information loss. In this paper, statistical distributions, normal distribution and uniform distribution, are placed on the intervals of attribute weights and attribute values of the alternatives. By adopting a simulation method, means together with standard deviations and correlations of the overall values of alternatives are used to conduct the comparisons. The proposed statistical approach simplifies and enriches Bryson and Mobolurin's approach by providing superiority possibilities between alternatives, means, standard deviations, and correlations for alternative comparisons. The simulation results show that under a uniform distribution, the intervals of the overall values of alternatives coincide with the ‘level 3 composite’ intervals of Bryson and Mobolurin. Comparisons between the alternatives associated with their evaluated intervals are also discussed for the case of normal distribution on the intervals of attribute weights and crisp values for the attribute values of alternatives.