Evidential reasoning approach for MADM based on incomplete interval value

In a multiple attribute decision making (MADM) problem, quantitative and qualitative attributes can be assessed by numerical values and subjective judgements. Numerical value can be accurate or uncertain, while qualitative attribute can be evaluated by linguistic variables. The evidential reasoning (ER) approach provides a process for dealing with MADM problems of both a quantitative and qualitative nature under uncertainty. In the existing MADM literature, interval value is assumed to be uniformly distributed and complete in the sense that any value in the interval is equally likely and that the probabilities of values in the interval being taken sum to one. In real life decision situations, however, interval value could be incomplete in that the sum of probabilities of values in the interval being taken can be less than one. In this paper, incomplete interval value is introduced to a decision making process, and the transformation rule of incomplete interval value to belief degrees in the frame of discernment under the ER framework is analyzed. The characteristics of the transformation rule are studied. A case study is provided to illustrate the implementation of the proposed new concept and technique and the potential in supporting MADM under uncertainty.