A novel approach to mathematical multiple criteria decision making methods based on information theoretic measures

Abstract

In this paper, first we propose a new approach for mathematical multiple criteria decision making (MCDM) methods using information theoretic measures, entropy and divergence. Using the concept of entropy, we determine the impact of each criterion in decision making process. The Shannon's entropy has been previously employed for this purpose. In this paper we use Renyi's entropy and the concept of information potential of each criterion for weight assessment. Next, we introduce divergence as new separation measure for MCDM methods. The results indicate that the new measure outperforms the conventional Euclidean distance measure. These techniques employed in MCDM methods are new and may be of independent interest. Also, we introduce a new perspective for the decision making problems. We propose time as a new dimension for conventional mathematical MCDM methods. This dimension opens a new horizon for future MCDM methods which are based on given decision matrix. To the best of our knowledge, no prior work has studied the MCDM methods from this point of view. Using the criteria values for each candidate at different time instances, we estimate the probability distribution of each criterion in order to accommodation to the criteria value uncertainty. Finally, by utilizing the generalized correlation function, i.e. correntropy, we study the statistical dependencies of criteria in the same and different time instances.