Multi-Criteria Decision Making Method for n-wise Criteria Comparisons and Inconsistent Problems

The purpose of this paper is to present an alternative of a hybrid method based on Saaty’s Analytical Hierarchy Process and on the Technique for Order Preference by using the Similarity to Ideal Solution method (AHP-TOPSIS) and, based on the AHP and its use of pairwise comparisons, to extend it to a new method called α-D MCDMTOPSIS (α-Discounting Method for multi-criteria decision making-TOPSIS). The new method overcomes the limits of AHP, which works only for pairwise comparisons of criteria, to any-wise (n-wise) comparisons, with crisp coefficients or with intervalvalued coefficients. An extended MCMD method (called Extended α-D MCDM) of α-D MCDM, introduced by Smarandache to solve decision making problems, is developed. α-D MCDM-TOPSIS and Extended α-D MCDM are verified on several examples, to demonstrate how they work with consistent, weak inconsistent or strong inconsistent problems. Finally, we discuss and compare all methods. Keyword Decision making, Extended α-D MCDM, Consistency, Inconsistency, n-wise criteria comparisons, AHP TOPSIS.