Base-criterion on multi-criteria decision-making method and its applications

What is it about?

Propose a new MCDM method.

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Why is it important?

In the pairwise comparisons between criteria, the direction and strength of the comparisons is questionable. In the proposed approach for pairwise comparisons in AHP, it is recommended to make a pairwise comparisons those are independent among all criteria. For example, if the relative importance of C1 is stronger than C2 and C2 is also stronger than C3then here is not required that the relative importance of C1 takes stronger than C3 (Saaty, 1977). On the other hand, the AHP discusses the consistency ratio which is a contradiction with independent pairwise comparison. In fact, this way disrupts the pairwise comparisons direction and leads to inconsistency. Several methods have been proposed to improve AHP consistency, none of which able to solve the basic problem of inconsistency (Harker, 1987a; Weiss & Rao, 1987). With these conditions, the pairwise comparisons among the criteria in the AHP method is ambiguous, and there is not exact relationship between the pairwise comparisons to obtain weights in terms of direction and strength. The weights obtained by this approach are not accurate and will have errors. Unlike the pairwise comparison in AHP, secondary comparisons of the BWM are completely dependent. For example, if the relative importance of C1 to C2 be 4 and the relative importance of C2 is equal to C3, then the relative importance of C1 to C3 will be 4. With these conditions, if the relative importance of C1 to C3 instead of 4 is 3 or 5, an inconsistency occurs in the strength that is also observed in the secondary comparisons of BWM method. In our proposed method (BCM), we consider the pairwise comparisons as dependent. We also believe that by performing a one-step pairwise comparison between a base (e.g. preferential, selective) criterion and other criteria, we can determine the relative importance of each criterion in relation to another criterion so that it is the perfect consistency in terms of direction and strength.