&amp;#945;-Discounting Method for Multi-Criteria Decision Making (&amp;#945;-D MCDM)

Florentin Smarandache

doi:10.2139/ssrn.2725497

Abstract

In this paper we introduce a new procedure called α -Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or non-homogeneous equations and/or inequalities. Many consistent, weak inconsistent, and strong inconsistent examples are given.

Highlights

Introduction α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM) is an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP) - see [1,2,3,4,5,6,7,8,9,10,11] for more information on AHP since it is not the main subject of this chapter
We have introduced a new method in the multi-criteria decision making, - Discounting MCDM
In the second part of the method, one chooses a principle for finding the numerical values of the parameters {we have proposed the Fairness Principle, or Expert’s Opinion on Discounting, or setting a Consistency Threshold}

Summary

Introduction

Discounting Method for Multi-Criteria Decision Making (α-D MCDM) is an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP) - see [1,2,3,4,5,6,7,8,9,10,11] for more information on AHP since it is not the main subject of this chapter. The general idea of α-D MCDM is to assign non-null positive parameters α1, α2, ..., αp to the coefficients in the right-hand side of each preference that diminish or increase them in order to transform the above linear homogeneous system of equations which has only the null-solution, into a system having a particular non-null solution. For consistent decision-making problems with pairwise comparisons, α-Discounting Method together with the Fairness Principle give the same result as AHP. For weak inconsistent decision-making problem, α-Discounting together with the Fairness Principle give a different result from AHP. In 2010 we have introduced a new method [3], called α-

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Discussion

Conclusion