Classical MCDM Methods and Their Operators on Grey Numbers Through Operator Overloading

Abstract

This study investigates the possibilities of applying classical MCDM methods to grey numbers by leveraging operator overloading and multiple dispatch features of Julia programming language. Grey versions of the classical MCDM methods differ in some of their computational steps. In this paper, it is shown that a set of MCDM methods, including TOPSIS, ARAS, WASPAS, and EDAS are directly applicable to grey numbers through operator overloading without changing their core algorithms. These processes are implemented by re-defining arithmetic and comparison operators for grey numbers. We also compared our methodology with two existing Grey TOPSIS methods. It is shown that the sorted grey scores can yield the same rankings as the existing methods in some cases. When the results are not the same, we show that an appropriate whitening parameter can be found to obtain the same rankings. This approach preserves the uncertainty from the very beginning to the end of the process and provides a clear distinction between objective computational steps and subjective ranking steps. Switching the whitening parameter from zero to one also provides a sensitivity analysis tool to investigate how uncertainty affects the final rankings.

Keywords

• multi-criteria decision making
• grey numbers
• operator overloading

References

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