  This chapter assesses the sensitivity of multi-criteria decision-making
(MCDM) methods to modifications within the decision or objective matrix (DOM)
in the context of chemical engineering optimization applications. Employing
eight common or recent MCDM methods and three weighting methods, this study
evaluates the impact of three specific DOM alterations: linear transformation
of an objective (LTO), reciprocal objective reformulation (ROR), and the
removal of alternatives (RA). Our comprehensive analysis reveals that the
weights generated by entropy method are more sensitive to the examined
modifications compared to the criteria importance through intercriteria
correlation (CRITIC) and standard deviation (StDev) methods. ROR is found to
have the largest effect on the ranking of alternatives. Moreover, certain
methods, gray relational analysis (GRA) without any weights, multi-attributive
border approximation area comparison (MABAC), combinative distance-based
assessment (CODAS), and simple additive weighting (SAW) with entropy or CRITIC
weights, and CODAS, SAW, and technique for order of preference by similarity to
ideal solution (TOPSIS) with StDev weight are more robust to DOM modifications.
This investigation not only corroborates the findings from the previous study,
but also offers insights into the stability and reliability of MCDM methods in
the context of chemical engineering.
