Piecewise linear value functions for multi-criteria decision-making

Multi-criteria decision-making (MCDM) concerns selecting, ranking or sorting a set of alternatives which are evaluated with respect to a number of criteria. There are several MCDM methods, the two core elements of which are (i) evaluating the performance of the alternatives with respect to the criteria, (ii) finding the importance (weight) of the criteria. There are several methods to find the weights of the criteria, however, when it comes to the alternative measures with respect to the criteria, usually the existing MCDM methods use simple monotonic linear value functions. Usually an increasing or decreasing linear function is assumed between a criterion level (over its entire range) and its value. This assumption, however, might lead to improper results. This study proposes a family of piecewise value functions which can be used for different decision criteria for different decision problems. Several real-world examples from existing literature are provided to illustrate the applicability of the proposed value functions. A numerical example of supplier selection (including a comparison between simple monotonic linear value functions, piecewise linear value functions, and exponential value functions) shows how considering proper value functions could affect the final results of an MCDM problem.