- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
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.
6. Conclusion, limitations and future research
This study proposes a set of piecewise value functions for multi-criteria decision-making (MCDM) problems. While the existing applications of MCDM methods usually use two general simple increasing and decreasing linear value functions, this study provides several real-world examples to support the applicability of some other forms of value functions for the criteria used in MCDM. It is also explicated how, in some decision problems, a combination of two or more value functions can be used for a particular decision criterion. The proposed functions can be used for different MCDM methods in different decision problems. A numerical example of supplier selection problem (including a comparison between simple monotonic linear value functions, piecewise linear value functions, and exponential value functions) showed how the use of the proposed value functions could affect the final results. Considering these value functions could better represent the real preferences of the decision-maker. It can also help reduce the inappropriate compensations of the decision criteria, for instance, through using a level-increasing function which assigns zero value to any value of the criterion below a certain threshold. The proposed value functions are presented in a general form such that they can be tailor-made for a specific decision-maker. That is to say, not only it is possible for two different decision-makers to use two different value functions for a single criterion. It is also possible to use different domain (e.g. min and max) values for that particular value function.