Piecewise linear value functions for multi-criteria decision-making

Abstract

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.

Anchoring bias in eliciting attribute weights and values in multi-attribute decision-making

“…Another essential part of multi-attribute decision-making problem is the identification of the attribute values a kj ; and their normalised values v kj a kj À � . There exist several approaches to find the (normalised) attribute values, which are mainly discussed under value functions in literature (French, 1989;Ghaderi & Kadziński, 2020;Kakeneno & Brugha, 2017;Keeney & Raiffa, 1976;Kirkwood, 1997;O'Brien & Brugha, 2010;Rezaei, 2018;Von Winterfeldt & Edwards, 1986). Methods such as AHP, ANP, BWM, SMART, and Swing are also used to find the normalised attribute values v kj a kj À � ; when an attribute is evaluated subjectively (e.g., comfort) or when there is no access to the attribute values when they are objective (e.g., price).…”

Circular economy practices in the leather industry: A practical step towards sustainable development

“…According to Table 1, evaluating the challenges to CE practices is a multi-criteria problem; the MCDA technique can help to solve such problems. Several MCDA methods such as AHP, ANP and TOPSIS are available (refer to the study by Triantaphyllou, 2000;Rezaei, 2018). The current study applies the BWM, an MCDA method that has not been previously utilized in this area.…”

A preference learning framework for multiple criteria sorting with diverse additive value models and valued assignment examples

“…All criteria are assumed to be monotone (gain-or cost-type), i.e., for any alternative a, either the greater g j (a), the better is a on g j (in case of gain-type criteria), or the less g j (a), the better is a on g j (in case of cost-type criteria). For dealing with non-monotonic criteria, see [12,23,28]. For the sake of simplicity, but without loss of generality, we suppose that all criteria are of gain-type and that the performances on criteria have a monotone increasing direction of preferences.…”