Families of methods to deal with criterion uncertainties in multicriteria decision analysis

Question

In MCDA, which family methods deal with uncertain criterion-specific values?

What is MCDA?

Multiple-criteria decision analysis, refereed as MCDA, is a sub-field of Operations Research for aiding in decision making when several objectives have to be considered.

Suppose you have $m\in \mathbb N^*$ alternatives which can be projects, candidates, drugs and so on, depending on your decision problem. And suppose you have $n\in\mathbb N^*$ criteria which asset the $m$ alternatives.

A simple instance of this is:

• You have $m=100$ projects
• You have $n=3$ criteria which are:
  1. Cost of each project
  2. Environmental impact of each project
  3. Probability of success of each project

An example of uncertainty

Then you have a dataset of $m$ rows and $n$ columns. When considering this dataset, you could ask yourself which criteria are most important and which aren't? Is the environmental impact of each project more important than the cost of each project? This question defines the criteria's weights. Many MCDA techniques have already been developed for weights infering (e.g. ELECTRE family) or dealing with incomplete weight information (e.g. SMAA family or RPM family).

Criterion-specific values uncertainty

Another question about this dataset is what if the evaluations of the alternatives' criterion-specific values are uncertain? (e.g. we only know that the cost of one project is within $[3,6]$M€ for interval uncertainty, but it can be fuzzy intervals, distribution laws, missing values and so on). As far as I know, RPM family as well as SMAA methods deal with this kind of uncertainties, and my question is, are there other MCDA family methods dealing with such uncertainties?

Answer 1

There are many applications of different MCDM (Multi-Criteria Decision Making) method families when there is some kind of uncertainty in weights or amount of objectives or criteria. Mosadeghi et al. (1), in their paper, explained the dimensions of uncertainty in the MCDM problems as follow:

• the location of uncertainty – where the uncertainty manifests itself within the model structure;
• the level of uncertainty – where the uncertainty manifests itself along the spectrum between deterministic knowledge and total ignorance;
• the nature of uncertainty – whether the uncertainty is due to the imperfection of our knowledge or is due to the inherent variability of the phenomena being described.

They also categorized the methods and approaches that can be used to handle various kind of uncertainty as follow:

"Most of the current works have focused on addressing uncertainty in criteria weights estimation. The resulting methodological approaches can be subdivided into two main groups:

• The first concentrate on developing more sophisticated MCDM techniques, which can process uncertain or inaccurate criteria information. Such advanced MCDM methods include ELECTRE, PROMETHEE, MAUT, Fuzzy set theory, and Random set theory. The Fuzzy set theory techniques are the most common techniques for dealing with imprecise and uncertain problems.
• The second group of methodologies addressing uncertainty in criteria weightings consists of uncertainty analysis techniques, mostly sensitivity analysis tools. Sensitivity analyses can be performed for both stakeholder weights and attribute weights and provide DMs with an understanding of the system's behavior under the varying nature of the preference parameters."

The following table, from their paper (1), will also be helpful in finding the related literature:

(1) Razieh Mosadeghi, Jan Warnken, Rodger Tomlinson & Hamid Mirfenderesk (2012): Uncertainty analysis in the application of multi-criteria decision-making methods in Australian strategic environmental decisions, Journal of Environmental Planning and Management, DOI:10.1080/09640568.2012.717886

Answer 2

There is a whole body of literature in the Analytic Hierarchy Process / Analytic Neural Process (AHP/ANP) that examines precisely the issue of stability of the results. For example, Saaty and Vargas (2013) is a good reference, although you can also look at some of Luis Vargas' recent papers in the area.