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

## 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?

• I hesitated adding a MCDA short summary in the beginning of my question. Don't hesitate telling me if the summary isn't necessary or even if it's too short :) – JKHA Jun 17 '19 at 13:53
• I think it's good to have the summary, but your actual question is a little lost. I think your question is the last sentence in the post, but are you also asking the questions that are in the "An example of uncertainty" section, or are those rhetorical? Maybe put your actual question(s) as a new paragraph, or boldface, to highlight them? – LarrySnyder610 Jun 17 '19 at 13:58
• It's typically best to get to the crux of your question first, and then add background information as it clarifies the post. It's the news article format: headline → lead → explanation → additional information. – Robert Cartaino Jun 17 '19 at 14:00
• @RobertCartaino Is there a post on main meta or somewhere else that fleshes out that idea a little more? It might be nice to have a post to link to if we want to help askers structure questions more clearly. – LarrySnyder610 Jun 17 '19 at 14:38
• @LarrySnyder610 Unfortunately, I don't know of one. It may exist in the vast ocean of meta subjects, so perhaps someone else can recall such a conversation. – Robert Cartaino Jun 17 '19 at 16:23

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

• I don't know if it is alright to write something about my own work in the answer that's why I did include it, in which fuzzy TOPSIS, have been used to handle the uncertainty of linguistic variables. – Oguz Toragay Jul 25 '19 at 1:20
• @OguzTaragay Here is one recommendation about citing your own work. If you cite a previous Q|A use the cite link (if the other site has them) or the share link (and include a relevant quote so it's not link-only - it's possible to be deleted on the other site, leaving some people here unable to see it). BTW: Thanks for the answer. – Rob Jul 25 '19 at 1:28
• @Rob Thanks for your recommendation regarding the issue of citing myself. I just wanted to mention an example (in my own paper) of the approaches that I mentioned in the answer, and I think I have already put all the necessary information in the comment. – Oguz Toragay Jul 25 '19 at 1:40
• Comments are temporarily, if you have additional information that you want to include you can do so with another edit. You can leave it as-is and let the answer stand as it is (without the comment). – Rob Jul 25 '19 at 1:45

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.