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Introduction to decision aid

Concepts and definitions

These pages are by no mean an exhaustive course on decision aid or operational research methods, and many concepts explained here are extremely simplified.

The reader should definitely look in the books pages and in the internet links for more details, in particular to obtain the theoretical background (mathematical approaches, paradigms, hypotheses, limitations, etc.).

In order to clarify the vocabulary used in these pages, let's quickly explain what we mean when we use some words :

  • DECISION-MAKER: the decision-maker is the (group of) person(s) who need(s) to take a decision. It can be yourself when you want to buy a new car, your boss when he wants to recruit an assistant or a government that needs to choose a location for a new airport.
  • ACTION: the actions are the choices you need to compare to take your decision. They can be a list of car models, a list of candidates or a list of sites where an airport could be built.
  • CRITERION: the criteria are the elements that are relevant to the decision-maker to make the choice and take the decision. They can be the price and the power of a car, the education and the experience of a candidate, the cost and the impact on the environment for an airport.
  • DECISION MATRIX : in these pages, we will use the following presentation for our actions and criteria, and we will call it a decision matrix :
Criterion 1 Criterion 2 Criterion 3
Action 1 value value value
Action 2 value value value
Action 3 value value value
Action 4 value value value
Action 5 value value value
The decision aid methods use this matrix, sometimes together with weighting information, to help finding the best solutions.
Click here to see a decision matrix sheet generated by the Promethee wizard.
The quality of the results you will get from the methods available with DECIDE are directly related to the quality of the information you will put in the decision matrix. You need to analyse the problem properly and formalize the available data in an adequate decision matrix in order to get useful results.
  • WEIGHT : the weight of a criterion represents the importance of the given criterion to the decision-maker.
When comparing cars, the decision-maker can take in account the price, the power and the size of the clock. It seems clear that the impact of the size of the clock on the decision will be lower than the impact of the price. By giving a weight to each criterion, the decision-maker can influence the way the data for each criterion will be taken into account.
DECIDE also includes methods to determine "objective" weights (see DECIDE__ObjectiveWeights(), [DECIDE.xls / All functions / ObjectiveWeights]), based only on the actual data available for each criterion (for example, if the price of all the cars considered is nearly the same, the impact of this criterion on the decision is minimal, and the decision-maker might want not to give a high weight to it in this case).
One of the most interesting aid given by decision aid methods is the variation of the results depending upon the weights the decision maker gives to the criteria. This helps a lot in explaining why actions are preferred to others.
This important issue will be covered more in detail in the weighting page.
  • DOMINANCE : when an action A is compared with an action B, A is said to dominate B if, for every criterion, A is at least as good as B, and A is better than B for at least one criterion. See DECIDE__Dominate() [DECIDE.xls / All functions / Dominate] for more information.
  • EFFECTIVENESS : In a decision matrix, an action is said to be effective if it is not dominated by any other action. See DECIDE__Effective() [DECIDE.xls / All functions / Effective] for more information.
  • ZENITH : based on a decision matrix, the zenith would be the ideal action that would have for each criterion the best value in the matrix. It is also called ideal point or target point. See DECIDE__Zenith_Nadir() [DECIDE.xls / All functions / Zenith_Nadir] for more information.
  • ANTI-ZENITH : The opposite of the zenith. Based on a decision matrix, the anti-zenith would be the worst possible action that would have for each criterion the worst value in the matrix. See DECIDE__Zenith_Nadir() [DECIDE.xls / All functions / Zenith_Nadir] for more information.
  • PREFERENCE : When comparing actions, two attitudes are possible : either one action is preferred to the other, or they are both equally acceptable, in which case we talk about indifference.
The decision aid methods aggregate the values supplied in the decision matrix for every action on every criterion in order to determine the preferences of the actions against the others. This property can lead to many developments, as the cup of tea paradox illustrates.
  • PAYOFF MATRIX : The payoff matrices for actions with n criteria are the square matrices
Note that the components of the zenith are on the matrices diagonal, and that the payoff matrix is unique only if every criterion is at its maximum for only one action.
See DECIDE__PayoffMatrix() [DECIDE.xls / All functions / PayoffMatrix] for more information.
  • NADIR : Depending upon the authors, the nadir is what we have defined above as the anti-zenith (Pomerol and Barba-Romero 1993 page 228), or the point with co-ordinates
in a given payoff matrix (Vincke 1989 page 58).
See DECIDE__PayoffMatrix() and DECIDE__Zenith_Nadir() [DECIDE.xls / All functions / Zenith_Nadir] for more information.
  • NORMALIZATION : the numbers in decision matrices are normally expressed in units that are relevant to the decision maker, like euros for a price or days for a duration. Though, some decision aid methods need to have all the values in the decision matrix between 0 and 1, and a calculation needs to be made to convert all data.
Unfortunately, this process sometimes generates side effects that can have a negative impact on the validity of the results obtained. Also, normalization can be made in several ways, giving different results, and therefore leading to different results for the decision aid methods.
Bear in mind that normalization can have side effects, and be careful when using it.
When in doubt, give preference to methods that do not require normalization, like Promethee for example.
The DECIDE library offers several ways to normalize data : see DECIDE__Normalize() [DECIDE.xls / All functions / Normalize] for more information.
The cup of tea paradox illustrates the problem of the transitivity of the indifference, which is the absence of preference.
At first glance, it seems obvious that if the actions A and B are indifferent to you, and if the actions B and C are also indifferent to you, then necessarily the actions A and C are indifferent to you too... This is not always true, and needs to be considered with care when studying a decision aid method.
Say you like your tea with 5 grams of sugar per cup. As you cannot notice the difference between a cup with 5 grams of sugar and a cup with 4.95 grams of sugar, these two cups will be indifferent to you. As will cups with 4.95 grams and 4.90 grams, and so on up to cups with 0.5 gram and 0 gram... which would mean that you have no preference between tea with sugar and tea without sugar.
The easy way around this is to consider that the indifference is not transitive, and to avoid using this property in decision aid methods. The subject is a lot more complex in reality, and the reader will find that it has been covered by several authors, like Pomerol and Barba-Romero 1993.

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