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 :
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.
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.
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.
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.
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.
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.