Modeling Preferences

To be able to find the best solution for MCDA problems we need to know subjective preferences:

So given two alternatives $a$ and $b$ a decision maker can say if

  • $a \ P \ b$ or $b \ P \ a$: $a$ is preferred to $b$ - the preference relation
  • $a \ I \ b$ - the indifference relation
  • $a \ J \ b$ - the incomparability relation, when you cannot compare things

Main properties:

  • $P$ is asymmetric
    • $a \ P \ b \equiv b \ \overline{P} \ a$
  • $I$ is reflexive and symmetric:
    • $a \ I \ a$ and $a \ I \ b \equiv b \ I \ a$
  • $J$ is irreflexible and symmetric
    • $a \ \overline{J} \ a$ and $a \ J \ b \equiv b \ J \ a$


We can show the preferences of a decision maker with a graph:

  • preference-modelling.png

Preference Structures

How to build a mathematical model from statements of a decision maker?


There are several preference structures that can do that:

Preferential Independence

Main Article: Preferential Independence

This is an important condition between preferences and criteria: the criteria should be preferentially independent.