Introduction to MCDM

Multi-Criteria Decision Problem:

  • Finite set of alternative actions (solutions/variants) to attain specified goal(s)
  • Consistent family of (gain/cost) criteria - real-valued functions reflecting a worth of actions from a particular point of view:
    • Complete - if two actions have the same evaluations on all criteria then they have to be indifferent
    • Monotonic
    • Non-redundant - elimination of any criterion violates at least on of the above properties
  • 4 categories of decision problems:
    • Choice problem (optimization)
    • Classification problem (sorting)
    • Ordering problem (ranking)
    • Description problem

Modelling a decision problem:

  • Mathemathical modelling
    • Linear programming
    • Modelling preference relation, ordinal regression
  • Machine learning - supervised learning from examples
    • Decision rules
    • Decision trees

Dominance and preference relations:

  • (Weak) Pareto-dominance and Pareto optimality
  • Dominance relation provides objective information but leaves too many actions non-comparable
  • Preference information obtained from the decision maker can be used to built a preference model (i.e. criteria aggregation model) which enriches the dominance relation
  • Decision maker's preferences are consistent with unknown utility function
  • The most intuitive is the model of additive utility function ("weighted sum")


Ordinal regression - ranking learning

  • "Important supervised problem of learning a ranking or ordering on instances, which has the property of both classification and metric regression. The learning task of ordinal regression is to assign data points into a set of finite ordered categories. Ordinal regression is different from classification due to the order of categories. In contrast to metric regression, the categories in ordinal regression is discrete and finite." A Neural Network Approach to Ordinal Regression
  • Support Vector Ordinal Regression