1 / 25

Hierarchical reference approach to multi-criteria analysis of discrete alternatives

Hierarchical reference approach to multi-criteria analysis of discrete alternatives. JANUSZ GRANAT National Institute of Telecommunications,Warsaw, and Warsaw University of Technology, Poland MAREK MAKOWSKI International Institute for Applied System Analysis, Laxenburg, Austria

glendao
Download Presentation

Hierarchical reference approach to multi-criteria analysis of discrete alternatives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hierarchical reference approach to multi-criteria analysisof discrete alternatives JANUSZ GRANAT National Institute of Telecommunications,Warsaw, and Warsaw University of Technology, Poland MAREK MAKOWSKI International Institute for Applied System Analysis, Laxenburg, Austria ANDRZEJ P. WIERZBICKI Center for Strategic Development of Science and Technology, Japan Advanced Institute of Science and Technology, Ichikawa, Japan, and National Institute of Telecommunications,Warsaw, Poland CSM 2006, Laxenburg, 28-30 August 2006

  2. Outline • Motivation • The limitation of the existing approaches • Hierarchical criteria aggregations • Applications • Conclusions CSM 2006, Laxenburg, 28-30 August 2006

  3. The criteria for selection of energytechnologies CSM 2006, Laxenburg, 28-30 August 2006

  4. 0,4 0,6 0,8 0,2 0,1 0,1 0,8 0,12 0,48 0,04 0,32 0,04 Hierarchical weighting CSM 2006, Laxenburg, 28-30 August 2006

  5. Bottom-up weighting 0,7 0,3 0,1 0,2 0,1 0,5 0,1 0,2 0,1 0,5 0,1 0,1 CSM 2006, Laxenburg, 28-30 August 2006

  6. Compensatory versus noncompensatory criteria • Compensatory criteria–an improvement of a criterion can be rationally substantiated to compensate a deterioration of another criterion. e.g. operational costs and investment costs • Noncompensatory criteriaare such that no rational substantiation exists for defining weighting coefficients. e.g. costs and loss of human life CSM 2006, Laxenburg, 28-30 August 2006

  7. Ranking „classification” „ranking” „partial ordering” CSM 2006, Laxenburg, 28-30 August 2006

  8. Subjective versus objective ranking Fullobjectivity is obviously – after Heisenberg and Quine – not attainable, but in many situations we must try to be as much objective as possible. CSM 2006, Laxenburg, 28-30 August 2006

  9. Objective ranking Weighting coefficients and/or aspiration and reservation levels should be determined in some objective or intersubjectively fair fashion. We shall consider three possible ways of achieving this goal: • neutral • statistical • voting CSM 2006, Laxenburg, 28-30 August 2006

  10. Neutral • weights - objective weightingcoefficients for compensatory criteria and weighting coefficients equal in size for all noncompensatory criteria • aspirations/reservations - a neutral definition of reference points e.g. all aspiration levels equal to 67% of criteria ranges, all reservation levels equal to 33% of these ranges CSM 2006, Laxenburg, 28-30 August 2006

  11. Voting • A voting procedure between a group of decision makers. • Many voting procedures, see H.Nurmi (1999). • Voting results actually only in intersubjective aggregation. CSM 2006, Laxenburg, 28-30 August 2006

  12. Statistical Based on some meaningfulstatistics. • weights- it is very difficult to find statistical data to substantiate weighting coefficients • aspirations/reservations - the average score of all options, e.g.: qai= qmi+(qmaxi–qmi)/2; qri= qmi-(qmi –qmini)/2 qmi- is average value of the i-th criterion for all decision options qai, qri - aspiration and the reservation levels, respectively CSM 2006, Laxenburg, 28-30 August 2006

  13. Approaches to hierarchical criteria aggregation • Compensatory aggregation on lower level, noncompensatory analysis on upper level. • Noncompensatory aggregation both on lower and on upper level • Noncompensatory aggregation with weighting coefficients as importancefactors CSM 2006, Laxenburg, 28-30 August 2006

  14. Compensatory aggregation on lower level,noncompensatory analysis on upper level. qB qA q2 q1 q3 q1 q2 qC= ∑i є C wiqifor allC = A,…H CSM 2006, Laxenburg, 28-30 August 2006

  15. Noncompensatory aggregation both on lower and on upper level qB qA q2 q1 q3 q1 q2 CSM 2006, Laxenburg, 28-30 August 2006

  16. Noncompensatory aggregation with weighting coefficients treated as importance factors The weights are interpreted as importance factors and are used for modification of neutral aspiration and reservation levels e.g.: CSM 2006, Laxenburg, 28-30 August 2006

  17. Noncompensatory aggregation with weighting coefficients treated as importance factors - weights q2 a b c d q2 e CSM 2006, Laxenburg, 28-30 August 2006

  18. Noncompensatory aggregation with weighting coefficients treated as importance factors – neutral aspiration q2 a (0.73, 0,73) b c d (0.23, 0,23) q2 e CSM 2006, Laxenburg, 28-30 August 2006

  19. Noncompensatory aggregation with weighting coefficients treated as importance factors – weighted aspiration q2 w=(0.7, 0.3) a b c (0.51, 0,22) d q2 (0.16, 0,07) e CSM 2006, Laxenburg, 28-30 August 2006

  20. Preservation of Pareto optimality afterhierarchical aggregation Theorem. In a hierarchical aggregation of criteria, suppose that the functions used to aggregate criteria in groups on the lower level are strictly monotone with respect to the partial orders defining the vector optimization problems on lower level. Then any decision option that is Pareto optimal in the space of aggregated criteria is also Pareto optimal in the original space of all lower level criteria (with respect to the overall partial order induced by the partial orders for all groups of criteria). CSM 2006, Laxenburg, 28-30 August 2006

  21. Electricity supply technologies - hierarchical weighting Equal weights (0.5,0.5,0.5) Economy(1,0,0) Environment (0, 1,0) Social (0,0, 1) CSM 2006, Laxenburg, 28-30 August 2006

  22. Compensatory aggregation on lower level, noncompensatory analysis on upper level noncompensatory upper level compensatory lower level Equal weights (0.5,0.5,0.5) Aspirations/reservations CSM 2006, Laxenburg, 28-30 August 2006

  23. Noncompensatory aggregation both on lower and on upper level compensatory upper level noncompensatory lower level noncompensatory upper level compensatory lower level noncompensatory upper level noncompensatory lower level CSM 2006, Laxenburg, 28-30 August 2006

  24. Conclusions (I) • Distinction between subjective and objective ranking • Distinction between compensatory and noncompensatory groups of criteria. • Approaches to hierarchical aggregation of criteria: • Compensatory aggregation on lower level, noncompensatory analysis on upper level; • Noncompensatory aggregation both on lower and on upper level; • Noncompensatory aggregation with weighting coefficients treated as importance factors. CSM 2006, Laxenburg, 28-30 August 2006

  25. Conclusions (II) • The discussion and a theorem on the preservation of Pareto optimality after hierarchical aggregation with strictly monotone aggregating functions. • The resulting approaches will be used on the problem of the selection of electricity supply technologies CSM 2006, Laxenburg, 28-30 August 2006

More Related