Skip to main content
SpringerLink
Log in

Interactive outranking approaches for multicriteria decision-making problems with imprecise information

  • Theoretical Paper
  • Published:
Journal of the Operational Research Society

Abstract

PROMETHEE is a powerful method, which can solve many multiple criteria decision making (MCDM) problems. It involves sophisticated preference modelling techniques but requires too much a priori precise information about parameter values (such as criterion weights and thresholds). In this paper, we consider a MCDM problem where alternatives are evaluated on several conflicting criteria, and the criterion weights and/or thresholds are imprecise or unknown to the decision maker (DM). We build robust outranking relations among the alternatives in order to help the DM to rank the alternatives and select the best alternative. We propose interactive approaches based on PROMETHEE method. We develop a decision aid tool called INTOUR, which implements the developed approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11

Similar content being viewed by others

References

  • Ahn BS, Park KS, Han CH and Kim JK (2000). Multi-attribute decision aid under incomplete information and hierarchical structure. Eur J Opl Res 125: 431–439.

    Article  Google Scholar 

  • Belton V and Stewart TJ (2002). Multiple Criteria Decision Analysis: An Integrated Approach. Kluwer Academic Publishers: Boston.

    Book  Google Scholar 

  • Bouyssou D (1992). Ranking methods based on valued preference relations: A characterization of the net flow method. Eur J Opl Res 60: 61–67.

    Article  Google Scholar 

  • Bouyssou D and Perny P (1992). Ranking methods for valued preference relations: A characterization of a method based on entering and leaving flows. Eur J Opl Res 61: 186–194.

    Article  Google Scholar 

  • Brans JP and Mareschal B (1992). PROMETHEE V: MCDM problems with segmentation constraints. INFOR 30: 85–96.

    Google Scholar 

  • Brans JP and Vincke P (1985). A preference ranking organization method. Mngt Sci 31: 647–656.

    Article  Google Scholar 

  • Brans JP, Vincke P and Mareschal B (1986). How to select and how to rank projects: The PROMETHEE method. Eur J Opl Res 44: 228–238.

    Article  Google Scholar 

  • Carrizosa E, Conde E, Fernandez FR and Puerto J (1995). Multi-criteria analysis with partial information about the weighting coefficients. Eur J Opl Res 81: 291–301.

    Article  Google Scholar 

  • Dias LC and Clímaco JN (1999). On computing ELECTRE's credibility indices under partial information. J Multi-Crit Decis Anal 8: 74–92.

    Article  Google Scholar 

  • Dias LC and Clímaco JN (2000). Additive aggregation with variable interdependent parameters: The VIP analysis software. J Opl Res Soc 51: 1070–1082.

    Article  Google Scholar 

  • Dias LC and Clímaco JN (2002). Exploring the consequences of imprecise information in choice problems using ELECTRE. In: Bouyssou D., Jacquet-Lagrèze E., Perny P., Slowinski R., Vanderpooten D. and Vincke P. (eds). Aiding Decisions with Multiple Criteria—Essays in Honor of Bernard Roy. Kluwer: Boston, pp. 175–193.

    Chapter  Google Scholar 

  • Dias LC and Mousseau V (2006). Inferring ELECTRE'S veto-related parameters from outranking examples. Eur J Opl Res 170: 172–191.

    Article  Google Scholar 

  • Dias LC, Mousseau V, Figueira J and Clímaco JN (2002). An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI. Eur J Opl Res 138: 332–348.

    Article  Google Scholar 

  • Eum Y, Park KS and Kim SH (2001). Establishing dominance and potential optimality in multi-criteria analysis with imprecise weight and value. Comput Opns Res 28: 397–409.

    Article  Google Scholar 

  • Gilboa I, Schmeidler D and Wakker PP (2002). Utility in case-based decision theory. J Econ Theory 105: 483–502.

    Article  Google Scholar 

  • Goumas M and Lygerou V (2000). An extension of the PROMETHEE method for decision making in fuzzy environment: Ranking of alternative energy exploitation projects. Eur J Opl Res 123: 606–613.

    Article  Google Scholar 

  • Hazen G (1986). Partial information, dominance and potential optimality in multiattribute utility theory. Opns Res 34: 296–310.

    Article  Google Scholar 

  • Hyde K, Maier HR and Colby C (2005). Incorporating uncertainty in the PROMETHEE MCDA method. J Multi-Crit Decis Anal 12: 245–259.

    Article  Google Scholar 

  • Jacquet-Lagreze E and Siskos Y (1982). Assessing a set of additive utility functions for multicriteria decision making: The UTA method. Eur J Opl Res 10: 151–164.

    Article  Google Scholar 

  • Jaszkiewicz A and Ferhat AB (1999). Solving multiple criteria choice problems by interactive trichotomy segmentation. Eur J Opl Res 113: 271–280.

    Article  Google Scholar 

  • Jaszkiewicz A and Slowinski R (1997). The LBS-discrete interactive procedure for multiple-criteria analysis of decision problems. In: Clímaco J. (ed). Multicriteria Analysis, Proceedings of the 11th International Conference on MCDM. Springer-Verlag: Berlin, pp. 320–330.

    Google Scholar 

  • Karasakal EK and Michalowski W (2003). Incorporating wealth information into a multiple criteria decision making model. Eur J Opl Res 150: 204–219.

    Article  Google Scholar 

  • Keeney RL and Raiffa H (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley: New York.

    Google Scholar 

  • Kim SH and Ahn BS (1999). Interactive group decision making procedure under incomplete information. Eur J Opl Res 116: 498–507.

    Article  Google Scholar 

  • Kirkwood CW and Sarin RK (1985). Ranking with partial information: A method and an application. Opns Res 33: 38–48.

    Article  Google Scholar 

  • Köksalan M and Karasakal E (2006). An interactive approach for multiobjective decision making. J Opl Res Soc 57: 532–540.

    Article  Google Scholar 

  • Köksalan MM and Sagala PNS (1995). Interactive approaches for discrete alternative multiple criteria decision making with monotone utility functions. Mngt Sci 41: 1158–1171.

    Article  Google Scholar 

  • Korhonen P (1988). A visual reference direction approach to solving discrete multiple criteria problems. Eur J Opl Res 34: 152–159.

    Article  Google Scholar 

  • Lee KS, Park KS, Eum YS and Park K (2001). Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information. Eur J Opl Res 134: 557–563.

    Article  Google Scholar 

  • Lotfi V, Theodor JS and Zionts S (1992). An aspiration-level interactive model for multiple criteria decision making. Comput Opl Res 19: 671–681.

    Article  Google Scholar 

  • Malakooti B (1989). Identifying nondominated alternatives with partial information for multiple-objective discrete and linear programming problems. IEEE T Syst Man Cybernet A 19: 95–107.

    Article  Google Scholar 

  • Malakooti B (2000). Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences. IEEE T Syst Man Cybernet A 30: 355–368.

    Article  Google Scholar 

  • Mareschal B and Brans JP (1988). Geometrical representations for MCDA. Eur J Opl Res 34: 69–77.

    Article  Google Scholar 

  • Mareschal B and Brans JP (1995). The PROMETHEE VI Procedure: How to differentiate hard from soft multicriteria problems. J Decis Syst 4: 213–223.

    Article  Google Scholar 

  • Marmol AM, Puerto J and Fernandez FR (2002). Sequential incorporation of imprecise information in multiple criteria decision processes. Eur J Opl Res 137: 123–133.

    Article  Google Scholar 

  • Miettinen K and Salminen P (1999). Decision-aid for discrete multiple criteria decision making problems with imprecise data. Eur J Opl Res 119: 50–60.

    Article  Google Scholar 

  • Mousseau V (2005). A general framework for constructive learning preference elicitation in multiple criteria decision aid. Cahier du Lamsade 223: Université Paris Dauphine.

    Google Scholar 

  • Mousseau V, Figueira J, Dias LC, Gomes da Silva C and Clímaco JN (2003). Resolving inconsistencies among constraints on the parameters of an MCDA model. Eur J Opl Res 147: 72–93.

    Article  Google Scholar 

  • Ngo The A and Mousseau V (2002). Using assignment examples to infer category limits for the ELECTRE TRI method. J Multi-Crit Decis Anal 11: 29–43.

    Article  Google Scholar 

  • Park KS and Kim SH (1997). Tools for interactive multi-attribute decision making with incompletely identified information. Eur J Opl Res 98: 111–123.

    Article  Google Scholar 

  • Park KS, Kim SH and Yoon WC (1996). Establishing strict dominance between alternatives with special type of incomplete information. Eur J Opl Res 96: 398–406.

    Article  Google Scholar 

  • Pomerol JC and Barba-Romero S (2000). Multicriteria Decision in Management, Principles and Practice. Kluwer Academic Publishers: Boston.

    Book  Google Scholar 

  • Puerto J, Mármol AM, Monroy L and Fernández FR (2000). Decision criteria with partial information. Int Trans Opl Res 7: 51–65.

    Article  Google Scholar 

  • Roy B (1991). The outranking approach and the foundations of ELECTRE methods. Theor Decis 31: 49–73.

    Article  Google Scholar 

  • Roy B and Hugonnard JC (1982). Ranking of suburban line extension projects on the Paris metro system by a multicriteria method. Transport Res 16A: 301–312.

    Article  Google Scholar 

  • Saaty TL (1980). The Analytic Hierarchy Process. McGraw-Hill: New York.

    Google Scholar 

  • Vetschera R (2002). An outranking relation based on incomplete additive preferences. Working Paper OP 2002-02, University of Vienna, Vienna, Austria.

  • Vincke P (1992). Multicriteria Decision-Aid. Wiley: Chichester.

    Google Scholar 

  • Weber M (1985). A method for multiattribute decision making with incomplete information. Mngt Sci 31: 1365–1371.

    Article  Google Scholar 

  • Zionts S (1981). A multiple criteria method for choosing among discrete alternatives. Eur J Opl Res 7: 143–147.

    Article  Google Scholar 

  • Zionts S and Wallenius J (1976). An interactive programming method for solving the multiple criteria problem. Mngt Sci 22: 652–663.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Middle East Technical University, Ankara, Turkey

    G Özerol & E Karasakal

Authors
  1. G Özerol
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E Karasakal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E Karasakal.

Appendices

Appendix A: INPRO-A Algorithm

Step 1::

Take the f i (x k) ∀i and ∀k and convert them into r i k ∀i and ∀k.

Step 2::

Ask the DM for q i , p i or σ i ∀i. If no thresholds are given, assign q i =p i =σ i =0 ∀i. Compute P i (x k,x j) ∀i and ∀k, j, j ≠ k and φ i (x k) ∀i and ∀k.

Ask the DM for initial partial information on criterion weights, W.

Step 3::

In order to find φ̲(x k) and of each alternative, solve LPO for each alternative. (If the optimal objective function value of LPO is infeasible, then ask the DM to delete one or more of the constraints in order to resolve inconsistency.)

Present the following results to the DM with corresponding weight vectors:

• φ̲(x k), , alternatives ranked by descending order of lower and upper bounds.

Find and display the following information on the current solution to the DM:

• φ p, sets of OAs and NOAs, number of OAs and NOAs.

Step 4::

If the DM wants to make a final decision using the results of the current iteration or if single alternative is left in the set of NOAs, STOP. Display φ̲(x k) and with corresponding weight vectors, and the sets of OAs and NOAs along with further ranks of OAs, if any. Otherwise, go to Step 5.

Step 5::

(a) If the DM wants to put a threshold on φ p, update φ p and the sets of NOAs and OAs.

(b) If the DM wants to provide additional constraints on criterion weights, update W. Go to Step 3.

(c) If the DM wants to make a pairwise comparison, update W. Go to Step 3.

Appendix B: INPRO-B Algorithm

Step 1::

Take f i (x k) ∀i and ∀k and convert them into r i k ∀i and ∀k.

Step 2::

Ask the DM for q i , p i or σ i ∀ i . If no thresholds are given, assign q i =p i =σ i =0 ∀i. Compute P i (x k,x j) ∀i and ∀k,j,j≠k, and φ i +(x k) and φ i −(x k) ∀i and ∀k.

Ask the DM for initial partial information on criterion weights, W.

Step 3::

In order to find φ̲ +(x k) and of each alternative, solve LPOL for each alternative (If LPOL is infeasible, then ask the DM to delete one or more of the constraints in order to resolve inconsistency.) In order to find φ̲ −(x k) and of each alternative, solve LPOE for each alternative. Present the following results to the DM with corresponding weight vectors:

• φ +(x k), , φ −(x k), , alternatives ranked by descending order of upper bound on leaving flows and lower bound on entering flows.

Find and display the following information on the current solution to the DM:

• φ p+, φ p−, sets of OAs and NOAs, number of OAs and NOAs.

Step 4::

If the DM wants to make a final decision using the results of the current iteration, STOP.

Display φ +(x k), , φ −(x k) and with corresponding weight vectors, and sets of OAs and NOAs along with further ranks of OAs, if any. Otherwise, go to Step 5.

Step 5::

(a) If the DM wants to put a threshold on φ p+ and/or φ p−, update φ p+ and/or φ p− and the sets of NOAs and OAs.

(b) If the DM wants to provide additional constraints on criterion weights, update W. Go to Step 3.

(c) If the DM wants to make a pairwise comparison, update W. Go to Step 3.

Appendix C: INPRO-C Algorithm

All steps except Step 2 and 3 are the same as those of INPRO-A. Steps 2 and 3 of INPRO-A algorithm are to be read as follows:

Step 2::

Ask the DM for p, p̄, q and q̄

Compute P i (x k,x j) ∀i and ∀k, j,j≠k, first for p and q and then for p̄ and q̄.

Ask the DM for initial partial information on criterion weights, W.

Step 3::

In order to find φ̲(x k) and of each alternative follow Steps 3.1 and 3.2.

Step 3.1::

Set p=p and q=q, compute φ i +(x k) ∀i and ∀k, and then set p=p̄ and q=q̄ and compute φ i −(x k) ∀i and ∀k.

Solve LPO1 for each alternative in order to find the upper bound on the net flow of each alternative.

Step 3.2::

Set p=p̄ and q=q̄, compute φ i +(x k) ∀i and ∀k, and then set p=p and q=q and compute φ i −(x k) ∀i and ∀k.

Solve LPO2 for each alternative in order to find the lower bound on the net flow of each alternative.

If the optimal objective function value of LPO1 is infeasible, then ask the DM to delete one or more of the constraints in order to resolve inconsistency. Otherwise continue as in INPRO-A algorithm.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Özerol, G., Karasakal, E. Interactive outranking approaches for multicriteria decision-making problems with imprecise information. J Oper Res Soc 59, 1253–1268 (2008). https://doi.org/10.1057/palgrave.jors.2602458

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/palgrave.jors.2602458

Keywords

Search

Navigation