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A Ranking Method Based on the Aggregate Distance Measure Function in the Value Space

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  • Piotr Zielniewicz

    (Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland)

Abstract

The aim of this paper is to introduce a new MCDA method for ranking a finite set of alternatives evaluated on multiple criteria. The proposed method uses the idea of the robust ordinal regression (ROR) approach to establish the ranking scores determined by the distance measure function, however not in the criteria space, but in the value space. The preference model is composed of a set of additive value functions compatible with the preference information provided by the decision maker (DM). From among many forms of an additive preference model, we consider the model having as simple form as possible, i.e., the model that is the “closest to linear”. We define an achievement scalarizing function representing closeness to the ideal solution in the value space. A set of mix-integer linear programming (MILP) problems is then solved to determine the minimum distance scores of each alternative on the set of compatible value functions. Then, the obtained distance scores are used to rank all alternatives. A hypothetical case study is then performed to illustrate the proposed method. Finally, the result of our method is discussed and compared with results obtained by other methods based on the distance measure function (i.e., TOPSIS and VIKOR).

Suggested Citation

  • Piotr Zielniewicz, 2017. "A Ranking Method Based on the Aggregate Distance Measure Function in the Value Space," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 685-710, May.
    • Handle: RePEc:wsi:ijitdm:v:16:y:2017:i:03:n:s0219622017500122
    DOI: 10.1142/S0219622017500122
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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, September.
    2. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    3. Kadziński, Miłosz & Greco, Salvatore & Słowiński, Roman, 2012. "Selection of a representative value function in robust multiple criteria ranking and choice," European Journal of Operational Research, Elsevier, vol. 217(3), pages 541-553.
    4. V. Srinivasan & Allan Shocker, 1973. "Estimating the weights for multiple attributes in a composite criterion using pairwise judgments," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 473-493, December.
    5. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2007. "Extended VIKOR method in comparison with outranking methods," European Journal of Operational Research, Elsevier, vol. 178(2), pages 514-529, April.
    6. Bell, Michelle L. & Hobbs, Benjamin F. & Ellis, Hugh, 2003. "The use of multi-criteria decision-making methods in the integrated assessment of climate change: implications for IA practitioners," Socio-Economic Planning Sciences, Elsevier, vol. 37(4), pages 289-316, December.
    7. Adler, Nicole & Yazhemsky, Ekaterina & Tarverdyan, Ruzanana, 2010. "A framework to measure the relative socio-economic performance of developing countries," Socio-Economic Planning Sciences, Elsevier, vol. 44(2), pages 73-88, June.
    8. Fuad Aleskerov & Hasan Ersel & Reha Yolalan, 2004. "Multicriterial Ranking Approach For Evaluating Bank Branch Performance," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 321-335.
    9. Yu-Ping Ou Yang & How-Ming Shieh & Jun-Der Leu & Gwo-Hshiung Tzeng, 2009. "A Vikor-Based Multiple Criteria Decision Method For Improving Information Security Risk," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 267-287.
    10. Bernard Roy & Roman Slowinski, 2013. "Questions guiding the choice of a multicriteria decision aiding method," Post-Print hal-00874292, HAL.
    11. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    12. Mousseau, Vincent & Figueira, Jose & Dias, Luis & Gomes da Silva, Carlos & Climaco, Joao, 2003. "Resolving inconsistencies among constraints on the parameters of an MCDA model," European Journal of Operational Research, Elsevier, vol. 147(1), pages 72-93, May.
    13. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
    14. Dov Pekelman & Subrata K. Sen, 1974. "Mathematical Programming Models for the Determination of Attribute Weights," Management Science, INFORMS, vol. 20(8), pages 1217-1229, April.
    15. Alçada-Almeida, Luís & Coutinho-Rodrigues, João & Current, John, 2009. "A multiobjective modeling approach to locating incinerators," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 111-120, June.
    16. repec:hal:wpaper:hal-00874292 is not listed on IDEAS
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    3. Susmaga, Robert & Szczȩch, Izabela & Zielniewicz, Piotr & Brzezinski, Dariusz, 2023. "MSD-space: Visualizing the inner-workings of TOPSIS aggregations," European Journal of Operational Research, Elsevier, vol. 308(1), pages 229-242.

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