Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


2017 | 12 | 36-48

Article title

Bipolar Mix – A Method for Mixed Evaluations and its Application to the Ranking of European Projects



Title variants

Languages of publication



A great variety of multi-criteria decision aiding (MCDA) methods has already been developed but few papers have dealt with mixed data (qualitative and quantitative). MCDA techniques accepting different types of evaluations (such as deterministic, stochastic and/or fuzzy ones) are rather rare and not very well known, even though this issue is crucial from a practical point of view, since mixed evaluations occur very frequently in appraising and selecting projects and organizations, as well as in risk management modelling, among other fields. This paper presents a new discrete MCDA tool developed for mixed performances of alternatives called BIPOLAR MIX. It is based on the classical BIPOLAR method proposed by Konarzewska-Gubała (1989), and on its modification, namely the BIPOLAR method with stochastic dominance (SD) rules, proposed by Górecka (2009). A numerical example at the end of the paper illustrates the problem of ordering projects applying for co-financing from the European Union (EU).






Physical description


  • Nicolaus Copernicus University in Toruń. Faculty of Economic Sciences and Management. Department of Econometrics and Statistics. Toruń, Poland


  • Ben Amor S., Jabeur K., Martel J.M. (2007), Multiple Criteria Aggregation Procedure for Mixed Evaluations, European Journal of Operational Research, 18(3), 1506-1515.
  • Chojnacka E., Górecka D. (2016), Evaluating Public Benefit Organizations in Poland with the EVAMIX Method for Mixed Data, Multiple Criteria Decision Making, 11, 36-50.
  • Goovaerts M.J., De Vylder F., Haezendonck J. (1984), Insurance Premiums: Theory and Applications, North-Holland, Amsterdam.
  • Górecka D. (2009), Wielokryterialne wspomaganie wyboru projektów europejskich, TNOiK ,,Dom Organizatora”, Toruń.
  • Górecka D. (2010a), Wykorzystanie metod wielokryterialnych w procesie oceny i wyboru wniosków o dofinansowanie realizacji projektu z funduszy Unii Europejskiej, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, 108, 76-91.
  • Górecka D. (2010b), Zastosowanie metod wielokryterialnych opartych na relacji przewyższania do oceny europejskich projektów inwestycyjnych [in:] M. Nowak (red.), Metody i zastosowania badań operacyjnych’10, Wydawnictwo Uniwersytetu Ekonomicznego w Katowicach, Katowice, 100-125.
  • Górecka D. (2011), On the Choice of Method in Multi-criteria Decision Aiding Process Concerning European Projects [in:] T. Trzaskalik, T. Wachowicz (eds.), Multiple Criteria Decision Making ’10-11, Publisher of The University of Economics in Katowice, Katowice, 81-103.
  • Górecka D. (2012), Sensitivity and Robustness Analysis of Solutions Obtained in the European Projects’ Ranking Process [in:] T. Trzaskalik, T. Wachowicz (eds.), Multiple Criteria Decision Making’12, Publisher of the University of Economics in Katowice, Katowice, 86-111.
  • Górecka D. (2012), Applying Multi-Criteria Decision Aiding Techniques in the Process of Project Management within the Wedding Planning Business, Operations Research and Decisions, 22(4), 41-67.
  • Górecka D. (2014a), Metoda BIPOLAR z dominacjami stochastycznymi [in:] T. Trzaskalik (red.), Wielokryterialne wspomaganie decyzji. Metody i zastosowania, PWE, Warszawa, 149-152.
  • Górecka D. (2014b), Metoda PROMETHEE II z progami weta i dominacjami stochastycznymi [in:] T. Trzaskalik (red.), Wielokryterialne wspomaganie decyzji. Metody i zastosowania, PWE, Warszawa, 122-124.
  • Górecka D. (2014c), Reguły wyboru oparte na relacji prawie dominacji stochastycznej dla kryteriów ocenianych w skali porządkowej [in:] T. Trzaskalik (red.), Wielokryterialne wspomaganie decyzji. Metody i zastosowania, PWE, Warszawa, 31-32.
  • Guitouni A., Martel J.-M., Bélanger M., Hunter C. (1999), Managing a Decision Making Situation in the Context of the Canadian Airspace Protection, Working paper 1999-021, F.S.A., Université Laval, Canada.
  • Hadar J., Russel W. (1969), Rules for Ordering Uncertain Prospects, American Economic Review, 59, 25-34.
  • Konarzewska-Gubała E. (1989), Bipolar: Multiple Criteria Decision Aid Using the Bipolar Reference System, Cahiers et Documents du LAMSADE, Université Paris IX, Paris.
  • Konarzewska-Gubała E. (1991), Wspomaganie decyzji wielokryterialnych: system BIPOLAR, Wydawnictwo Uczelniane Akademii Ekonomicznej we Wrocławiu, Wrocław.
  • Leshno M., Levy H. (2002), Preferred by “All” and Preferred by “Most” Decision Makers: Almost Stochastic Dominance, Management Science, 48, 1074-1085.
  • Lootsma F.A., Mensch T.C.A., Vos F.A. (1990), Multi-criteria Analysis and Budget Reallocation in Long-term Research Planning, “European Journal of Operational Research”, 47, 293-305.
  • Martel J.-M., Kiss L.R., Rousseau A. (1997), PAMSSEM: Procédure d’agrégation multicritère de type surclassement de synthèse pour évaluations mixtes, Manuscript, F.S.A., Université Laval.
  • Munda G. (1995), Multicriteria Evaluation in a Fuzzy Environment, Physica-Verlag, Heidelberg.
  • Munda G., Nijkamp P., Rietveld P. (1995), Qualitative Multicriteria Methods for Fuzzy Evaluation Problems: An Illustration of Economic-ecological Evaluation, European Journal of Operational Research, 82(1), 79-97.
  • Nowak M. (2004), Preference and Veto Thresholds in Multicriteria Analysis Based on Stochastic Dominance, European Journal of Operational Research, 158(2), 339-350.
  • Nowak M. (2005), Investment Project Evaluation by Simulation and Multiple Criteria Decision Aiding Procedure, Journal of Civil Engineering and Management, 11(3), 193-202.
  • Olson D.L., Fliedner G., Currie K. (1995), Comparison of the REMBRANDT System with Analytic Hierarchy Process, “European Journal of Operational Research”, 82, 522-531.
  • Quirk J.P., Saposnik R. (1962), Admissibility and Measurable Utility Functions, Review of Economic Studies, 29, 140-146.
  • Roy B. (1990), Wielokryterialne wspomaganie decyzji, Wydawnictwa Naukowo-Techniczne, Warszawa.
  • Spector Y., Leshno M., Ben Horin M. (1996), Stochastic Dominance in an Ordinal World, European Journal of Operational Research, 93, 620-627.
  • Voogd H. (1982), Multicriteria Evaluation with Mixed Qualitative and Quantitative Data, Environment and Planning B, 9, 221-236.
  • Voogd H. (1983), Multicriteria Evaluation for Urban and Regional Planning, Pion, London.
  • Whitmore G.A. (1970), Third-Degree Stochastic Dominance, American Economic Review, 60, 457-459.
  • Zaras K. (1989), Les dominances stochastiques pour deux classes de fonction d’utilité: concaves et convexes, RAIRO/RO, 23, 57-65.
  • Zaras K. (2004), Rough Approximation of a Preference Relation by a Multi-attribute Dominance for Deterministic, Stochastic and Fuzzy Decision Problems, European Journal of Operational Research, 159(1), 196-206.
  • (www 1) European Commission: Regional Policy – Inforegio, http://ec.europa.eu/regional_policy/en/ (accessed: 1.06.2017).

Document Type

Publication order reference



YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.