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


2015 | 10 | 32-47

Article title

A decision rule for uncertain multicriteria mixed decision making based on the coefficient of optimism


Title variants

Languages of publication



This paper is devoted to multicriteria decision making under uncertainty with scenario planning. This topic has been explored by many researchers since almost all real-world decision problems contain multiple conflicting criteria and a deterministic criteria evaluation is often impossible. We propose a procedure for uncertain multi-objective optimization which may be applied when a mixed strategy is sought after. A mixed strategy, as opposed to a pure strategy, allows the decision maker to select and perform a weighted combination of several accessible alternatives. The new approach takes into account the decision maker’s preference structure and attitude towards risk. This attitude is measured by the coefficient of optimism on the basis of which a set of the most probable events is suggested and an optimization problem is formulated and solved.






Physical description



  • Aghdaie M.H., Zolfani S.H., Zavadskas E.K. (2013), Market Segment Evaluation and Selection Based on Application of Fuzzy AHP and COPRAS-G Methods, Journal of Business Economics and Management, 14(1), 213-233.
  • Bana e Costa C.A., Chakas M.P. (2004), A Carter Choice Problem: An Example of How to Use MACBETH to Build a Quantitative Value Model Based on Qualitative Value Judgements, European Journal of Operational Research, 153.
  • Basili M. (2006), A Rational Decision Rule with Extreme Events, Risk Analysis, 26, 1721-1728.
  • Basili M., Chateauneuf A., Fontini F. (2008), Precautionary Principle as a Rule of Choice with Optimism on Windfall Gains and Pessimism on Catastrophic Losses, Ecological Economics, 67, 485-491.
  • Basili M., Chateauneuf A. (2011), Extreme Events and Entropy: A Multiple Quantile Utility Model, International Journal of Approximate Reasoning, 52, 1095-1102.
  • Ben Amor S., Jabeur K., Martel J. (2007), Multiple Criteria Aggregation Procedure for Mixed Evaluations, European Journal of Operational Research, 181(3), 1506-1515.
  • Brans J.P., Mareschal B., Vincke Ph. (1984), PROMETHEE: A New Family of Outranking Methods in Multicriteria Analysis [in:] J.P. Brans (ed.), Operational Research’84, North-Holland, Amsterdam.
  • Chang C.-T. (2011), Multi-choice Goal Programming with Utility Functions, European Journal of Operational Research, 215, 439-445.
  • Churchman C.W., Ackoff R.L. (1954), An Approximate Measure of Value, Journal of Operations Research of America, 2(1), 172-187.
  • Courtney H., Kirkland J., Viquerie P. (1997), Strategy under Uncertainty, Harvard Business Review, 75(6), 66-79.
  • Czerwinski Z. (1969), Matematyka na usługach ekonomii, Państwowe Wydawnictwo Naukowe, Warszawa.
  • Dominiak C. (2006), Multicriteria Decision Aid under Uncertainty, Multiple Criteria Decision Making’ 05, 63-81.
  • Dominiak C. (2009), Multi-criteria Decision Aiding Procedure under Risk and Uncertainty, Multiple Criteria Decision Making’ 08, 61-88.
  • Durbach I.N. (2014), Outranking under Uncertainty Using Scenarios, European Journal of Operational Research, 232(1), 98-108.
  • Durbach I.N., Stewart T.J. (2012), Modeling Uncertainty in Multi-criteria Decision Analysis, European Journal of Operational Research, 223(1), 1-14.
  • Edwards W., Barron F.H. (1994), SMARTS and SMARTER: Improved Simple Methods for Multiattribute Measurement, Organizational Behaviour and Human Decision Process, 60.
  • Eiselt H.A., Marianov V. (2014), Multicriteria Decision Making under Uncertainty: A Visual Approach, International Transactions in Operational Research, 21(4), 525-540.
  • Ellsberg D. (2001), Risk, Ambiguity and Decision, Garland Publishing, New York.
  • Etner J., Jeleva M., Tallon J.-M. (2012), Decision Theory under Ambiguity, Journal of Economic Surveys, 26(2), 234-270.
  • Fishburn P.C. (1984), Foundations of Risk Measurement. I. Risk or Probable Loss, Management Science, 30, 396-406.
  • Gaspars H. (2007), Resource Allocation under Uncertainty: Choice Models and Computational Procedures [Alokacja zasobu w warunkach niepewności: modele decyzyjne i procedury obliczeniowe], Operations Research and Decisions, 1, 5-27 (in Polish).
  • Gaspars-Wieloch H. (2011), Metakryterium w ciągłej wersji optymalizacji wielocelowej – analiza mankamentów metody i próba jej udoskonalenia [The Aggregate Objective Function in the Continuous Version of the Multicriteria Optimization – An Analysis of the Shortcomings of the Method and Attempt at Improving It] [in:] E. Konarzewska-Gubała (ed.), Zastosowania badań operacyjnych. Zarządzanie projektami, decyzje finansowe, logistyka, Wydawnictwo Uniwersytetu Ekonomicznego, Wrocław, 313-332 (in Polish).
  • Gaspars-Wieloch H. (2012), Limited Efficiency of Optimization Methods in Solving Economic Decision Problems [Ograniczona skuteczność metod optymalizacyjnych w rozwiązywaniu ekonomicznych problemów decyzyjnych], Ekonomista, 3, 303-324 (in Polish).
  • Gaspars-Wieloch H. (2013), On a Decision Rule Supported by a Forecasting Stage Based on the Decision Maker’s Risk Aversion [in:] L. Zadnik Stirn, J. Zerovnik, J. Povh, S. Drobne, A. Lisec (eds.), SOR’13 Proceedings, The 12th International Symposium on Operational Research in Slovenia, 25-27 September, Dolenjske Toplice, Slovenia, Slovenian Society INFORMATIKA, Section for Operational Research, 53-59.
  • Gaspars-Wieloch H. (2014a), A Hybrid of the Hurwicz and Bayes Rules in Decision Making under Uncertainty [Propozycja hybrydy reguł Hurwicza i Bayesa w podejmowaniu decyzji w warunkach niepewności] [in:] T. Trzaskalik (ed.), Modelowanie Preferencji a Ryzyko 2014, Studia Ekonomiczne. Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach nr 178, Wydawnictwo Uniwersytetu Ekonomicznego, Katowice, 74-92 (in Polish).
  • Gaspars-Wieloch H. (2014b), On a Decision Rule for Mixed Strategy Searching under Uncertainty on the Basis of the Coefficient of Optimism, Procedia – Social and Behavioral Sciences, Elsevier, 110, 923-931.
  • Gaspars-Wieloch H. (2014c), Modifications of the Hurwicz’s Decision Rules, Central European Journal of Operations Research, 22(4), 779-794.
  • Gaspars-Wieloch H. (2014d), Modifications of the Maximin Joy Criterion for Decision Making under Uncertainty, Quantitative Methods in Economics, XV, 84-93.
  • Gaspars-Wieloch H. (2014e), The Use of a Modification of the Hurwicz’s Decision Rule in Multicriteria Decision Making under Complete Uncertainty, Business, Management and Education, 12(2), 283-302.
  • Gaspars-Wieloch H. (2015a), Modifications of the Omega Ratio for Decision Making under Uncertainty, Croatian Operational Research Review, 6(1), 181-194.
  • Gaspars-Wieloch H. (2015b), On a Decision Rule Supported by a Forecasting Stage Based on the Decision Maker’s Coefficient of Optimism, Central European Journal of Operations Research, 23(3), 579-594.
  • Gaspars-Wieloch H. (2015c), Innovative Products and Newsvendor Problem under Uncertainty without Probabilities [in:] L. Zadnik Stirn, J. Zerovnik, M. Kljajic Borstnar, S. Drobne (eds.), SOR’15 Proceedings, The 13th International Symposium on Operational Research in Slovenia, 23-25 September, Bled, Slovenia, Slovenian Society INFORMATIKA, Section for Operational Research, 343-350.
  • Ghirardato P., Maccheroni F., Marinacci M. (2004), Differentiating Ambiguity and Ambiguity Attitude, Journal of Economic Theory, 118, 133-173.
  • Gilboa I. (2009), Theory of Decision under Uncertainty, Cambridge University Press, Cambridge, New York.
  • Gilboa I., Schmeidler D. (1989), Maxmin Expected Utility with Non-unique Prior, Journal of Mathematical Economics, 18, 141-153.
  • Ginevičius R., Zubrecovas V. (2009), Selection of the Optimal Real Estate Investment Project Basing on Multiple Criteria Evaluation Using Stochastic Dimensions, Journal of Business Economics and Management, 10(3), 261-270.
  • Goodwin P., Wright G. (2001), Enhancing Strategy Evaluation in Scenario Planning: A Role for Decision Analysis, Journal of Management Studies, 38(1), 1-16.
  • Grigorieva X. (2014), Multicriteria Coalitional Model of Decision-making over the Set of Projects with Constant Payoff Matrix in the Noncooperative Game, Applied Mathematical Sciences, 8(170), 8473-8479.
  • Groenewald M.E., Pretorius P.D. (2011), Comparison of Decision Making Under Uncertainty Investment Strategies with the Money Market, Journal of Financial Studies and Research.
  • Guo P. (2014), One-shot Decision Theory: A Fundamental Alternative for Decision under Uncertainty, Human-Centric Decision-Making Models for Social Sciences, 2014, 33-55.
  • Guo P. (2013), One-Shot Decision Making with Regret, International Conference on Information Science and Technology, 23-25 March, Yangzhou, China, 493-495.
  • Guo P. (2011), One-shot Decision Theory, IEEE Transactions on Systems, Man, and Cybernetics, Part A, 41(5), 917-926.
  • Guo P. (2010), Private Real Estate Investment Analysis within One-shot Decision Framework, International Real Estate Review, 13(3), 238-260.
  • Guzik B. (2009), Introduction to Operations Research [Wstęp do badań operacyjnych], Wydawnictwo Uniwersytetu Ekonomicznego, Poznań (in Polish).
  • Hayashi T. (2008), Regret Aversion and Opportunity Dependence, Journal of Economic Theory, 139(1), 242-268.
  • Hopfe C.J., Augenbroe G.L.M., Hensen J.L.M. (2013), Multicriteria Decision Making under Uncertainty in Building Performance Assessment, Building and Environment, 69, 81-90.
  • Hurwicz L. (1952), A Criterion for Decision Making under Uncertainty, Technical Report, 355. Cowles Commission.
  • Hwang C.L., Yoon K. (1981), Multiple Attribute Decision Making Methods and Applications: A State of the Art Survey, Springer-Verlag, New York.
  • Ignasiak E. (ed.) (1996), Badania operacyjne [Operations Research], Polskie Wydawnictwo Ekonomiczne, Warsaw (in Polish).
  • Ioan C., Ioan G. (2011), A Method of Choice of the Best Alternative in the Multiple Solutions Case in the Games Theory, The Journal of Accounting and Management, 1(1), 5-8.
  • Janjic A., Andjelkovic A., Docic M. (2013), Multiple Criteria Decision Making under Uncertainty Based on Stochastic Dominance, Proceedings of the 2013 International Conference on Applied Mathematics and Computational Methods in Engineering 16-19 July, Rhodes Island, Greece, 86-91.
  • Knight F.H. (1921), Risk, Uncertainty, Profit, Hart, Schaffner & Marx, Houghton Mifflin Co., Boston, MA.
  • Konarzewska-Gubała E. (1989), Bipolar: Multiple Criteria Decision Aid Using Bipolar Reference System. LAMSADE, Cahiers et Documents, 56.
  • Korhonen A. (2001), Strategic Financial Management in a Multinational Financial Conglomerate: A Multiple Goal Stochastic Programming Approach, European Journal of Operational Research, 128, 418-434.
  • Larichev O.I., Moshkovich H.M. (1995), ZAPROS-LM – A Method and System for Ordering Multiattribute Alternatives, European Journal of Operational Research, 82.
  • Lee Y.-H. (2012), A Fuzzy Analytic Network Process Approach to Determining Prospective Competitive Strategy in China: A Case Study for Multinational Biotech Pharmaceutical Enterprises, Journal of Business Economics and Management, 13(1), 5-28.
  • Liu M., Zhao L. (2009), Optimization of the Emergency Materials Distribution Network with Time Windows in Anti-bioterrorism System, International Journal of Innovative Computing, Information and Control, 5 (11A), 3615-3624.
  • Liu Y., Fan Z., Hang Y. (2011), A Method for Stochastic Multiple Criteria Decision Making Based on Dominance Degrees, Information Sciences, 181(19), 4139-4153.
  • Lootsma F.A. (1993), Scale Sensitivity in the Multiplicative AHP and SMART, Journal of Multicriteria Decision Analysis, 2(2), 87-110 .
  • Lotfi V., Yoon Y.S., Zionts S. (1997), Aspiration-based Search Algorithm (ABSALG) for Multiple Objective Linear Programming Problems: Theory and Comparative Tests, Management Science, 43, 1047-1059.
  • Lozan V., Ungureanu V. (2013), Computing the Pareto-Nash Equilibrium Set in Finite Multiobjective Mixed-strategy Games, Computer Science Journal of Moldova, 21, 2(62), 173-203.
  • Luce R.D., Raiffa H. (1957), Games and Decisions, Wiley, New York.
  • Marinacci M. (2002), Probabilistic Sophistication and Multiple Priors, Econometrica, 70, 755-764.
  • Marler R., Arora J. (2004), Survey of Multiobjective Methods for Engineering, Structural and Multidisciplinary Optimization, 26(6), 369-395.
  • Michnik J. (2012), What Kinds of Hybrid Models Are Used in Multiple Criteria Decision Analysis and Why? Multiple Criteria Decision Making ’12, 161-168.
  • Michnik J. (2013), Multi-criteria Methods Supporting Decisions in Innovation Process [Wielokryterialne metody wspomagania decyzji w procesie innowacji], Wydawnictwo Uniwersytetu Ekonomicznego, Katowice (in Polish).
  • Mikhaidov L., Tsvetinov P. (2004), Evaluation of Services Using a Fuzzy Analytic Hierarchy Process, Applied Soft Computing Journal, 5(1), 23-33.
  • Milnor J. (1954), Games against Nature in Decision Processes, Wiley, New York, 49-60.
  • Montibeller G., Gummer H., Tumidei D. (2006), Combining Scenario Planning and Multi-criteria Decision Analysis in Practice, Journal of Multi-criteria Decision Analysis, 14, 5-20.
  • Neumann J. von, Morgenstern O. (1944), Theory of Games and Economic Behavior, Princeton University Press, Princeton, New York.
  • Officer R.R., Anderson J.R. (1968), Risk, Uncertainty and Farm Management Decisions, Review of Marketing and Agricultural Economics, 36(01).
  • Ogryczak W., Śliwiński T. (2009), On Efficient WOWA Optimization for Decision Support under Risk, International Journal of Approximate Reasoning, 50, 915-928.
  • Opricovic S. (1998), Multicriteria Optimization of Civil Engineering Systems, Technical Report. Faculty of Civil Engineering, Belgrade.
  • Piasecki K. (1990), Decisions and Reliable Forecasts [Decyzje i wiarygodne prognozy], Akademia Ekonomiczna, Poznań (in Polish).
  • Pomerol J.C. (2001), Scenario Development and Practical Decision Making under Uncertainty, Decision Support Systems, 31(2), 197-204.
  • Puppe C., Schlag K. (2009), Choice under Complete Uncertainty when Outcome Spaces Are State Dependent, Theory and Decision, 66, 1-16.
  • Ram C., Montibeller G., Morton A. (2010), Extending the Use of Scenario Planning and MCDA for the Evaluation of Strategic Options, Journal of Operational Research Society, 62(5), 817-829.
  • Ramík J., Hanclova J., Trzaskalik T., Sitarz S. (2008), Fuzzy Multiobjective Methods in Multistage Decision Problems, Multiple Criteria Decision Making ‘07, 186-201.
  • Ravindran A.R. (2008), Operations Research and Management Science Handbook, CRS Press, Boca Raton, London, New York.
  • Render B., Stair R.M., Hanna M.E. (2006), Quantitative Analysis for Management, Pearson Prentice Hall, Upper Saddle River, New Jersey.
  • Roy B., Bouyssou D. (1993), Aide Multicritère à la Decision: Méthodes et Cas, Economica, Paris.
  • Savage L. (1961), The Foundations of Statistics Reconsidered, Studies in Subjective Probability, Wiley, New York, 173-188.
  • Saaty T.L. (1980), The Analytic Hierarchy Process, McGraw-Hill, New York.
  • Saaty T.L. (1996), Decision Making with Dependence and Feedback: Analytic Network Process, RWS Publications, Pittsburgh.
  • Schmeidler D. (1986), Integral Representation without Additivity, Proceedings of the American Mathematical Society, 97, 255-261.
  • Sikora W. (ed.) (2008), Badania Operacyjne [Operations Research], Polskie Wydawnictwo Ekonomiczne, Warszawa (in Polish).
  • Stewart T.J. (2005), Dealing with Uncertainties in MCDA. Multiple Criteria Decision Analysis: State of the Art Surveys, International Series in Operations Research & Management Science, 78, 445-466.
  • Suo M.Q., Li Y.P., Huang G.H. (2012), Multicriteria Decision Making under Uncertainty: An Advanced Ordered Weighted Averaging Operator for Planning Electric Power Systems, Engineering Applications of Artificial Intelligence, 25(1), 72-81.
  • Triantaphyllou E., Lin C. (1996), Development and Evaluation of Five Fuzzy Multiattribute Decision-making Methods, International Journal of Approximate Reasoning, 14(4), 281-310.
  • Trzaskalik T. (2008), Wprowadzenie do badań operacyjnych z komputerem [Introduction to Operations Research with Computer], 2nd ed., Polskie Wydawnictwo Ekonomiczne, Warsaw (in Polish).
  • Trzaskalik T. (2014), Wielokryterialne wspomaganie decyzji [Multicriteria Decision Aiding], Polskie Wydawnictwo Ekonomiczne, Warsaw (in Polish).
  • Tsaur S., Chang T., Yen C. (2002), The Evaluation of Airline Service Quality by Fuzzy MCDM, Tourism Management, 23(2), 107-115.
  • Tversky A., Kahneman D. (1992), Advances in Prospect Theory: Cumulative Representation of Uncertainty, Journal of Risk and Uncertainty, 5, 297-323.
  • Urli B., Nadeau R. (2004), PROMISE/scenarios: An Interactive Method for Multiobjective Stochastic Linear Programming under Partial Uncertainty, European Journal of Operational Research, 155(2), 361-372.
  • Van der Heijden K. (1996), Scenarios: The Art of Strategic Conversation, John Wiley and Sons,Chichester.
  • Voorneveld M., Vermeulen D., Borm P. (1999), Axiomatizations of Pareto Equilibria in Multicriteria Games, Games and Economic Behavior, 28, 146-154.
  • Voorneveld M., Grahn S., Dufwenberg M. (2000), Ideal Equilibria in Noncooperative Multicriteria Games, Mathematical Methods of Operations Research, 52, 65-77.
  • Wald A. (1950), Statistical Decision Functions, Wiley, New York.
  • Walliser B. (2008), Cognitive Economics, Springer, Berlin-Heidelberg.
  • Wang Y., Elhag T. (2006), Fuzzy TOPSIS Method Based on Alpha Level Sets With an Application to Bridge Risk Assessment, Expert Systems with Applications, 31(2), 309-319.
  • Williams C., Smith M., Young P. (1997), Risk Management and Insurance, McGraw-Hill.
  • Wojewnik P., Szapiro T. (2010), Bireference Procedure FBI for Interactive Multicriteria Optimization with Fuzzy Coefficients, Central European Journal of Economic Modelling and Econometrics, 2, 169-193.
  • Xu R. (2000), Fuzzy Least-squares Priority Method in the Analytic Hierarchy Process, Fuzzy Sets and Systems, 112(3), 395-404.
  • Yu C. (2002), A GP-AHP Method for Solving Group Decision-making Fuzzy AHP Problems, Computers and Operations Research, 29(14), 1969-2001.

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.