Decision Support under Risk by Optimization of Scenario Importance Weighted OWA Aggregations

• Autorzy: Ogryczak W. , Śliwiński T.
• Języki publikacji: EN

Abstrakty

EN

The problem of evaluation outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. The WOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e., to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective functions related to decisions under risk. Linear programming formulations are introduced for optimization of theWOWA objective representing risk averse preferences. Their computational efficiency is demonstrated.

Słowa kluczowe

EN

aggregation methods; decisions under risk; OWA; scenarios; WOWA

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2009
• Tom: nr 3
• Strony: 5--13
• Opis fizyczny: Bibliogr. 29 poz., tab.

Twórcy

autor

Ogryczak W.

autor

Śliwiński T.

• Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska st 15/19, 00-665 Warsaw, Poland,

Bibliografia

• [1] W. Ogryczak, “Multiple criteria optimization and decisions under risk”, Contr. Cyber., vol. 31, pp. 975–1003, 2002.
• [2] R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decision making”, IEEE Trans. Syst., Man Cyber., vol. 18, pp. 183–190, 1988.
• [3] M. Grabisch, S. A. Orlovski, and R. R. Yager, “Fuzzy aggregation of numerical preferences”, in Fuzzy Sets in Decision Analysis, Operations Research and Statistics. Dordrecht: Kluwer, 1999, pp. 31–68.
• [4] R. R. Yager and D. P. Filev, Essentials of Fuzzy Modeling and Control. New York: Wiley, 1994.
• [5] R. R. Yager and J. Kacprzyk, The Ordered Weighted Averaging Operators: Theory and Applications. Dordrecht: Kluwer, 1997.
• [6] W. Ogryczak, “Multiple criteria linear programming model for portfolio selection”, Ann. Oper. Res., vol. 97, pp. 143–162, 2000.
• [7] R. R. Yager, “Constrained OWA aggregation”, Fuzzy Sets Syst., vol. 81, pp. 89–101, 1996.
• [8] W. Ogryczak and T. Śliwiński, “On solving linear programs with the ordered weighted averaging objective”, Eur. J. Opnl. Res., vol. 148, pp. 80–91, 2003.
• [9] W. Ogryczak and A. Tamir, “Minimizing the sum of the k largest functions in linear time”, Inform. Proc. Let., vol. 85, pp. 117–122, 2003.
• [10] R. R. Yager, “Including importances in OWA aggegations using fuzzy systems modeling”, IEEE Trans. Fuzzy Syst., vol. 6, pp. 286–294, 1998.
• [11] H. L. Larsen, “Importance weighted OWA aggregation of multicriteria queries”, in Proc. North Amer. Fuzzy Inform. Proc. Soc. Conf. NAFIPS’99, New York, USA, 1999, pp. 740–744.
• [12] V. Torra, “The weighted OWA operator”, Int. J. Intell. Syst., vol. 12, pp. 153–166, 1997.
• [13] V. Torra and Y. Narukawa, Modeling Decisions Information Fusion and Aggregation Operators. Berlin: Springer-Verlag, 2007.
• [14] A. Valls and V. Torra, “Using classification as an aggregation tool for MCDM”, Fuzzy Sets Syst., vol. 115, pp. 159–168, 2000.
• [15] E. Damiani, S. De Capitani di Vimercati, P. Samarati, and M. Viviani, “A WOWA-based aggregation technique on trust values connected to metadata”, Electr. Notes Theor. Comp. Sci., vol. 157, pp. 131–142, 2006.
• [16] D. Nettleton and J. Muniz, “Processing and representation of meta-data for sleep apnea diagnosis with an artificial intelligence approach”, Medic. Inform., vol. 63, pp. 77–89, 2001.
• [17] W. Ogryczak and T. Śliwiński, “On decision support under risk by the WOWA optimization”, in Ninth European Conference on Symbolic and Quanlitative Approaches to Reasoning with Uncertainty ESQARU 2007, LNAI, vol. 4724. Heidelberg: Springer, 2007, pp. 779–790.
• [18] W. Ogryczak and T. Śliwiński, “On optimization of the importance weighted OWA aggregation of multiple criteria”, in International Conference Computational Science and Its Applica- tions ICCSA 2007, LNCS, vol. 4705. Heidelberg: Springer, 2007, pp. 804–817.
• [19] V. Torra, “The WOWA operator and the interpolation function W*: Chen and Otto’s interpolation method revisited”, Fuzzy Sets Syst., vol. 113, pp. 389–396, 2000.
• [20] W. Ogryczak and T. Śliwiński, “On equitable approaches to resource allocation problems: the conditional minimax solution”, J. Telecom- mun. Inform. Technol., no. 3, pp. 40–48, 2002.
• [21] W. Ogryczak and M. Zawadzki, “Conditional median —a parametric solution concept for location problems”, Ann. Oper. Res., vol. 110, pp. 167–181, 2002.
• [22] W. Ogryczak and A. Ruszczyński, “Dual stochastic dominance and related mean-risk models”, SIAM J. Opt., vol. 13, pp. 60–78, 2002.
• [23] R. Mansini, W. Ogryczak, and M. G. Speranza, “Conditional value at risk and related linear programming models for portfolio opti- mization”, Ann. Oper. Res., vol. 152, pp. 227–256, 2007.
• [24] R. R. Yager, “Quantifier guided aggregation using OWA operators”, Int. J. Intell. Syst., vol. 11, pp. 49–73, 1988.
• [25] X. Liu, “Some properties of the weighted OWA operator”, IEEE Trans. Syst. Man Cyber. B, vol. 368, pp. 118–127, 2006.
• [26] A.M¨uller and D. Stoyan, Comparison Methods for Stochastic Models and Risks. Chichester: Wiley, 2002.
• [27] M. E. Yaari, “The dual theory of choice under risk”, Econometrica, vol. 55, pp. 95–115, 1987.
• [28] C. Acerbi, “Spectral measures of risk: a coherent representation of subjective risk aversion”, J. Bank. Finan., vol. 26, pp. 1505–1518, 2002.
• [29] F. Glover and D. Klingman, “The simplex SON method for LP/embedded network problems”, Math. Progr. Study, vol. 15, pp. 148–176, 1981.