Abstract
A graphical method for the modeling of compromise in multiple criteria problems solution is proposed. The method is based on the analysis of the strategic games characteristics and takes into account both the players cooperation for the compromise solution searching and the influence of rejection of the better solutions in favor of the compromise ones. The visualization of the considered problem is based on triangle type representation of the local criteria and can be realized both in deterministic and interval or fuzzy versions. The methodology for building the models of compromise based on the comparative analysis of possible solutions is proposed. In comparison with the approaches based the on the polygon method in games theory [32], our proposition is evidently less algorithmic complex and seems as more suitable for the comparative analysis. Its usefulness becomes especially apparent is the case of small number of local criteria.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Antonson, E.K., Otto, K.N.: Improving Engineering Design with Fuzzy Sets Department of Mechanical Engineering. MIT Press, Cambridge (1995)
Aumann, R.: Survey of repeated games, Easy in game theory and Mathematical Economics in Honor of Oscar Morgenstern, Institute Mannheim, Vein (1981)
Baas, S.M., Kwakernaak, H.: Rating and Raking of Multiple-Aspects Alternatives Using Fuzzy Sets. Automatica 1, 47–58 (1977)
Baebera, S., Jackson, M.O.: Choosing of Barbera Jackson model-Stable Majority Rules. In: V Conference SAET, Iscia (2001)
Bawa, V.S.: Optimal Rules for Ordering Uncertain Prospect. Journal of Economic 2, 95–121 (1975)
Best, M.: Fisible Conjugate Direction Method to Solve Linearly Constrained Optimization Problems. Journal of Optimization Theory and Applications 16 (1975)
Brans, J.P., Mareshal, B.: The PromCalc and GAIA decision support system for multicriteria decision aid. Decision Support Systems 12, 297–310 (1994)
Buckley, J.J.: The multiple - judge multiple criteria ranking problem. A fuzzy set approach. Fuzzy Sets and Systems 13, 23–37 (1984)
Bustnce, H., Burillo, P.: Interval valued fuzzy relations in a set structures. J. Fuzzy Math. 4, 765–785 (1996)
Caprani, O., Madsen, K.: Mean Value Forms in Interval Analysis. Computing 25, 147–154 (1980)
Choi, D.Y., Oh, K.W.: Asa and its Application to Multi- criteria Decision Making. Fuzzy sets and Systems 114, 89–102 (2000)
Chu, A., Kalaba, R., Springarn, R.: A comparition of Two Methods for Determining the Weights Belonging to Fuzzy Sets. Journal of Optimization (1996)
Czogala, E., Perdycz, W.: Elementy i metody teorii zbiorów rozmytych, PWN, Warszawa (1985)
Deluca, A., Termini, S.: A Definition of a nonprobabilistic entropy the of Fuzzy sets theory. Information and Control 20, 301–312 (1972)
Dubois, D., Koenig, J.L.: Social choise axioms for fuzzy set aggregation. Fuzzy sets and Systems 43, 257–274 (2003)
Eschenauer, H., Kolski, J., Osyczka, A.: Multicriteria Design Optimalization. Springer, Berlin (1990)
Fuller, R., Carlson, C.: Fuzzy Multiple Criteria Decision Making. Fuzzy Sets and Systems 78, 139–153 (1996)
Hauke, W.: Using Jager’s t-noms for Aggregation of Fuzzy Intervals. Fuzzy sets and Systems 101, 59–65 (1999)
Hofbauer, J.: Stability for Best Response Dynamic. University of Viena (1995)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysiss. Springer, London (2001)
Kacprzyk, J.: Wieloetapowe sterowanie rozmyte, WNT, Warszawa (2001)
Kalynmoy, D., Lother, T., Laumans, M., Zitzler, E.: Scalable Multi-objective Opimization Test Problems (2002)
Kaufman, A., Gupta, M.: Introduction to Fuzzy Arithmetic-Theory and applications, p. 349. Van Nostrand Reinhold, New York (1985)
Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncerteinty and Information. Prentice-Hall, Englewood Cliffs (1988)
Lachwa, A.: Fuzzy world of files, numbers, relations, facts, rules and decisions, Akademicka Oficyna Wydawnicza Exit, Warsaw (in polish) (2001)
Papadimitriou, C.H.: Games against nature. J. Comp.System Sci. 31, 288–301 (1985)
Piegat, A.: Fuzzy modelling and controlling. Akademicka Oficyna Wydawnicza Exit, Warsaw (2003) (in polish)
Roy, B.: Wielokryterialne wspomaganie decyzji, WNT, Warszawa (1990)
Straffin, P.D., Gier, T.: Wydawnictwo Naukowe Scholar, Warszawa (2001)
Syslo, M., Deo, N., Kowalik, J.: Discrete optimisation algorithms. PWN, Warsaw (1995) (in polish)
Vavock, V.: Aggregating Strategies. In: Conference on Computational Learning Theory (1990)
Watson, J.: Strategia. Wprowadzenie do teorii gier. WNT, Warszawa (2005)
Wrather, C., Yu, P.L.: Probability Dominance. Journal of Optimization Theory and Application 36 (1982)
Yager, R.: Modeling Uncertainty Using Partial Information. Information Sciences 121, 233–294 (1999)
Yager, R.: Non Numeric Multicriteria, Multiperson Decision Making. Group Decision and Negotiations 2, 81–93 (1993)
Yager, R.: On the Measure of Fuzziness and Negation, Membership in the Unit Interval. Int. J. Gen. Systems 5, 221–229 (1979)
Zadeh, L.A.: Fuzzy limitations calculus; design and systems, methodological problems. Ossolineum (1980) (in polish)
Zeleny, M.: Multiple Criteria Decision Making. In: Business Venturing, vol. 7, pp. 505–518. Mc-Grow-Hill, New York (1987)
Zorychta, K., Ogryczak, W.: Programowanie liniowe i cakowitoliczbowe. WNT, Warszawa (1981)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Piech, H., Figat, P. (2008). A Method for Evaluation of Compromise in Multiple Criteria Problems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2008. ICAISC 2008. Lecture Notes in Computer Science(), vol 5097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69731-2_103
Download citation
DOI: https://doi.org/10.1007/978-3-540-69731-2_103
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69572-1
Online ISBN: 978-3-540-69731-2
eBook Packages: Computer ScienceComputer Science (R0)