Abstract
In Multi Criteria Decision Making one is generally concerned with decisions under certainty, i. e. decisions for which the “state” is assumed to be known with certainty. Multi Criteria Decision Making under risk or uncertainty would imply the super-imposition of the problem structures of classical MCDM and that of single criteria decision making under risk, i. e., for instance, the combinations of goal programming with stochastic programming. This would, obviously, become very involved mathematically! In this paper we are not concerned with uncertainties (probabilities) of the Kolmogroroff type but rather with uncertainties as they are considered in the theory of fuzzy sets, possibility theory and the like. It will be shown that for this type of uncertainty (vagueness) which is assumed to be more relevant for MCDM, models and methods exist, which are also adequate for MCDM and which are computationally still feasable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baas, M.S. and Kwakernaak, H. (1977), “Rating and ranking of multiple-aspect alternatives using fuzzy sets”, Automatica, 13, 47–58.
Baldwin, J.F. and Guild, N.C.F. (1979), “Comparison of fuzzy sets on the same decision space”, Fuzzy sets and Systems, 2, 213–232.
Bellman, R.E. and Zadeh, L,A. (1970), “Decision-making in a fuzzy environment”, Mgt. Sc., 17, B141–164.
Bortolan, G. and Degani, R. (1985), “A review of some methods for ranking fuzzy subsets”, Fuzzy Sets and Systems, 15, 1–20.
Buckley, J.J. (1985), “Ranking alternatives using fuzzy numbers”, Fuzzy Sets and Systems, 15, 21–32.
Chames, A. and Cooper, W.W. (1961), Management Models and Industrial Applications of Linear Programming, Wiley, New York, 1961.
Chen, S.H. (1985), “Ranking fuzzy numbers with maximizing set and minimizing set”, Fuzzy Sets and Systems, 17, 113–130.
Dubois, D. and Prade, H. (1984), “Criteria aggregation and ranking of alternatives in the framework of fuzzy set theory”, in H.-J. Zimmermann et al. ( 1984 ), 209–240.
Hannan, E.L. (1981), “Linear programming with multiple fuzzy goals”, Fuzzy Sets and Systems, 6, 235–248.
Hwang, Ch.-L. and Yoon,K. (1981), Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, Berlin.
Hwang, Ch.-L., Masud, A.S. (1979), Multiple Objective Decision Making: Methods and Applications, Springer-Verlag, Berlin.
Jain, R. (1977), “Procedure for multi-aspect decision making using fuzzy sets”, Int. Journal Systems Science, 8, 1–7.
Kahne, H.W. and Tucker, A.W. (1951), “Nonlinear Programming”, in J. Neyman (ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability.
Van Laarhoven, P.J.M. and Pedrycz, W. (1983), “A fuzzy extension of Saaty’s priority theory”, Fuzzy Sets and Systems, 11, 229–241.
Leberling, H. (1981), “On finding compromise solutions in multi-criteria problems using the fuzzy min-operator”, Fuzzy Sets and Systems, 6, 105–118.
Roy, B. (1986), “Partial Preference Analysis and Decision Aid; The Fuzzy Outranking Relation Concept”, SEMA, Paris.
Rubin, P.A. and Narasimhan, R. (1984), “Fuzzy goal programming with rested priorities”, Fuzzy Sets and Systems, 14, 115–130.
Saaty, Th.L. (1978), “Exploring the interface between hierarchies, multiple objectives and fuzzy sets”, Fuzzy Sets and Systems, 1, 57–68.
Saaty, Th.L. (1980), The Analytic Hierarchy Process, McGraw-Hill, New York.
Siskos, J., Lochard, J. and Lombard, J. (1984), “A multicriteria decision making methodology under fuzziness: appreciation to the evaluation of radiological protection in nuclear power plants”, in H.-J. Zimmermann et al. ( 1984 ), 261–284.
Tong, R.M. and Bonissone, P.P. (1984), “Linguistic solutions to fuzzy decision problems”, in H.-J. Zimmermann et al. ( 1984 ), 323–334.
Werners, B. (1984), Interaktive Entscheidungsunterstützung durch ein flexibles mathematisches Programmierungssystem, Mühchen.
Yager, R.R. (1978), “Fuzzy decision making including unequal objectives”, Fuzzy Sets and Systems, 1, 87–95.
Zadeh, L.A. (1977), “ Linguistic characterization of preference relations as a basis for choice in social systems”, Memo UCB/ERL M77/24, Berkeley.
Zimmermann, H.-J. (1976), “Description and optimization of fuzzy systems, Internat. J. Gen. Systems, 2, 209–215.
Zimmermann, H.-J. (1978), “Fuzzy programming and linear program-ming with several objective functions”, Fuzzy Sets and Systems, 1, 45–55.
Zimmermann, H.-J. and Zysno, P. (1983), “Decisions and evaluations by hierarchical aggregation of information”, Fuzzy Sets and Systems, 10, 243–266.
Zimmermann, H.-J., Zadeh, L.A. and Gaines, B.R. (eds.) (1984), Fuzzy Sets and Decision Analysis, North-Holland, New York.
Zimmermann, H.-J. (1985), Fuzzy Set Theory and Its Applications, Kluwer-Nijhoff Publishing, Boston.
Zimmermann, H.-J. (1987), Fuzzy Sets, Decision Making, and Expert Systems, Kluwer-Nijhoff Publishing, Boston.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Zimmermann, HJ. (1990). Decision Making in Ill-Structured Environments and with Multiple Criteria. In: Bana e Costa, C.A. (eds) Readings in Multiple Criteria Decision Aid. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75935-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-75935-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75937-6
Online ISBN: 978-3-642-75935-2
eBook Packages: Springer Book Archive