Abstract
The operations of fuzzy maximum, Mãx, and minimum, Mĩn, defined on a crisp set, and their multivariable analogon, i.e. the concept of a fuzzy Pareto optimum, are introduced. A model of fuzzy choice based on the concept of fuzzy concentration and on rules of fuzzy logic is presented. The rules of fuzzy choices are classified by a number of options chosen by infinitely concentrated, therefore crisp, rules. The correctness of the given definitions is shown by applying the extension principle. The probability distribution of the height of a fuzzy Pareto optimum, and an asymptotic result for the expected value of the height are calculated. The rate at which the concentrated fuzzy set converges to the limit crisp set is estimated. Some properties of fuzzy choice classes are discussed.
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
Dubois, D., and H. Prade (1978). Operations on fuzzy numbers, Int. J. Syst, Sci. 9, 613–626.
Sakawa, M. (1983). Interactive computer programs for fuzzy linear programming with multiple objectives. Int. J. Man-Machine Stud. 18, 489–503.
Takatsu, S. (1984). Multiple-objective satisficing decision problems. Kybernetes 13, 21–26.
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part 1, 2, and 3. Inf. Sci. 8, 199–249;
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part 1, 2, and 3. Inf. Sci.; 8, 301–357;
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part 1, 2, and 3. Inf. Sci.; 8, 301–357;
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part 1, 2, and 3. Inf. Sci.; 9, 43–80.
Zadeh, L.A. (1976). The linguistic approach and its application to decision analysis. In Y.C. Ho, and S.K. Mitter (eds.), Directions in Large-Scale Systems, Many-Person-Qptimization and Decentralized Control. Plenum Press, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Kuz’min, V.B., Travkin, S.I. (1987). Fuzzy Choice. In: Kacprzyk, J., Orlovski, S.A. (eds) Optimization Models Using Fuzzy Sets and Possibility Theory. Theory and Decision Library, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3869-4_7
Download citation
DOI: https://doi.org/10.1007/978-94-009-3869-4_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8220-4
Online ISBN: 978-94-009-3869-4
eBook Packages: Springer Book Archive