Abstract
We consider the problem of decision making under uncertainty. The fuzzy measure is introduced as a general way of representing available information about the uncertainty. It is noted that generally in uncertain environments the problem of comparing alternative courses of action is difficult because of the multiplicity of possible outcomes for any action. One approach is to convert this multiplicity of possible of outcomes associated with an alternative into a single value using a valuation function. We describe various ways of providing a valuation function when the uncertainty is represented using a fuzzy measure. We then specialize these valuation functions to the cases of probabilistic and possibilistic uncertainty.
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References
Bernstein, P. L. (1998). Against the Gods: The Remarkable Story of Risk. New York: John Wiley & Sons.
Haykin, S. (1994). Neural Networks: A Comprehensive Foundation. New York: IEEE Press.
Yager, R. R. and D. P. Filev. (1994) Essentials of Fuzzy Modeling and Control. New York: John Wiley.
Mitchell, T. M. (1997). Machine Learning. New York: McGraw-Hill.
Zadeh, L. A. (1996). “Fuzzy logic = computing with words,” IEEE Transactions on Fuzzy Systems 4, 103–111.
Yager, R. R. (1988). “On ordered weighted averaging aggregation operators in multi-criteria decision making,” IEEE Transactions on Systems, Man and Cybernetics 18, 183–190.
O'Hagan, M. (1990). “Using maximum entropy-ordered weighted averaging to construct a fuzzy neuron,” Proceedings 24th Annual IEEE Asilomar Conf. on Signals, Pacific Grove, Ca: Systems and Computers, pp. 618–623.
Dyckhoff, H. and W. Pedrycz. (1984). “Generalized means as model of compensative connectives,” Fuzzy Sets and Systems 14, 143–154.
Zadeh, L. A. (1978). “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems 1, 3–28.
Sugeno, M. (1974). “Theory of fuzzy integrals and its application,” Doctoral Thesis, Tokyo Institute of Technology.
Sugeno, M. (1977). “Fuzzy measures and fuzzy integrals: a survey.” In M. M. Gupta, G. N. Saridis, and B. R. Gaines (eds.), Fuzzy Automata and Decision Process. Amsterdam: North-Holland Pub., pp. 89–102.
Dubois, D. and H. Prade. (1988). Possibility Theory: An Approach to Computerized Processing of Uncertainty. New York: Plenum Press.
Zadeh, L. A. (1979). “A theory of approximate reasoning,” In J. Hayes, D. Michie, and L. I. Mikulich (eds.), Machine Intelligence, Vol. 9. New York: Halstead Press, pp. 149–194.
Yager, R. R. (2000). “On the entropy of fuzzy measures,” IEEE Transactions on Fuzzy Sets and Systems 8, 453–461.
Murofushi, T. (1992) “A technique for reading fuzzy measures (i): the Shapely value with respect to a fuzzy measure,” Proceedings Second Fuzzy Workshop, Nagaoka, Japan (in Japanese), 39–48.
Grabisch, M. (1977). “Alternative representations of OWA operators,” In R. R. Yager and K. Kacprzyk (eds.), The Ordered Weighted Averaging Operators: Theory and Applications. Norwell, MA: Kluwer Academic Publishers, pp. 73–85.
Choquet, G. (1953). “Theory of Capacities,” Annales de l'Institut Fourier 5, 131–295.
Denneberg, D. (1994). Non-Additive Measure and Integral. Norwell, MA: Kluwer Academic.
Grabisch, M. (1977). “Fuzzy measures and integrals: A survey of applications and recent issues,” In D. Dubois, H. Prade, and R. R. Yager (eds.), Fuzzy Information Engineering: A Guided Tour of Applications. New York: John Wiley & Sons, pp. 507–529.
Dubois, D. and H. Prade. (1995). “Possibility theory as a basis for qualitative decision theory,” Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Montreal, pp. 1924–1930.
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Yager, R.R. On the Evaluation of Uncertain Courses of Action. Fuzzy Optimization and Decision Making 1, 13–41 (2002). https://doi.org/10.1023/A:1013715523644
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DOI: https://doi.org/10.1023/A:1013715523644