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An optimal stopping problem in dynamic fuzzy systems with fuzzy rewards. (English) Zbl 0870.60040

Summary: This paper deals with an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards, and shows that the optimal discounted fuzzy reward is characterized by a unique solution of a fuzzy relational equation. We define a fuzzy expectation with a density given by fuzzy goals and we estimate discounted fuzzy rewards by the fuzzy expectation. This paper characterizes the optimal fuzzy expected value and gives an optimal stopping time.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
03E72 Theory of fuzzy sets, etc.
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[1] Bellman, R.E.; Zadeh, L.A., Decision-making in a fuzzy environment, Management sci. ser. B, 17, 141-164, (1970) · Zbl 0224.90032
[2] Baldwin, J.E.; Pilsworth, B.W., Dynamic programming for fuzzy systems with fuzzy environment, J. math. anal. appl., 85, 1-23, (1982) · Zbl 0491.90090
[3] Esogbue, A.O.; Bellman, R.E., Fuzzy dynamic programming and its extensions, TIMS/studies in management sci., 20, 147-167, (1984)
[4] Kurano, M.; Yasuda, M.; Nakagami, J.; Yoshida, Y., A limit theorem in some dynamic fuzzy systems, Fuzzy sets and systems, 51, 83-88, (1992) · Zbl 0796.93076
[5] Yoshida, Y., Markov chains with a transition possibility measure and fuzzy dynamic programming, Fuzzy sets and systems, 66, 39-57, (1994) · Zbl 0844.90114
[6] Yoshida, Y.; Yasuda, M.; Nakagami, J.; Kurano, M., A potential of fuzzy relations with a linear structure: the contractive case, Fuzzy sets and systems, 60, 283-294, (1993) · Zbl 0802.90004
[7] Yoshida, Y.; Yasuda, M.; Nakagami, J.; Kurano, M., A potential of fuzzy relations with a linear structure: the unbounded case, Fuzzy sets and systems, 66, 83-95, (1994) · Zbl 0860.90005
[8] M. Kurano, M. Yasuda, J. Nakagami and Y. Yoshida, Markov-type fuzzy decision processes with a discounted reward on a closed interval, European Journal of Operational Research (to appear). · Zbl 0914.90264
[9] Kacprzyk, J., Decision making in a fuzzy environment with fuzzy termination time, Fuzzy sets and systems, 1, 169-179, (1978) · Zbl 0403.93004
[10] Stein, W.E., Optimal stopping in a fuzzy environment, Fuzzy sets and systems, 3, 253-259, (1980) · Zbl 0435.90105
[11] Novák, V., Fuzzy sets and their applications, (1989), Adam Hilder Bristol · Zbl 0683.94018
[12] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[13] Gähler, S.; Gähler, W., Fuzzy real numbers, Fuzzy sets and systems, 66, 137-158, (1994) · Zbl 0934.26012
[14] Birkhoff, G., Lattice theory, Amer. math. soc., coll. pub., 25, (1940) · Zbl 0126.03801
[15] Shiryaye, A.N., Optimal stopping rules, (1979), Springer New York
[16] Ralescu, D.; Adams, The fuzzy integral, J. math. anal. appl., 75, 562-570, (1980) · Zbl 0438.28007
[17] Sugeno, M., Fuzzy measures and fuzzy integral: A survey, (), 89-102
[18] Sakawa, M.; Nishizaki, I., MAX-MIN solutions for fuzzy multiobjective matrix games, Fuzzy sets and systems, 67, 53-69, (1994) · Zbl 0844.90117
[19] Yoneda, M.; Fukami, S.; Grabisch, M., Interactive determination of a utility function represented as a fuzzy integral, Inform. sci., 71, 43-64, (1993) · Zbl 0769.90010
[20] Kuratowski, K., Topology I, (1966), Academic Press New York · Zbl 0158.40901
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