Abstract
A decision making problem in an upper decision level is described in this chapter by a set of fuzzy satisfaction levels given by decision makers. Fuzzy solutions are used to approximate the feasible region of decision variables left by the given fuzzy satisfaction levels. Two different possibility distributions, i.e., symmetrical triangular possibility distributions and exponential possibility distributions are considered and their upper and lower possibility distributions are obtained. It can be said that a fuzzy solution associated with an upper possibility distribution leaves more rooms than the one associated with a lower possibility distribution.
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Bibliography
R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment,Management Science, 17 (1970) 141–164.
M. Inuiguchi, H. Ichihashi, and H. Tanaka, Fuzzy Programming: A survey of recent developments, in: R. Slowinski and J. Teghem, Eds., Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Kluwer Academic Publishers, Dordrecht, (1990) 45–68.
M. Inuiguchi, T. Tanino, and M. Sakawa: Membership Function Elicitation in Possibilistic Programming Problems, Fuzzy Sets and Systems, Vol. 111, No. 1, pp.29–45 (2000).
P. Guo, H. Tanaka and H.-J. Zimmermann, Upper and lower possibility distributions of fuzzy decision variables in upper level decision problems, Fuzzy Sets and Systems, 111 (2000) 71–79.
P. Guo, T. Entani, and H. Tanaka, Fusion of multi-dimensional possibilistic information via possibilistic linear programming, Journal of the Operations Research Society of Japan, 44 (2001) 220–229.
Z. Pawlak, Rough set, International Journal of Computer and Information Science, 11 (1982) 341–356.
H. Rommelfange, Fuzzy linear programming and applications, European Journal of Operational Research, 92 (1996) 512–527.
M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization (Plenum Press, New York, 1993).
H. Tanaka, P. Guo, and H.-J. Zimmermann, Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems, Fuzzy Sets and Systems, 113 (2000) 323–332.
H. Tanaka and P. Guo, Possibilistic Data Analysis for Operations Research, (Physica-Verlag, Heidelberg, 1999).
H. Tanaka and P. Guo, Portfolio selection based on upper and lower exponential possibility distributions, European Journal of Operational Research 114 (1998) 131–142.
H. Tanaka and H. Ishibuchi, Evidence theory of exponential possibility distributions, International Journal of Approximate Reasoning, 8 (1993) 123–140.
H. Tanaka and K. Asai, Fuzzy solution in fuzzy linear programming problems, IEEE Transactions on Systems, Man, and Cybernetics, 14 (1984) 325–328.
H.-J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1 (1978) 45–56.
L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning – I, Information Science, 8 (1975) 199–249.
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Guo, P. (2010). Decision Making under Uncertainty by Possibilistic Linear Programming Problems. In: Computational Intelligence in Complex Decision Systems. Atlantis Computational Intelligence Systems, vol 2. Atlantis Press. https://doi.org/10.2991/978-94-91216-29-9_3
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DOI: https://doi.org/10.2991/978-94-91216-29-9_3
Publisher Name: Atlantis Press
Online ISBN: 978-94-91216-29-9
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