Geodesic
On decision-making in possibility theory
Kybernetika, Tome 51 (2015) no. 3, pp. 457-468
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We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision function, but also appears to play an important role exactly in the framework of possibility theory due to its sensitivity. Furthermore, the optimality of a decision function is easily verifiable.
We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision function, but also appears to play an important role exactly in the framework of possibility theory due to its sensitivity. Furthermore, the optimality of a decision function is easily verifiable.
DOI : 10.14736/kyb-2015-3-0457
Classification : 62C20, 91B06
Keywords: possibility measures and distributions; upper envelopes of probability distributions; decision functions; minimax principle 
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Vejnarová, Jiřina. On decision-making in possibility theory. Kybernetika, Tome 51 (2015) no. 3, pp. 457-468. doi: 10.14736/kyb-2015-3-0457

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