Kybernetika 51 no. 3, 457-468, 2015

On decision-making in possibility theory

Jiřina VejnarováDOI: 10.14736/kyb-2015-3-0457


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.


possibility measures and distributions, upper envelopes of probability distributions, decision functions, minimax principle


91B06, 62C20


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