在复杂的以人为中心的系统中，每天的决策都具有决策相关信息不完全的特点。现有决策理论的主要问题是，它们没有能力处理概率和事件不精确的情况。在这本书中，我们描述了一个新的理论的决策与不完全的信息。其目的是将决策分析和经济行为的基础从领域二价逻辑转向领域模糊逻辑和Z约束，从行为决策的外部建模转向组合状态的框架。

这本书将有助于在模糊逻辑，决策科学，人工智能，数学经济学，和计算经济学的专业人员，学者，经理和研究生。

读者:专业人士，学者，管理者和研究生在模糊逻辑，决策科学，人工智能，数学经济学，和计算经济学。

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信息论
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** This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $\epsilon$-variable-length resolvability. We derive the general formula of the $\epsilon$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint the value of the average variational distance is smaller than or equal to some constant. Our result clarifies a dual relationship between the general formula of $\epsilon$-variable-length resolvability and that of $\epsilon$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula. **

信息论
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** We consider an energy harvesting transmitter equipped with two batteries having finite storage capacities, communicating over an additive white Gaussian channel. The work is motivated by an observation that many practical batteries, when repeatedly charged after being partially discharged, suffer from degradation in the usable capacity. The capacity can be recovered by completely discharging the battery before charging it fully again. Hence, in this work, we impose the constraint that a battery must be charged (discharged) only after it is fully discharged (charged). Our goal is to maximize the longterm average throughput with non-causal and causal knowledge of the energy arrivals, which we assume to be Bernoulli. We propose two sub-optimal policies and obtain an upper bound on the performance gap (G) from the optimal long-term average throughput that is achieved with infinite capacity batteries. We find that G remains constant as the amount of energy harvested per arrival increases. Numerically, we also find that G decreases with the battery capacity faster than the inverse of the square root of the battery capacity for a specific energy arrival parameters. **

信息论
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