Generalized information theory: aims, results, and open problems
Generalized information theory: aims, results, and open problems
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DOI：
10.1016/j.ress.2004.03.003
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发表时间：
2004-07
期刊：
影响因子：
--
通讯作者：
G. Klir
中科院分区：
文献类型：
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作者：
G. Klir
本文的主要目的是对广义信息论（GIT）进行全面的概述：广义信息论是一项研究计划，其目标是对基于不确定性的信息进行广泛的处理，而不仅仅局限于经典的不确定性概念。在对经典信息理论的简要概述之后，勾画了一个广泛的框架，用于形式化不确定性和相关的基于不确定性的大量可想象类型的信息。然后调查了在这个框架内已经发展起来的各种不精确概率理论，主要集中在适用于所有这些理论的一些重要的统一原则上。随后介绍了两个更高层次的不精确概率理论：(i)在每个给定理论中可形式化的任何情况下测量相关不确定性（预测性、追溯性、规定性、诊断性等）数量的水平，以及（ii）不确定性的一些方法学原则的水平，这些原则取决于测量不确定性和相关不确定性信息的能力。讨论了有关不确定度测量和不确定度原理的各种问题。同样，重点是适用于所有理论的统一原则。最后，对该领域的研究现状进行了评价，并对未来的研究方向进行了展望。
The principal purpose of this paper is to present a comprehensive overview of generalized information theory (GIT): a research program whose objective is to develop a broad treatment of uncertainty-based information, not restricted to classical notions of uncertainty. After a brief overview of classical information theories, a broad framework for formalizing uncertainty and the associated uncertainty-based information of a great spectrum of conceivable types is sketched. The various theories of imprecise probabilities that have already been developed within this framework are then surveyed, focusing primarily on some important unifying principles applying to all these theories. This is followed by introducing two higher levels of the theories of imprecise probabilities: (i) the level of measuring the amount of relevant uncertainty (predictive, retrodictive, prescriptive, diagnostic, etc.) in any situation formalizable in each given theory, and (ii) the level of some methodological principles of uncertainty, which are contingent upon the capability to measure uncertainty and the associated uncertainty-based information. Various issues regarding both the measurement of uncertainty and the uncertainty principles are discussed. Again, the focus is on unifying principles applicable to all the theories. Finally, the current status of GIT is assessed and future research in the area is discussed.