Principals of Uncertainty and Information in Expert Systems

本研究的主要目的是发展适当的原则，以处理专家系统中的不确定性。重点是四个相对较新的数学理论的不确定性：可能性理论，模糊集理论，随机集理论，和证据的Dempster-Shafer理论。在这些理论中，就像在概率论中一样，测量不确定性的合理函数现在已经很好地建立起来了。这些函数对于研究以下三个不确定性原则至关重要：最大不确定性原则、最小不确定性原则和不确定性不变性原则。根据最大不确定性原则，在任何形式的扩展推理中，结论都是通过最大化相关的不确定性函数来确定的，该函数受到代表可用信息的约束。最小不确定性原则对于涉及不可避免地增加相关不确定性的各种问题，例如简化或解决冲突问题，是至关重要的。根据这一原则，在表示每个问题需求的约束条件下，通过最小化相关的不确定性函数来确定解决方案。不确定性不变性原理涉及不同不确定性理论之间的信息保持转换。这个项目正在发展这三个原则的数学和计算基础，并研究它们在专家系统中的实际作用。

The principal objective of this research is to develop adequate principles for dealing with uncertainty in expert systems. The focus is on four relatively new mathematical theories of uncertainty: possibility theory, fuzzy set theory, random set theory, and the Dempster-Shafer theory of evidence. In each of these theories, as in probability theory, well-justified functions that measure uncertainty are now well established. These functions are crucial for the following three principles of uncertainty to be investigated: principles of maximum uncertainty, minimum uncertainty, and uncertainty invariance. According to the principle of maximum uncertainty, conclusions in any form of ampliative reasoning are determined by maximizing relevant uncertainty function subject to constraints that represent information available. The principle of minimum uncertainty is fundamental to a variety of problems involving unavoidable increase of relevant uncertainty, such as simplification or conflict-resolution problems. According to this principle, solutions are determined by minimizing relevant uncertainty function within constraints representing the requirements of each problem. The principle of uncertainty invariance is concerned with information-preserving transformations between distinct theories of uncertainty. This project is developing mathematical and computational foundation of the three principles as well as investigating their practical role in expert systems.