分层异蕴涵可变支持度推理及其构造的模糊系统研究

Fuzzy reasoning is the core of theory basis of fuzzy control technology. The triple I (triple implications) method of fuzzy reasoning is highly recognized by the researchers all over the world by virtue of its advantages of strict logic basis, excellent reversibility and so on. However, the triple I method is imperfect from the viewpoint of fuzzy systems, which is embodied as inferior response ability and practicability. This will hold back its broad application to a large extent, resulting in that the triple I method is faced with its development bottleneck. To solve this problem, following the basic differently implicational method (previously proposed by us as a generalization of the triple I method), aiming at the general case of multidimensional fuzzy reasoning, the ideas of variable sustaining degree and hierarchical structure are successively introduced, and then the more reasonable method, called the hierarchical and differently implicational method with variable sustaining degrees is put forward. This proposal will investigate the new fuzzy reasoning method, which includes three parts. First, the mechanism to solve this method is researched for some specific implication operators and familiar kinds of implication operators (e.g. R-implication operators and S-implication operators). Second, the reversibility properties of the new method are analyzed for its most basic case, and then the approximation principle of new method is researched, which are to verify its rationality together. Lastly, the fuzzy systems based on the new method are established, and then response abilities of related fuzzy systems are investigated, and finally more usable fuzzy systems are obtained. This purpose of this proposal is to try to break the development bottleneck of triple I method, and improve the theory development and practical applications of fuzzy reasoning.

模糊推理是模糊控制技术的理论基础的核心。模糊推理的三I算法因其具有严格逻辑根据、还原性等优势而受到国内外高度认可。但是，从整体模糊系统的角度来看，三I算法在响应性能、可实用性等方面显得不理想。这对其的应用和广泛推广造成很大的阻碍，导致三I算法面临其发展的瓶颈期。为了解决该难题，在我们前期提出的基本异蕴涵算法（三I算法的一种推广）的基础上，本申请面向一般性的多维模糊推理情形，先后引入可变支持度、分层的理念，提出更为合理的分层异蕴涵可变支持度算法，并围绕该算法进行全面探讨。研究内容包括：①针对某些具体的蕴涵算子，以及R-蕴涵算子、S-蕴涵算子等常见类型的蕴涵算子，探讨该算法的求解问题；②分析该算法在最基本情形下的还原性，考察该算法的逼近原则，以此来验证其合理性；③构建基于该算法的模糊系统，分析其响应性能，获得更多较优的模糊系统。试图以此打破三I算法面临的瓶颈，推动模糊推理的理论发展与实际应用。

模糊推理的三I 算法因其具有严格逻辑根据、还原性等优势而受到国内外高度认可。但是，从整体模糊系统的角度来看，三I算法在响应性能、可实用性等方面显得不理想，导致三I 算法面临其发展的瓶颈期。为此，本项目提出并系统研究了更为合理的分层异蕴涵可变支持度算法。1）研究了分层异蕴涵可变支持度算法的求解。针对FMP和FMT问题，面向第二算子取R-蕴涵算子、S-蕴涵算子、QL-蕴涵算子的情形，建立了该算法的统一形式的解。针对常见的主流蕴涵算子，给出了具体形式的优化解。并且，针对多输入单输出的FMP和FMT问题，给出了相应的优化解。进一步地，分别面向连续模糊集和离散模糊集两种情形，给出了具体的计算实例，并应用于模糊分类中。通过分层异蕴涵可变支持度算法的提出，将当前的相关模糊推理算法整合起来，从而形成了统一的、紧密的模糊推理体系。2）探究了分层异蕴涵可变支持度算法的合理性。考察分层异蕴涵可变支持度算法中的基本情形，即基本异蕴涵算法。从扩展型算子、缩减型算子、其他类型算子的角度，研究了基本异蕴涵算法的还原性，效果良好。特别第二算子取(0,1)-蕴涵算子或R-蕴涵算子时，还原性能最为理想。发现对于R-蕴涵算子和主要的S-蕴涵算子，分层异蕴涵可变支持度算法都具有面向FMP和FMT问题的逼近性和连续性。指出所提算法中的第一算子、第二算子分别展现了规则库的作用和推理机制。3）开展了基于分层异蕴涵可变支持度算法的模糊系统研究。首先，面向基本异蕴涵算法建立了模糊系统，获得了190种可用的模糊系统。在同样环境中，仅2个基于三I算法的模糊系统和19个基于CRI算法的模糊系统可用。因此，基本异蕴涵算法在模糊系统方面拥有更为广泛的选择空间，其实用性比CRI算法、三I算法要强。其次，以分层异蕴涵可变支持度算法为内核建立了模糊系统，同样获得了较为理想的模糊系统响应性能。由于分层异蕴涵可变支持度算法是基本异蕴涵算法的拓展，从而获得了更为精细的推理机制和更广阔的推理空间，得到了更多的、更优的模糊系统。并将这些成果编写成软件仿真平台。通过本项目的实施，已发表（或录用）论文18篇，其中SCI论文7篇。获得第二届“吴文俊人工智能科学技术奖”创新奖一等奖（第5完成人）、第四届“吴文俊人工智能科学技术奖”进步奖三等奖（第9完成人）。本课题负责人作为组织委员会主席成功举办2015年模糊逻辑与智能计算学术研讨会。