非可换逻辑证明论与模糊推理算法研究

项目名称： 非可换逻辑证明论与模糊推理算法研究

项目编号： No.61273018

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 罗敏霞

作者单位： 中国计量学院

项目金额： 60万元

中文摘要： 非经典逻辑是智能信息处理技术的重要基础理论之一，近年受到研究学者的广泛关注。本项目将围绕两个新方向开展研究：非可换逻辑证明论、模糊推理算法。在非可换逻辑证明论方向上，研究伪一致范数诱导的左、右蕴涵的本质特性，拟构建基于伪一致范数非可换逻辑psUL的希尔伯特公理系统，证明其可靠性与完备性；探寻刻画连续一致范数"连续性"的逻辑规则，拟构造基于连续一致范数模糊逻辑BUL超串演算系统；构造左、右蕴涵公理的逻辑规则，拟创建非可换逻辑psUL的超串演算系统。在模糊推理算法方向上，将全蕴涵三I算法思想分别与模糊逻辑UL、非可换逻辑psUL结合起来，给出基于模糊逻辑UL的模糊推理三I算法、基于非可换逻辑psUL的模糊推理左R-型（右R-型）三I算法，并将其纳入模糊逻辑框架，给出模糊推理算法的严格逻辑论证。该项目研究进一步深化模糊逻辑理论研究成果，在模糊推理、模糊控制与决策等实际应用中有重要意义。

中文关键词： 伪一致范数；希尔伯特系统；超串演算系统；三I算法；模糊推理

英文摘要： Non-classical logic, one of the most important foundation theory of intelligent information processing technology, has received extensive attention from research scholars in recent years. Taking into account this situation, this project will focus on the research in the two new directions such as the proof theory of non-commutative logics and fuzzy reasoning algorithms. As for the proof theory of non-commutative logics, we will conduct the study on the essential characteristics of the left and right residual operations induced by the pseudo-uninorms and intend to build the Hilbert system for the non-commutative logic psUL based on pseudo-uninorms as well as the proof of its soundness and completeness. Concurrently, we will do the research on the logic rules characterizing the continuity of the continuous uninorms and intend to construct the Hypersequent calculus for fuzzy logic BUL based on continuous uninorms. Also the logic rules for the axioms of the residual implications induced by pseudo-uninorms will be investigated to establish the the Hypersequent calculus for the non-commutative logic psUL. In regard to the fuzzy reasoning algorithms, respectively combining the idea of the full implication triple I method with the fuzzy logic UL and non-commutative logic psUL, we will obtain the triple I algorithm for

英文关键词： Pseudo-uninorm；Hilbert system；Hypersequent calculi system；Triple I algorithm；Fuzzy inference