基于对合否定的SBL公理化扩张系统的程度化推理及逻辑控制研究

项目名称： 基于对合否定的SBL公理化扩张系统的程度化推理及逻辑控制研究

项目编号： No.11471007

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 惠小静

作者单位： 延安大学

项目金额： 62万元

中文摘要： 模糊逻辑控制是人工智能领域的重要课题，受到国内外的广泛重视。本项目以完备且满足演绎定理，带有对合否定算子的SBL公理化扩张系统为基础，从理论上系统研究模糊推理中前提与结论之间的数值关系，并将所得结果应用于逻辑控制。其一，通过引入△真值状态和非均匀概率分布，运用0-1转换词和△演绎定理，得出模糊推理前提与结论之间的真值关系。其二，结合L* 和Lukasiewicz模糊逻辑系统中已有的计量逻辑学研究成果，在L∏模糊命题逻辑系统中提出△真度，建立△度量空间，实现△模糊逻辑系统的程度化并展开近似推理研究，为逻辑控制奠定程度化推理基础。其三，把if-then多维模糊条件语句构造为模糊逻辑系统中的模糊语言变量，给出模糊控制中输入值，规则库与输出值之间的程度化推理方法。本项目的研究成果将丰富和完善模糊逻辑推理的程度化理论，并运用该理论建立起逻辑控制的程度化推理模型。

中文关键词： 模糊逻辑；模糊推理；真值；真度；逻辑控制

英文摘要： Fuzzy logic control is an important topic in the field of artificial intelligence, it received extensive attention both at home and abroad. Based on SBL axiomatic extension systems with involutive negation that satisfies deduction and completeness theorem, this project systematically studies numerical relationship between premises and conclusions in fuzzy reasoning, and applies the results to logic control. Firstly, through the introduction of truth states and non uniform probability distribution, one will obtain the truth value relation between premises and conclusions in fuzzy reasoning by use of 0-1 projector and △ deduction theorem. Secondly, combined with quantitative results in L* and ?ukasiewicz fuzzy logic system, △truth degree is proposed, △ metric space is established in ?∏ fuzzy propositional logic system so as to △ fuzzy logic system is graded and approximate reasoning is carried out. The results will lay graded reasoning foundation for logic control. Thirdly, this work structures‵if-then′ multidimensional fuzzy conditional statements for fuzzy linguistic variables in fuzzy logic system, gives the graded reasoning methods about input values, reasoning rules and output values. The project not only enriches the graded reasoning theory of fuzzy logic reasoning, but also can establish graded reasoning model in logic control.

英文关键词： fuzzy logic;fuzzy reasoning;truth value;truth degree;logic control