新型模糊蕴涵、模糊函数方程的研究及其在模糊系统中的应用

Fuzzy implications and fuzzy functional equations play important roles in fuzzy reasoning, fuzzy systems and other related fields, fuzzy implications are closely related to the results of fuzzy reasoning, solving a series of fuzzy functional equations can avoid effectively the problem of rule explosion in fuzzy systems. Based on the above, the project will investigate systematically fuzzy implications and fuzzy functional equations. The main research contents are as follows: to solve problems of well known classes of fuzzy implications, to construct new classes of fuzzy implications and analyze their properties and describe their characterization, to solve and generalize fuzzy functional equations and to design fuzzy systems. There are two research objectives, one is to establish a complete system of fuzzy implications and obtain solutions of fuzzy functional equations, the other is, with new classes of fuzzy implications and solutions of fuzzy functional equations, to modify the existing reasoning methods such as CRI and the triple I algorithm and design fuzzy systems with less number of rules.

模糊蕴涵和模糊函数方程在模糊推理和模糊系统等领域发挥着十分重要的作用，模糊蕴涵的选取和模糊推理结果的好坏密切相关，求解系列模糊函数方程可以有效地解决模糊系统中的规则爆炸等问题。基于此，本项目拟对模糊蕴涵和模糊函数方程开展全面深入的研究工作。主要研究内容包括解决常见模糊蕴涵类型的遗留问题、构造新型模糊蕴涵并分析其性质、求解和推广系列模糊函数方程以及设计模糊系统。研究目标有两个，一是建立比较完备的模糊蕴涵理论体系和获得系列模糊函数方程的解，二是基于新型模糊蕴涵和模糊函数方程的解，修正现有模糊推理方法（如，CRI和三I算法）并设计规则数目较少的模糊系统。

模糊蕴涵和模糊函数方程在模糊推理和模糊系统等领域发挥着十分重要的作用，模糊蕴涵的选取和模糊推理结果的好坏密切相关，求解模糊函数方程可以有效地解决模糊系统中的规则爆炸等问题。本项目重点研究了模糊蕴涵和模糊函数方程问题，另外还进行了一些拓宽性研究工作。主要研究内容包括：（1) 构造新型模糊蕴涵以及求解带有新型模糊蕴涵的函数方程， (2) 二型模糊算子的研究，（3) 有界格上一致模的研究。重要结果有： 构造了新型模糊蕴涵（h,c）-蕴涵，求解了包含（h,c）-蕴涵的模糊函数方程；研究了二型模糊蕴涵（余蕴涵）、二型一致模和二型零模；在有界格上，构造了一致模，解决了一个公开问题。本项目的研究结果对于设计模糊系统具有一定的理论指导意义。