中文摘要：

对于模糊系统中的否定知识的认识,首先从哲学层面上对潘正华提出的3种否定关系进行了研究,提出了矛盾否定关系、对立否定关系和中介否定关系的本质特征.接着,在Zadeh提出的语言变量中引入3种否定的概念,得到了带有3种否定的语言变量.为了能够刻画这些否定关系的本质特征和内在联系,进一步研究了它们的集合基础,定义了一种新的带有矛盾否定、对立否定和中介否定的模糊集GFScom,并讨论了GFScom的一些基本运算及性质.在此基础上,给出了基于GFScom的具有一阶逼近精度和二阶逼近精度的模糊系统的设计方法,并分析了所设计的模糊系统的逼近性能.应用示例表明,GFScom不仅丰富了模糊系统的推理功能,而且能在仅知道部分隶属函数分布的情况下设计出具有给定精度的模糊系统.

英文摘要：

For negative knowledge cognition in fuzzy systems, three different sorts of negation developed by Pan are investigated and the intrinsic natural characteristic of contradictory, opposite and medium negative relationship is proposed. Subsequently, a linguistic variable with three types of negation is presented by considering three kinds of negation in the classical linguistic variable proposed by Zadeh. In order to sketch the natural features and intrinsic relationships between fuzzy knowledge and its three kinds of negation, we further investigate their set basis and define a novel type of generalized fuzzy sets with contradictory, opposite and medium negation, denoted by GFScom. And several basic algebraic operations of GFScom and its properties are studied. On this basis, the approach to construct the fuzzy system equipped with the first-order and second-order approximation accuracy is given, and the approximation capability of the systems is analyzed. The demonstrations in fuzzy systems show that using GFScom, we can, not only make the fuzzy reasoning capability of fuzzy systems much richer, but also design the fuzzy system to any degree of accuracy under condition of only knowing distribution of fewer membership functions.