具有三种否定的模糊推理算法及应用  

Fuzzy reasoning algorithm and its application with three types of negation

作　　者：吴晓刚 WU Xiaogang(School of Information Technology,Xingyi Normal University for Nationalities,Xingyi 562400,Guizhou,P.R.China;Department of Computer Science and Technology,Tongji University,Shanghai 201804,P.R.China)

机构地区：[1]兴义民族师范学院信息技术学院,贵州兴义562400 [2]同济大学计算机科学与技术系,上海201804

出　　处：《重庆大学学报》2024年第2期32-39,共8页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(61673301);贵州省科学技术基金资助项目(黔科合基础1458号);贵州省教育厅自然科学重点项目(黔教合KY字403)。

摘　　要：模糊推理中,合成规则推理方法(compositional rule of inference, CRI)与基于贴近度的方法(similarity based approximate reasoning,SAR)都是建立在只有一种否定的经典模糊集上。针对广义模糊集GFScom(generalized fuzzy sets with contradictory, opposite and medium negation)具有三种否定(矛盾否定、对立否定、中介否定)的特点,对模糊推理方法 CRI的蕴含算子作了扩展。提出了具有三种否定的GFScom贴近度定义和公式,得到模糊近似推理的一种新的计算形式GSAR方法,证明了GSAR该方法具有FMP(fuzzy modus ponens)还原性。通过应用实例对比,模糊推理GSAR的新方法不仅克服了CRI方法在建立模糊关系矩阵具有主观性和随意性的不足,而且客观有效地反映了模糊推理中的3种否定信息,丰富了模糊推理的形式。In fuzzy reasoning,both the compositional rule of inference(CRI)and the similarity-based approximate reasoning(SAR)methods are built on classical fuzzy sets with only one negation.With considering the characteristics of the generalized fuzzy set(GFScom)that possesses three types of negation(contradiction,opposite and medium negation),an extension is made to the implication operator of the CRI fuzzy reasoning method.The definition and formula of GFScom closeness degree,which incorporates three types of negation,are presented.A new computational method of fuzzy approximate reasoning,named GSAR(generalized similarity-based approximate reasoning),is proposed.The method is proven to have reducibility for fuzzy modus ponens(FMP).Through comparative examples,the new GSAR fuzzy reasoning method not only overcomes the subjectivity and arbitrariness of the CRI method in establishing fuzzy relation matrices, but also objectively and effectively reflects three types of negative information in fuzzy reasoning, thereby enriching the forms of fuzzy reasoning.

关 键 词：广义模糊集 三种否定 贴近度 模糊推理 

分 类 号：O159[理学—数学]