Goguen命题逻辑系统公理化扩张的k随机真度理论  

The Theory of k Randomized Truth Degree of Axiomatic Extension of Goguen Propositional Logic System

作　　者：高晓莉[1] 惠小静[1] 朱乃调 

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《模糊系统与数学》2017年第3期6-15,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11471007);陕西省自然科学基金资助项目(2014JM1020);延安大学研究生创新基金资助项目(YCX2016126)

摘　　要：通过对n值Goguen命题逻辑进行公理化扩张Goguen~,Δ(Π~,Δ)。利用赋值集随机化的方法,在Π~,Δ中提出了公式的k随机真度,讨论了k随机真度的MP规则,HS规则,给出了公式间的k随机相似度与k随机伪度量的概念和性质。同时介绍了三种近似推理模式并证明了三种推理模式之间的等价性。By axiomatic extension of n-valued Goguen propositional logic, which is denoted as Ⅱ～,△, using the randomization method of valuation set, the definition of k randomized truth degree of formula is put forward into Ⅱ～,△. The MP rule and HS rule of k randomized truth degree are also discussed. The concepts and properties of k randomized similarity degree and k randomized pseudometric for formulas are given. At the meantime, three different types of approximate reasoning patterns are introduced, and they are proved to be equivalent.

关 键 词：Goguen命题逻辑系统 k随机真度 k随机相似度 k随机伪度量 近似推理 

分 类 号：O141[理学—数学]