增加两类算子的G■del n值命题逻辑系统的t随机真度理论  

The Theory of t Randomized Truth Degree on G■del n-valued Propositional Logic System of Adding Two Operators

作　　者：朱乃调 惠小静[1] 高晓莉[1] ZHU Nai-diao;HUI Xiao-jing;GAO Xiao-li(College of Mathematics and Computer Science,Yan,an University,Yan'an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院

出　　处：《模糊系统与数学》2019年第6期62-72,共11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);多专业融合应用型人才培养模式创新实验区项目;延安大学研究生创新基金资助项目(YCX201612)

摘　　要：通过对Godel n值命题逻辑系统进行公理化扩张Godel〜,△,简记为G〜,△,利用赋值集随机化的方法,在Godel〜,△中提出了命题公式的t随机真度的定义(t任取〜,△),研究了t随机真度的MP规则、HS规则、交推理规则和并推理规则以及它的一些相关性质;给出了命题公式间的t随机相似度和I随机伪距离的概念,讨论了它们的一些相关性质;得到了命题公式间理论Г的t随机发散度和t随机相容度的概念以及它们的一些相关性质;最后在随机逻辑度量空间中提出了三种不同的近似推理模式,并证明了三种近似推理模式间的等价性。By adding new operators △ and〜,axiomatic expansion of Godel n-valued propositional logic system is introduced,which is denoted as Godel〜,△.In this paper,using the randomization method of valuation set,the definition of t randomized truth degree of propositional formula is put forward(t take△,〜),and the MP rule,HS rule and some related properties of t randomized truth degree are studied;the concepts of t randomized similarity degree,t randomized pseudo-metric between propositional formulas are given,and their some related properties are discussed;the concepts of t randomized divergent degree and t randomized consistent degree of theory Г between propositional formulas and their some related properties are obtained;three different types of approximate reasoning patterns are introduced in randomized logic metric space,and they are proved to be equivalent.

关 键 词：t随机真度 t随机相似度 t随机逻辑度量空间 近似推理 

分 类 号：O142[理学—数学]