多值逻辑中基于Camberra模糊距离的计量化方法  

A Kind of Quantitative Method Based on Camberra Fuzzy Distance in Multiple-Valued Logic

作　　者：赵彬[1] 于鹏[1,2] ZHAO Bin;YU Peng(College of Mathematics and Information Science,Shaanxi Normal University,Xi’an,Shaanxi 710119,China;School of Arts and Sciences,Shaanxi University of Science and Technology,Xi’an,Shaanxi 710021,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119 [2]陕西科技大学文理学院,陕西西安710021

出　　处：《电子学报》2018年第10期2305-2315,共11页Acta Electronica Sinica

基　　金：国家自然科学基金重点项目(No.11531009);中央高校基本科研业务费专项资金(No.GK201501001)

摘　　要：本文以模糊集间的Camberra距离为工具,给出了多值Lukasiewicz逻辑系统中公式间的Camberra-距离,Camberra-相似度与Camberra-真度的概念,讨论了Camberra-相似度与Camberra-真度的性质,证明了每一个公式φ的Camberra-真度都等于一些互不相容的公式的Camberra-真度之和.然后以Camberra-真度为依托,研究了Lukasiewicz逻辑度量空间的一些性质,证明了三值Lukasiewicz逻辑度量空间没有孤立点,以及每一个球形领域都是不相容理论等结论.为在公式集F(S)上展开程度化推理提供了一种新的方法.In this paper,by using Camberra fuzzy distance on fuzzy set,we propose the notions of Camberra-distance,Camberra-similarity degree between two formulas and Camberra-truth degree of one formula in multiple-valued ukasiewicz logic system,and discuss the properties of Camberra-similarity degree and Camberra-truth degree,prove that the Camberra-truth degree of formulaφis equal to the sum of Camberra-truth degrees of some incompatible formulas.And then,based on Camberra-truth degree,we study some properties of ukasiewicz logic metric space,prove that there is no isolated point,and arbitrarily sphere neighbourhood is an inconsistent theory in three valued ukasiewicz logic metric space and so on.Which provides a new method for expand the grade reasoning on formula set F(S).

关 键 词：计量逻辑学 Camberra模糊距离 近似推理 相容理论 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]