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

ZHAO Bin; YU Peng

doi:10.3969/j.issn.0372-2112.2018.10.001

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

更新时间：2025-07-16

- A Kind of Quantitative Method Based on Camberra Fuzzy Distance in Multiple-Valued Logic
- Acta Electronica Sinica Vol. 46, Issue 10, Pages: 2305-2315(2018)
- 作者机构：
  
  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
  3. 陕西师范大学数学与信息科学学院,陕西,西安,710119
  4. 陕西科技大学文理学院,陕西,西安,710021
- 作者简介：
- 基金信息：
  
  Key Program of National Natural Science Foundation of China (No.11531009);Fundamental Research Funds for the Central Universities (No.GK201501001)
- DOI：10.3969/j.issn.0372-2112.2018.10.001
  CLC： O141.1O153.1
- Published Online：25 October 2018，
  
  Published：2018
- 稿件说明：
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ZHAO Bin, YU Peng. A Kind of Quantitative Method Based on Camberra Fuzzy Distance in Multiple-Valued Logic[J]. Acta Electronica Sinica, 2018, 46(10): 2305-2315.
DOI：

ZHAO Bin, YU Peng. A Kind of Quantitative Method Based on Camberra Fuzzy Distance in Multiple-Valued Logic[J]. Acta Electronica Sinica, 2018, 46(10): 2305-2315. DOI： 10.3969/j.issn.0372-2112.2018.10.001.

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

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

（

）上展开程度化推理提供了一种新的方法.

Abstract

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 Lukasiewicz logic system

and discuss the properties of Camberra-similarity degree and Camberra-truth degree

prove that the Camberra-truth degree of formula

is equal to the sum of Camberra-truth degrees of some incompatible formulas. And then

based on Camberra-truth degree

we study some properties of Lukasiewicz logic metric space

prove that there is no isolated point

and arbitrarily sphere neighbourhood is an inconsistent theory in three valued L

ukasiewicz logic metric space and so on. Which provides a new method for expand the grade reasoning on formula set

(

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