多值逻辑中基于Camberra模糊距离的计量化方法

doi:10.3969/j.issn.0372-2112.2018.10.001

电子学报 ›› 2018, Vol. 46 ›› Issue (10): 2305-2315.DOI: 10.3969/j.issn.0372-2112.2018.10.001

• 学术论文 • 下一篇

多值逻辑中基于Camberra模糊距离的计量化方法

赵彬¹, 于鹏^1,2

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

收稿日期:2017-06-20 修回日期:2017-11-06 出版日期:2018-10-25
- 通讯作者:
- 于鹏
- 作者简介:
- 赵彬,男.1965年10月出生,陕西宝鸡人.1993年在四川大学获理学博士学位.现为陕西师范大学教授、博士生导师.主要从事格上拓扑、非经典数理逻辑等方面的研究.E-mail:zhaobin@snnu.edu.cn
- 基金资助:
- 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）

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

ZHAO Bin¹, YU Peng^1,2

1.College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119, China;
2.School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an, Shaanxi 710021, China

Received:2017-06-20 Revised:2017-11-06 Online:2018-10-25 Published:2018-10-25
- Corresponding author:
- YU Peng
- Supported by:
- Key Program of National Natural Science Foundation of China (No.11531009); Fundamental Research Funds for the Central Universities (No.GK201501001)

摘要/Abstract

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.

关键词: 计量逻辑学, Camberra模糊距离, 近似推理, 相容理论

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 φ 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 Lukasiewicz logic metric space and so on. Which provides a new method for expand the grade reasoning on formula set F(S).

Key words: quantitative logic, camberra fuzzy distance, approximate reasoning, consistent theory

中图分类号:

赵彬, 于鹏. 多值逻辑中基于Camberra模糊距离的计量化方法[J]. 电子学报, 2018, 46(10): 2305-2315.

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.

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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

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