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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (3): 37-43.doi: 10.6040/j.issn.1671-9352.0.2020.360

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非确定模糊有穷自动机的ε-语言逼近

王海辉(),赵路瑶,李平*()   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710119
  • 收稿日期:2020-07-13 出版日期:2021-03-20 发布日期:2021-03-16
  • 通讯作者: 李平 E-mail:wanghaihui@snnu.edu.cn;liping@snnu.edu.cn
  • 作者简介:王海辉(1994—), 男, 硕士研究生, 研究方向为模糊自动机及其应用. E-mail: wanghaihui@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(61673250);国家自然科学基金资助项目(61672023);中央高校基本科研业务费专项资金资助项目(GK201803008)

ε-language approximation of nondeterministic fuzzy finite automata

Hai-hui WANG(),Lu-yao ZHAO,Ping LI*()   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, Shaanxi, China
  • Received:2020-07-13 Online:2021-03-20 Published:2021-03-16
  • Contact: Ping LI E-mail:wanghaihui@snnu.edu.cn;liping@snnu.edu.cn

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摘要：

在max-*复合推理下引入了非确定模糊有穷自动机的概念, 其中*是t-模运算。为了比较2个非确定模糊有穷自动机的行为, 借助于[0, 1]上的一个实数ε, 定义了2种ε-语言逼近, 讨论了它们之间的关系。证明了非确定模糊有穷自动机和模糊有穷自动机之间是0-弱语言逼近的, 即二者可以接受相同的模糊语言。此外, 还讨论了2种ε-语言逼近的一些代数性质, 特别地给出ε-语言逼近在并运算、*运算以及连接运算下的性质。最后, 分析了ε-语言逼近的鲁棒性。

关键词: 模糊有穷自动机, 非确定模糊有穷自动机, 语言逼近, 鲁棒性

Abstract:

We have introduced the concept of nondeterministic fuzzy finite automata under max-* compositional inference for some t-norm *. In order to compare the behaviors of nondeterministic fuzzy finite automata, two ε-language approximations are given using some real number ε in [0, 1]. Then we discuss the relationship of two ε-language approximations, and prove that nondeterministic fuzzy finite automata and fuzzy finite automata are 0-language approximated, that is to say they can accept same fuzzy language. In addition, some algebraic properties of two ε-language approximations are studied. In particular, we obtain that properties of them under union operation, *operation, and concatenation operation. Finally, the robustness of ε-language approximations is analyzed.

Key words: fuzzy finite automata, nondeterministic fuzzy finite automata, language approximation, robustness

中图分类号: 

  • TP301.1

图1

2个NFFA*s"

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