摘要
模糊语言的可逼近条件是模糊计算理论的重要研究内容之一,本文对模糊语言可被确定型模糊有穷自动机逼近的条件进行了研究。首先研究了三个逼近条件之间的关系,证明了2λ-覆盖与λ-逼近等价关系这两个逼近条件的等价性。同时通过反例说明了文[13]给出的模糊语言可逼近的条件是充分非必要的且强于λ-覆盖这一个模糊语言的逼近条件。对于逼近条件的应用,本文通过举例说明了三个逼近条件各有优点。对于给定的模糊语言,文[13]的逼近条件适合用来判断该模糊语言是否可被一个确定型有穷自动机逼近,但并未给出具体的模糊自动机的构造方法;而λ-逼近等价关系这一逼近条件更侧重模糊正则语言的极小逼近,λ-覆盖相对于其他两个逼近条件更方便构造相应的模糊自动机,并给出了具体的构造方法。
The approximated conditions of fuzzy languages are one of the important research contents of fuzzy computational theory.In this paper,we study the conditions that the fuzzy languages can be approximated by deterministic fuzzy finite automata.And firstly,the relationships among the three approximation conditions are studied.The equivalence of two approximation conditions,λ-cover andλ-approximate equivalence relation,is proved.At the same time,a counter-example is given to illustrate that the sufficient non-essential condition of fuzzy languages approximation given in literature[13]is stronger than that ofλ-cover.For the application of approximation conditions,this paper uses concrete examples to illustrate the advantages of the three approximation conditions.For a given fuzzy language,the approximation condition in the literature[13]is suitable to judge whether the fuzzy language can be approximated,but the construction method of the fuzzy automata is not given.The approximation condition ofλ-approximation equivalence relation is more suitable for the minimal approximation of fuzzy regular languages.Compared with the other two approximation conditions,it is more convenient to construct the corresponding automata byλ-cover this approximation condition,and the concrete construction is given.
作者
贺永霞
李平
HE Yong-xia;LI Ping(College of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China)
出处
《模糊系统与数学》
北大核心
2023年第3期108-117,共10页
Fuzzy Systems and Mathematics
作者简介
贺永霞(1996-),女,研究生,研究方向:模糊自动机及其应用,计算智能;通讯作者:李平(1979-),女,副教授,博士,研究方向:模糊数学,模糊自动机理论,计算智能。
