模糊代数系统与模糊范式

张孟青1，马占有2

ZHANG Meng-qing1，MA Zhan-you2

（1.School of Preparatory Education,Beifang University of Nationalities,Yinchuan 750021;

2.School of Computer Science and Engineering,Beifang University of Nationalities,Yinchuan 750021,China）

Received:2015-09-11 Revised:2016-03-04 Online:2017-10-25 Published:2017-10-25

摘要：

模糊代数系统是研究模糊语言及模糊自动机的有力工具，语言的范式已有详细的研究。在模糊代数系统的基础上，给出模糊

范式的概念并进行分类，研究proper模糊代数系统与Chomsky模糊范式的关系，给出由proper模糊代数系统构造Chomsky模糊

范式的方法，这种方法使得proper模糊代数系统在表达形式上规范化。为了研究proper模糊代数系统的解，构造了operator

模糊范式，并得到结论：二者强解的第一分量相等，其余对应分量相差一个右逆算子。模糊范式提供了研究模糊代数系统的

不同视角，彰显了模糊范畴下代数系统比经典代数系统具有更好的性质。

关键词: 模糊半环, 模糊代数系统, 模糊范式

Abstract:

The fuzzy algebraic system is an important tool for research on fuzzy valued context-free languages and fuzzy

valued pushdown automata. Since the normal form of languages is studied in detail, we introduce the concept

of fuzzy valued normal form, and study the relationship between the proper fuzzy valued algebraic system and

the Chomsky fuzzy valued normal form. Then we provide the method of producing Chomsky fuzzy valued normal

form from the algebraic, which standardizes the expression of the fuzzy valued algebraic system. Finally, we

design the operator fuzzy valued normal form to study the solutions to the fuzzy valued algebraic system. Our

conclusions are that the first component of the strong solution to the proper fuzzy valued algebraic system

appears also as the first component of the strong solution to such a system in the operator normal form. The

fuzzy valued normal form provides a different view of studying the fuzzy algebraic system, which shows that

the algebraic system in the fuzzy domain has better properties than the classical algebraic system.

Key words: fuzzy valued semiring, fuzzy valued algebraic system, fuzzy valued normal form

张孟青1，马占有2. 模糊代数系统与模糊范式[J]. 计算机工程与科学.

ZHANG Meng-qing1，MA Zhan-you2. Fuzzy valued algebraic system and normal form[J]. Computer Engineering & Science.

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