Fuzzy valued algebraic system and normal form

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

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

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

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