Fuzzy grammar theory based on lattices

被引:4
|
作者
Jin, Jianhua [1 ]
Li, Qingguo [1 ]
机构
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
基金
美国国家科学基金会;
关键词
Fuzzy regular grammar; Fuzzy finite automata; Fuzzy language; Lattice equivalence; MEMBERSHIP VALUES; FINITE AUTOMATA; QUANTUM LOGIC;
D O I
10.1007/s00500-012-0845-1
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In this paper, on the basis of breadth-first and depth-first ways, we establish a fundamental framework of fuzzy grammars based on lattices, which provides a necessary tool for the analysis of fuzzy automata. The relationship among finite automata with membership values in lattices (l-VFAs), lattice-valued regular grammars (l-RGs) and lattice-valued deterministic regular grammars (l-DRGs) is investigated. It is demonstrated that, based on each semantic way, l-VFAs and l-RGs are equivalent in the sense that they accept or generate the same classes of fuzzy languages. Furthermore, it is proved that l-VFAs, l-valued deterministic finite automata, l-RGs and l-DRGs are equivalent based on depth-first way. For any l-RG, the language based on breadth-first way coincides with the language based on depth-first way if and only if the truth-valued domain l is a distributive lattice.
引用
收藏
页码:1415 / 1426
页数:12
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