Algebraic properties of L-fuzzy finite automata
Algebraic properties of L-fuzzy finite automata
复制标题
L-模糊有限自动机的代数性质
DOI：
10.1016/j.ins.2013.01.018
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发表时间：
2013-06-10
影响因子：
8.1
通讯作者：
Li, Yongming
中科院分区：
文献类型：
--
作者：
Jin, Jianhua;Li, Qingguo;Li, Yongming
关于格序幺半群的模糊自动机理论是由Li和Pedrycz提出的。本文从代数的观点出发，去掉分配律，提出并研究了基于一个更广义的结构L（称为Po-monoid）的模糊有限自动机（简称L-FFA）。引入了（强）后继算子和源算子、模糊后继算子和源算子的概念，并在一定条件下证明了它们是闭包算子。利用弱主子机，得到了基于格序幺半群的模糊有限自动机的唯一分解定理。以L为Quantale，证明了模糊子系统与L-FFA的模糊子机相同。特别地，发现了L的代数性质与L-FFA的某些算子性质之间的内在联系。证明了当L是格序幺半群时，模糊后继算子和模糊源算子的保并性可分别用左、右分配律充分刻画，后继算子的幂等元可等价地用零因子的不存在性刻画. (C)2013 Elsevier Inc. All rights reserved.
Fuzzy automata theory on lattice-ordered monoids was introduced by Li and Pedrycz. Dropping the distributive laws, fuzzy finite automata (L-FFAs for short) based on a more generalized structure L, named a po-monoid, are presented and investigated from the view of algebra in this paper. The notions of (strong) successor and source operators, fuzzy successor and source operators which are shown to be closure operators on certain conditions are introduced and discussed in detail. Using the weak primary submachines, a unique decomposition theorem of a fuzzy finite automaton based on a lattice-ordered monoid is obtained. Taking L as a quantale, fuzzy subsystems are proved to be the same as fuzzy submachines of an L-FFA. In particular, intrinsic connections between algebraic properties of L and properties of some operators of an L-FFA are discovered. It is shown that the join-preserving property of fuzzy successor and source operators can be fully characterized by the right and left distributive laws respectively, and the idempotence of successor operator can be characterized equivalently by the nonexistence of zero divisors when L is a lattice-ordered monoid. (C) 2013 Elsevier Inc. All rights reserved.