模糊有限状态机的积的代数性质  

Algebraic Properties of Products of Fuzzy Finite State Machines

作　　者：杨京开[1,2] 黄秋娇 李芳[1] 陈彩虹[1] 黄飞丹 盘春秀 

机构地区：[1]玉林师范学院数学与统计学院,广西玉林537000 [2]玉林师范学院广西高校复杂系统优化与大数据处理重点实验室,广西玉林537000 [3]贵州工程应用技术学院理学院,贵州毕节551700

出　　处：《模糊系统与数学》2016年第5期33-41,共9页Fuzzy Systems and Mathematics

基　　金：广西自然科学基金资助(2014GXNSFBA118018);贵州省科技合作计划项目(黔科合LH字[2016]7062号);广西高校复杂系统优化与大数据处理重点实验室开放基金资助(2015CSOBDP0104);广西壮族自治区大学生创新创业训练计划立项项目资助(201510606092)

摘　　要：文章利用代数的方法讨论了模糊有限状态机的全直积、级联积、圈积、模糊有限状态机的和的代数性质。证明了模糊有限状态机的和与其因子在子系统(强子系统)、交换性、连通性、可恢复性等方面的相似的结构性质;给出了模糊有限状态机的全直积、级联积、圈积与其因子之间的关系;获得了模糊有限状态机的各种积的容许划分与其因子的容许划分之间的关系、以及模糊有限状态机的积的商与模糊有限状态机的商的积之间的联系。In this paper, algebraic properties of products of fuzzy finite state machines, such as full direct product, cascade product, wreath product and sum, are discussed utilizing algebraic techniques. The similar properties between the sum of fuzzy finite state machines and the factors in subsystem （strong subsystem）, exchange properties, connectivity, retrievability and so on are proved; the relationship between the full direct product, cascade product, wreath product of fuzzy finite state machines and the factors are given; the relation between the several kinds of products of fuzzy finite state machines and the factors in admissible partition, the link between the quotient of products of fuzzy finite state machines and the products of quotient of fuzzy finite state machines are obtained.

关 键 词：模糊有限状态机 商 积 同态 容许划分 

分 类 号：TP301.1[自动化与计算机技术—计算机系统结构]