模糊识别器的乘积及其语言  

Products of Fuzzy Recognizers and Its Languges

作　　者：杨京开[1,2] 黄秋娇 李芳[1] 陈彩虹[1] 

机构地区：[1]玉林师范学院数学与信息科学学院,广西玉林537000 [2]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

出　　处：《模糊系统与数学》2015年第3期181-186,共6页Fuzzy Systems and Mathematics

基　　金：广西自然科学基金资助项目(2014GXNSFBA118018);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项目(2015CSOBDP0104);玉林师范学院2015年校级大学生创新创业训练计划立项项目(201510606092)

摘　　要：利用代数学的方法研究了模糊识别器的乘积及其语言问题。提出了模糊识别器的和、直和、级联积、圈积、笛卡尔积等几种积的定义;讨论了模糊识别器的笛卡尔积、和等几种乘积的语言特点;给出了模糊识别器在(强)同态作用下的一些代数性质;证明了模糊识别器的直积是完全确定型的当且仅当其每个因子是完全确定型的,笛卡尔积是完全可达确定型的当且仅当其每个因子是完全可达确定型的。In this paper, products of fuzzy recognizers and its languges are investigated by using algebraic techniques. Several kinds of products of fuzzy recognizers such as the sum, direct sum, cascade product, wreath product, cartesian composition are introduced. The language features of products of fuzzy recognizers, for example, cartesian composition, sum and so on are discussed. Some algebraic properties of fuzzy recognizers under （strong） homomorphism are given. It is proved that the direct product of two fuzzy recognizers is complete deterministic if and only if each of its factors is complete deterministic, cartesian composition of two fuzzy recognizers is complete accessible deterministic if and only if each of its factors is complete accessible deterministic.

关 键 词：模糊识别器 积 语言 同态 可达的 

分 类 号：O151.21[理学—数学]