MTL代数及由其MP滤子型商代数的局部有限性  

The Local Finiteness of MTL-algebra and Its Quotient Algebra Determined by MP Filters

作　　者：寇海燕[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2015年第2期45-53,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171196)

摘　　要：首先,将局部有限方法引入到MTL代数中,提出了局部有限MTL代数的概念,给出了局部有限MTL代数的一些基本性质,证明了局部有限MTL代数的线性性质;其次,讨论了MTL代数的MP滤子的相关性质;最后,证明了由MP滤子诱导的商贷数M/F是局部有限的非退化MTL代数的充分必要条件是MP滤子是极大MP滤子;证明了每一个MTL代数可以嵌入到一族局部有限的MTL代数的直积MTL代数中。Firstly, the concept of locally finite MTL-algebra is proposed by introducing locally finite method to MTL-algebra, some basic properties of locally finite MTL-algebra are given. Moreover, it is proved that locally finite MTL-algebra is linear; Secondly, some properties of MTL-algebra which are relative to MPfilters of MTL algebra are discussed; Thirdly, the sufficient and necessary conditions for quotient algebra of MTL algebra determined by MP filter to be locally finite MTL algebra are obtained, and it is proved that each MTL algebra can be embedded to direct product of a family of locally finite MTL algebras.

关 键 词：模糊逻辑 MTL-代数 局部有限 MP滤子 商代数 嵌入 

分 类 号：O141[理学—数学]