双极信息处理的代数描述  

Algebraic Description of Bipolar Information Processing

作　　者：周彤[1] 陆汝华[1] 张家录[2] 

机构地区：[1]湘南学院软件与通信工程学院,湖南郴州423000 [2]湘南学院数学与金融学院,湖南郴州423000

出　　处：《模糊系统与数学》2016年第6期65-73,共9页Fuzzy Systems and Mathematics

基　　金：湖南省自然科学基金资助项目(16JJ6138;17JJ3026);湖南省科技计划项目(2014SK3229);湖南省教育厅科学研究项目(2014A135;12C0885);湖南省社会科学基金资助项目(16YBA329)

摘　　要：在信息处理中,要考虑信息的双极特征:正面信息(也称为偏好信息)和负面信息(也称为禁止信息)。本文研究双极信息处理的代数刻画。首先,引进双极代数、约束双极代数、约束双极t-模、约束双极蕴含等概念并讨论这些概念的性质及其这些概念之间的关系。其次,给出约束双极t-模、约束双极蕴含等聚合算子可以分解为两个单极聚合算子的条件。In many domains of information processing, bipolarity is a core feature to be considered： positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. In this paper, we focus on the algebraic characterization of bipolar information processing. We introduce some concepts about bipolar information processing, such as bipolar algebra; constraint bipolar algebra; constraint bipolar t-norm; constraint bipolar implication, etc. We also discuss the properties of bipolar algebra and constraint bipolar algebra, and investigate under which conditions a constraint bipolar operator to be decomposed into two unipolar operators.

关 键 词：双极代数 单因素双极代数 双因素双极代数 约束双极代数 约束双极t-模 约束双极蕴含 

分 类 号：O143[理学—数学]