模糊数的一置信指标及其性质  

A Creditability Index of Fuzzy Number and Its Properties

作　　者：王占京[1] 米香云[1] 王志军[1] 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《河北师范大学学报（自然科学版）》2011年第2期124-129,共6页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(71071049)

摘　　要：采用水平截集与隶属程度相结合的方法,建立了衡量水平截集可靠程度的水平置信度概念,讨论了水平置信度的分析性质,其基本思想完全可以推广到一般可测论域上的模糊集.这些讨论将为建立更为合理的模糊信息之间的差异度量提取提供一种理论基础,为模糊聚类分析、图象识别、系统评估、质量管理、人文科学等问题的决策过程提供一种有效的工具,同时也可在满足某种置信度要求下确定模糊规划、模糊优化等问题的决策水平.Starting with level cut-sets and membership degree of fuzzy numbers, the concept of level creditability is introduced, and the basic properties of level creditability such as continuity, convelgence are discussed. These ideas can be extended to fuzzy sets on general range. All the discussions will offer a kind of tool and a theoretical foundation for processing fuzzy information in many application areas such as fuzzy decision-making, fuzzy programming, fuzzy optimization, expert system, image recognition, cluster analysis and social science etc.

关 键 词：模糊数 水平截集 水平置信度 优化 

分 类 号：O159[理学—数学]