基于凸面单形体的Vague集向Fuzzy集转化模型

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摘要利用Vague集与凸面单形体同一平面内3个三角形的对应关系，给出一种Vague集及其向Fuzzy集转化的单形体几何表示方法，有效解决Vague集向Fuzzy集转化方法或模型中的几何解释问题。提出Vague集向Fuzzy集转化的单形体转化模型(S-TM)，以及应满足的转化准则。与已有转化方法或模型相比，S-TM具有更直观的几何表示和更明确、更确定的几何解释，是一种更为有效的转化模型，并说明Vague集向Fuzzy集的转化具有模糊性和逐渐转化性。

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	韦波
	彭军还
	杨红磊

关键词 ： Vague集, Fuzzy集, 单形体转化模型(S-TM), 转化准则, 凸面单形体

Abstract：Making use of a corresponding relation between Vague sets and the three triangles within a same plane of convex simplex, a simplex geometric expression is presented for Vague sets and transforming them into Fuzzy sets. It effectively solves the problem of geometric interpretation in methods or models for transforming Vague sets into Fuzzy sets. A simplex transformation model(S-TM) is proposed for transforming Vague sets into Fuzzy sets, and the corresponding transformation rules are also presented. Compared with the existing transformation methods or models, the proposed S-TM is more effective and visualized in geometric expression, and more explicit and determinate in geometric interpretation. Comparative results show that transforming Vague sets into Fuzzy sets is fuzzy and gradual.

Key words： Vague Set Fuzzy Set Simplex Transformation Model(S-TM) Transformation Rule Convex Simplex

收稿日期: 2010-12-03

ZTFLH:

TP311

基金资助:国家自然科学基金项目(No.41074009,41071294,41064001)、广西科学研究与技术开发计划项目(No.10123012-9)、广西自然科学基金项目(No.0991248)和广西研究生教育创新计划项目(No.2011105960816M14)资助

作者简介: 韦波，男，1974年生，博士研究生，副教授，主要研究方向为测量、遥感与地理信息处理。E-mail:superweibo@126。com。彭军还，男，1964年生，教授，博士生导师，主要研究方向为测量误差理论、GPS与遥感数据处理。杨红磊，男，1983年生，博士研究生，主要研究方向为遥感图像数据处理。

引用本文:

韦波，彭军还，杨红磊. 基于凸面单形体的Vague集向Fuzzy集转化模型[J]. 模式识别与人工智能, 2012, 25(3): 426-434. WEI Bo, PENG Jun-Huan, YANG Hong-Lei. Model for Transforming Vague Sets into Fuzzy Sets Based on Convex Simplex. , 2012, 25(3): 426-434.

链接本文:

http://manu46.magtech.com.cn/Jweb_prai/CN/ 或 http://manu46.magtech.com.cn/Jweb_prai/CN/Y2012/V25/I3/426

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