星形模糊集的性质-徐伟华.pdf

Operations Research and Fuzziology 运筹与模糊学, 2011, 1, 6-10 doi:10.4236/orf.2011.11002 Published Online August 2011 (/journal/orf/) The Research of Several Propositions on Starshaped Fuzzy Sets Weihua Xu, Wenxin Sun, Yufeng Liu School of Mathematics and Statistics, Chongqing University of Technology, Chongqing Email: chxuwh@ Received: Jul. 7th, 2011; revised: Jul. 20th, 2011; accepted: Jul. 25th, 2011. Abstract: Starting from the definition of the starshaped fuzzy set, this paper introduces the concept of fuzzy quasi-starshaped set and fuzzy pseudo-starshaped set. Some equivalent discrimination conditions on the kind of starshaped fuzzy sets are given by studying the key propositions of them. Furthermore, the relationships among convex fuzzy, fuzzy numbers and them are deeply researched, which enrich and perfect the theory of the starshaped fuzzy set. Keywords: Starshaped Fuzzy Set; Convex Fuzzy Set; Fuzzy Numbers; Fuzzy Quasi-Starshaped Set; Fuzzy Pseudo-Starshaped Set 星形模糊集的若干性质研究 徐伟华，孙文鑫，刘玉锋 重庆理工大学数学与统计学院，重庆 Email: chxuwh@ 收稿日期：2011 年 7 月 7 日；修回日期：2011 年 7 月 20 日；录用日期：2011 年 7 月 25 日 摘 要：本文从星形模糊集的定义出发，引出了拟星形模糊集和伪星形模糊集的概念，通过研究其各 自重要性质给出了对应星形模糊集的若干等价判别条件；进一步，本文深入研究了它们与凸模糊集、 模糊数之间的关系，丰富和完善了星形模糊集的理论。 关键词：星形模糊集；凸模糊集；模糊数；拟星形模糊集；伪星形模糊集 1. 引言 方向就是对星形模糊集[4](starshaped fuzzy sets) 的研 究。目前，国际上对于星形模糊集理论的研究比较活 1965 年，美国计算机与控制论专家 L. A. Zedeh 跃，特别是将模糊集中的相关理论与方法推广到星形 教授在《信息与控制》杂志上发表了一篇开创性论文