Model for Transforming Vague Sets into Fuzzy Sets Based on Convex Simplex
WEI Bo1,2,3, PENG Jun-Huan1, YANG Hong-Lei1
1.School of Land Science and Technology,China University of Geosciences Beijing,Beijing 100083 2.College of Geomatics and Geoinformation,Guilin University of Technology,Guilin 541004 3.Guangxi Key Laboratory of Spatial Information and Geomatics,Guilin University of Technology,Guilin 541004
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.
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.
[1] Li Fan,Lü Zehua,Cai Lijing.The Entropy of Vague Sets Based on Fuzzy Sets.Journal of Huazhong University of Science and Technology: Natural Science Edition,2003,31(l): 1-3 (in Chinese) (李 凡,吕泽华,蔡立晶.基于Fuzzy集的Vague集的模糊熵.华中科技大学学报:自然科学版,2003,31(1): l-3) [2] Liu Huawen.Basis of Fuzzy Pattern Recognition-Similarity Measures.Pattern Recognition and Artificial Intelligence,2004,17(2): 141-145 (in Chinese) (刘华文.模糊模式识别的基础——相似度量.模式识别与人工智能,2004,17(2): 141-145) [3] Burillo P,Bustince H.Intuitionistic Fuzzy Relations (Part I).Mathware and Soft Computing,1995,2(1): 5-38 [4] Lin Zhigui,Liu Yingping,Xu Lizhong,et al.A Method for Transforming Vague Sets into Fuzzy Sets in Fuzzy Information Processing.Computer Engineering and Applications,2004,40(9): 24-25 (in Chinese) (林志贵,刘英平,徐立中,等.模糊信息处理中Vague集向模糊集转化的一种方法.计算机工程与应用,2004,40(9): 24-25) [5] Liu Yong,Wang Guoyin,Feng Lin.A General Model for Transforming Vague Sets into Fuzzy Sets // Proc of the 1st International Conference on Rough Sets and Knowledge Technology.Chongqing,China,2006: 341-348 [6] Fan Ping,Liang Jiarong,Li Tianzhi.A New Method for Transforming Vague Sets into Fuzzy Sets.Computer Engineering and Applications,2006,42(3): 50-52 (in Chinese) (范 平,梁家荣,李天志.关于Vague集向模糊集转化的一种新方法.计算机工程与应用,2006,42(3): 50-52) [7] Gau Wenlung,Daniel J.Vague Sets.IEEE Trans on Systems,Man and Cybernetics,1993,23(2): 610-614 [8] De Luca A,Termini S.A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory.Information and Control,1972,20(4): 301-312 [9] Szmidt E,Kacprzyk J.Entropy for Intuitionistic Fuzzy Sets.Fuzzy Sets and Systems,2001,118(3): 467-477 [10] Vlachos I K,Sergiadis G D.Intuitionistic Fuzzy Information-Applications to Pattern Recognition.Pattern Recognition Letters,2007,28(2): 197-206 [11] Liu Xuecheng.Entropy,Distance Measure and Similarity Measure of Fuzzy Sets and Their Relations.Fuzzy Sets and Systems,1992,52(3): 305-318 [12] Yan Deqin,Chi Zhongxian,Li Yanhong.Measures of Similarity between Vague Sets.Pattern Recognition and Artificial Intelligence,2004,17(1): 22-26 (in Chinese) (闫德勤,迟忠先,李艳红.关于Vague集的相似度量.模式识别与人工智能,2004,17(1): 22-26) [13] Lan Rong,Fan Jiulun.Similarity Measures on Vague Values and Three-Parameter Vague Values.Pattern Recognition and Artificial Intelligence,2010,23(3): 341-348 (in Chinese) (兰 蓉,范九伦.Vague值和三参数Vague值上的贴近度.模式识别与人工智能,2010,23(3): 341-348) [14] Geng Xiurui,Zhang Bing,Zhang Xia,et al.A Method for Unmixing of Hyperspectral Imagery Based on Volume of Convex Simplex in N-Space.Progressing in Nature Science,2004,14(7): 810-814 (in Chinese) (耿修瑞,张 兵,张 霞,等.一种基于高维空间凸面单形体体积的高光谱图像解混算法.自然科学进展,2004,14(7): 810-814) [15] Li Fan,Cai Lijing,Lü Zehua.Three-Dimension Expression of Vague Sets.Huazhong University of Science and Technology: Natural Science Edition,2002,30(10): 44-46 (in Chinese) (李 凡,蔡立晶,吕泽华.Vague集的三维表示.华中科技大学学报:自然科学版,2002,30(l0): 44-46) [16] Shi Yuqiang,Wang Hongxu.A Rule of Transforming Method from Vague Value to Fuzzy Membership Grade.Computer Engineering and Applications,2005,41(24): 169-171,187 (in Chinese) (石玉强,王鸿绪.Vague值向Fuzzy隶属度转化方法的准则.计算机工程与应用,2005,41(24): 169-171,187
2012, Vol. 25 
