TP 301Similarity Measures on Vague Values and Three-Parameter Vague Values
LAN Rong1,FAN Jiu-Lun2
1.School of Electronic Engineering,Xidian University,Xian 710071 2.Department of Information and Control,Xian Institute of Post and Telecommunications,Xian 710061W
Abstract：As an extension of vague values, the concept of three-parameter vague values is introduced in this paper, and a general similarity measure expression between three-parameter vague values is presented. Based on this expression, a corresponding general similarity measure between vague values is researched and a relatively general expression is given. When the parameters of the proposed similarity measure between vague values are selected as some special values, some existent similarity measure formulas between vague values can be obtained. The applications of proposed similarity measure in pattern recognition and medical diagnosis are shown.
[1] Bu Guangzhi, Zhang Yuwen. Gray Fuzzy Comprehensive Evaluation Method Based on Interval Numbers of Three Parameters. Systems Engineering and Electronics, 2001, 23(9): 43-62 (in Chinese) (卜广志,张宇文.基于三参数区间数的灰色模糊综合评判.系统工程与电子技术, 2001, 23(9): 43-62) [2] Zhu Jianjun, Liu Sifeng, Wang Hehua. Aggregation Approach of Two Kinds of Three-Point Interval Number Comparison Matrix in Group Decision Making. Acta Automatic Sinica, 2007, 33(3): 297-301 (in Chinese) (朱建军,刘思峰,王翯华.群决策中两类三端点区间数判断矩阵的集结方法.自动化学报, 2007, 33(3): 297-301) [3] Hu Qizhou, Zhang Weihua, Yu Li. The Research and Application of Interval Numbers of Three Parameters. Engineering Science, 2007, 9(3): 47-51 (in Chinese) (胡启洲,张卫华,于 莉.三参数区间数研究及其在决策分析中的应用.中国工程科学, 2007, 9(3): 47-51) [4] Zadeh L A. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning. Information Sciences, 1975, 8(3): 199-249 [5] Atanassov K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96 [6] Gau W L, Buehrer D J. Vague Sets. IEEE Trans on Systems, Man and Cybernetics, 1993, 23(2): 610-614 [7] Burillo P, Bustine H. Vague Sets Are Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1996, 79(3): 403-405 [8] Deschrijver G, Kerre E E. On The Relationship between Some Extensions of Fuzzy Set Theory. Fuzzy Sets and Systems, 2003, 133(2): 227-235 [9] Lan Rong, Fan Jiulun. TOPSIS Decision-Making Method on Three Parameters Interval-Valued Fuzzy Sets. Systems Engineering-Theory Practice, 2009, 29(5): 129-136 (in Chinese) (兰 蓉,范九伦.三参数区间值模糊集上的TOPSIS决策方法.系统工程理论与实践, 2009, 29(5): 129-136) [10] Chen S M, Tan J M. Handling Multicriteria Fuzzy Decision-Making Problems Based on Vague Set Theory. Fuzzy Sets and Systems, 1994, 67(2): 163-172 [11] Szmidt E, Kacprzyk J. Distance between Intuitionistic Fuzzy Sets and Their Applications in Reasoning // Kacprzyk J, ed. Studies in Computational Intelligence. Heidelberg, Germany: Springer-Verlag, 2005, Ⅱ: 101-116 [12] Szmidt E, Kacprzyk J. A Similarity Measure for Intuitionistic Fuzzy Sets and Its Applications in Supporting Medical Diagnostic Reasoning // Proc of the 7th International Conference on Artificial Intelligence and Soft Computing. Zakopane, Poland, 2004: 388-393 [13] Montero J, Gómez D, Bustince H. Atanassovs Intuitionistic Fuzzy Sets as a Classification Model // Proc of the 12th International Fuzzy Systems Association World Congress on Foundations of Fuzzy Logic and Soft Computing. Cancun, Mexico, 2007: 69-75 [14] Szmidt E, Kacprzyk J. An Intuitionistic Fuzzy Set Based Approach to Intelligent Data Analysis: an Approach to Medical Diagnosis // Abraham A, Jain L, Kacprzyk J, eds. Rcent Advances in Intelligent Paradigms and Applications. Heidelberg, Germany: Springer-Verlag, 2002: 57-70 [15] Chen S M. Measures of Similarity between Vague Sets. Fuzzy Sets and Systems, 1995, 74(2): 217-223 [16] Hong D H, Kim C. A Note on Similarity Measures between Vague Sets and between Elements. Information Sciences, 1999, 115(1/2/3/4): 83-96 [17] Li Fan, Xu Zhangyan. Measures of Similarity between Vague Sets. Journal of Software, 2001, 12(6): 922-927 (in Chinese) (李 凡,徐章艳.Vague集之间的相似度量.软件学报, 2001, 12(6): 922-927) [18] Fan Jiulun. Similarity Measures on Vague Values and Vague Sets. Systems Engineering-Theory Practice, 2006, 26(8), 95-100 (in Chinese) (范九伦. Vague值与Vague集上的贴近度. 系统工程理论与实践, 2006, 26(8), 95-100) [19] Zhang Qinghua. Study on Similarity Measure between Vague Values (Sets). Journal of Electronics Information Technology, 2007, 29(8): 1855-1859 (in Chinese) (张清华. Vague值(集)相似度量的研究. 电子与信息学报, 2007, 29(8): 1855-1859) [20] Hung W L, Yang M S. Similarity Measures of Intuitionistic Fuzzy Sets Based on Lp Metric. International Journal of Approximate Reasoning, 2007, 46(1): 120-136 [21] Yang M S, Wu K L. A Similarity-Based Robust Clustering Method. IEEE Trans on Pattern Analysis and Machine Intelligence, 2004, 26(4): 434-448
2010, Vol. 23 
