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第5期 王艳平,等:区间直觉模糊粗糙集的不确定性研究 ·617. puter and Information Sciences,1982(11):341-356. 本性质[J]重庆文理学院学报:自然科学版,2010,29 [2]ZADEH L A.Fuzzy sets [J].Information and Control,1965 (3):21-24. (8):338-353. QU K,TANG L,RONG W J.The construction and basic [3]ATANASSOV K.Intuitionistic fuzzy sets [J].Fuzzy Sets properties of entropy of interval-valued intuitionistic fuzzy and Systems,1986,20(2):87-96. sets [J].Journal of Chongqing University of Arts and Sci- [4]ATANASSOV K,GARGOV G.Interval-valued intuitionistic ences Natural Science Edition,2010,29(3):21-24. fuzzy sets[J].Fuzzy Sets and Systems,1989,31(3):343- [15]YE J.Two effective measures of intuitionstic fuzzy entropy 349. [J].Computing,2010,87(1/2):55-62. [5]张文修,吴伟志,梁吉业,等.粗糙集理论与方法[M].北 [16]LIANG J Y,CHIN K S,DANG C Y et al.A new method 京:科学出版社,2001:55-73. for measuring uncertainty and fuzziness in rough set theory [6]张文修,姚一豫,梁怡.粗糙集与概念格[M]西安:西安 [J].International Journal of General Systems,2002,31 交通大学出版社,2006:61-84. (4):331-342. [7]ZHANG Z M.An interval-valued rough intuitionistic fuzzy [17]ATANASSOV K.Operators over interval valued intuitionis- set model[].International Journal of General Systems, tic fuzzy sets [J].Fuzzy Sets and Systems,1994,64: 2010,39(2):135-164. 159-174. [8]张瑜,王艳平直觉模糊粗糙集模型[J刀辽宁工业大学学 [18]GONG Z T,SUN B Z,CHEN D G.Rough set theory for 报:自然科学版,2008,28(6):414-420. interval-valued fuzzy information systems[J].Information ZHANG Yu,WANG Yanpng.Intuitionistic fuzzy rough sets Sciences,2008,178:1968-1985. [J].Journal of Liaoning University of Technology Natural [19]彭振文,王周敏.区间直觉模糊关系及其性质[J].海南 Science Edition,2008.28(6):414-420. 师范大学学报:自然科学版,2008,(12):412415. [9]王艳平,孙静,陈美薇,区间直觉模糊粗糙集模型[J]计 PENG Z W,WANG Z J.The Interval-valued intuitionistic 算机工程与应用,2011,47(24):37-42. fuzzy relations and their properties[].Journal of Hainan WANG Yanping,SUN Jing,CHEN Meiwei.Interval-valued Normal University Natural Science Edition,2008,21 intuitionistic fuzzy rough sets Computer Engineering and (4):412-415. Applications,2011,47(24):37-42. [20]王培,魏翠萍.一种区间直觉模糊熵的构造方法[J].计 [10]魏翠萍,高志海,郭婷婷.一个基于三角函数的直觉模 算机工程与应用,2011,47(2):43-46. 糊嫡公式[J].控制与决策,2012,27(4):571-574. WANG P,WEI C P.Constructing method of interval-valued WEI Cuiping,GAO Zhihai,GUO Tingting.An intuitionis- intuitionistic fuzzy entropy []Computer Engineering and tic fuzzy entropy measure based on trigonometric function Applications,2011,47(2):43-45. J].Control and Decision,2012,27(4):571-574. 作者简介: [11]BURILLO P,BUSTINCE H.Entropy on intuitionistic fuzzy 刘洪伟,女,1989年生,硕士研究 sets and on interval-valued fuzzy sets [J].Fuzzy Sets and 生,主要研究方向为粗糙集理论,模糊 Systems,2001,118(3):305-316. 集理论。 [12]SZMIDT E,KACPRZYK J.Entropy for intuitionistic fuzzy sets [J].Fuzzy Sets and Systems,2001,118(3):467- 477. [13]郭效之.模糊不确定性度量的探讨及扩展[D].西安: 西北大学,2004:48-50. GUO X Z.The discussion and extension of fuzzy uncertain- 王艳平,女,1965年生,教授,主 ty measure[D].Xi 'an:northwestern university,2004: 要研究方向为粗糙集理论,模糊集理 48-50. 论,发表学术论文30余篇。 [14]屈克,汤磊,荣文静.区间直觉模糊集熵的构造及其基puter and Information Sciences, 1982(11): 341⁃356. [2]ZADEH L A. Fuzzy sets [J]. Information and Control,1965 (8):338⁃353. [3] ATANASSOV K. Intuitionistic fuzzy sets [ J]. Fuzzy Sets and Systems, 1986, 20(2): 87⁃96. [4]ATANASSOV K, GARGOV G. Interval⁃valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31(3): 343⁃ 349. [5]张文修,吴伟志,梁吉业,等.粗糙集理论与方法[M].北 京:科学出版社, 2001: 55⁃73. [6]张文修,姚一豫,梁怡.粗糙集与概念格[M].西安:西安 交通大学出版社, 2006: 61⁃84. [7] ZHANG Z M. An interval⁃valued rough intuitionistic fuzzy set model [ J]. International Journal of General Systems, 2010, 39(2): 135⁃164. [8]张瑜,王艳平.直觉模糊粗糙集模型[ J].辽宁工业大学学 报:自然科学版,2008,28(6):414⁃420. ZHANG Yu, WANG Yanpng. Intuitionistic fuzzy rough sets [J]. Journal of Liaoning University of Technology :Natural Science Edition, 2008, 28(6): 414⁃420. [9]王艳平,孙静,陈美薇,区间直觉模糊粗糙集模型[ J].计 算机工程与应用,2011,47 (24):37⁃42. WANG Yanping, SUN Jing, CHEN Meiwei. Interval⁃valued intuitionistic fuzzy rough sets[J]. Computer Engineering and Applications, 2011, 47 (24): 37⁃42. [10]魏翠萍,高志海,郭婷婷. 一个基于三角函数的直觉模 糊熵公式[J].控制与决策,2012, 27(4): 571⁃574. WEI Cuiping, GAO Zhihai, GUO Tingting. An intuitionis⁃ tic fuzzy entropy measure based on trigonometric function [J].Control and Decision, 2012, 27(4): 571⁃574. [11]BURILLO P, BUSTINCE H. Entropy on intuitionistic fuzzy sets and on interval⁃valued fuzzy sets [ J]. Fuzzy Sets and Systems, 2001, 118(3): 305⁃316. [12]SZMIDT E, KACPRZYK J. Entropy for intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems, 2001, 118( 3): 467⁃ 477. [13]郭效之. 模糊不确定性度量的探讨及扩展[D]. 西安: 西北大学,2004: 48⁃50. GUO X Z. The discussion and extension of fuzzy uncertain⁃ ty measure [D]. Xi ′ an: northwestern university, 2004: 48⁃50. [14]屈克,汤磊,荣文静. 区间直觉模糊集熵的构造及其基 本性质[J].重庆文理学院学报:自然科学版,2010, 29 (3): 21⁃24. QU K, TANG L, RONG W J. The construction and basic properties of entropy of interval⁃ valued intuitionistic fuzzy sets [J]. Journal of Chongqing University of Arts and Sci⁃ ences : Natural Science Edition, 2010, 29(3): 21⁃24. [15]YE J. Two effective measures of intuitionstic fuzzy entropy [J]. Computing, 2010, 87(1 / 2): 55⁃62. [16]LIANG J Y, CHIN K S, DANG C Y et al. A new method for measuring uncertainty and fuzziness in rough set theory [J]. International Journal of General Systems, 2002, 31 (4): 331⁃342. [17]ATANASSOV K.Operators over interval valued intuitionis⁃ tic fuzzy sets [ J]. Fuzzy Sets and Systems, 1994, 64: 159⁃174. [18]GONG Z T, SUN B Z, CHEN D G . Rough set theory for interval⁃valued fuzzy information systems [ J]. Information Sciences,2008, 178: 1968⁃1985. [19]彭振文,王周敏. 区间直觉模糊关系及其性质[ J].海南 师范大学学报:自然科学版, 2008, (12): 412⁃415. PENG Z W, WANG Z J. The Interval⁃valued intuitionistic fuzzy relations and their properties[ J]. Journal of Hainan Normal University : Natural Science Edition, 2008, 21 (4): 412⁃415. [20]王培,魏翠萍.一种区间直觉模糊熵的构造方法[ J]. 计 算机工程与应用,2011, 47(2): 43⁃46. WANG P,WEI C P. Constructing method of interval⁃valued intuitionistic fuzzy entropy [J]. Computer Engineering and Applications,2011, 47(2): 43⁃45. 作者简介: 刘洪伟,女,1989 年生,硕士研究 生,主要研究方向为粗糙集理论,模糊 集理论。 王艳平,女,1965 年生,教授,主 要研究方向为粗糙集理论,模糊集理 论,发表学术论文 30 余篇。 第 5 期 王艳平,等:区间直觉模糊粗糙集的不确定性研究 ·617·
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