摘要 犹豫模糊语言集(hesitant fuzzy linguistic term set,HFLTS)是指语言变量的取值为语言术语集的一个有序且连贯的子集.文章对基于HFLTS的理论发展进行了综述.首先介绍了HFLTS的含义及起源,随后分别对犹豫模糊语言信息的融合理论、测度理论、偏好关系理论以及决策方法进行了概述.最后展望了HFLTS理论未来的研究方向.
Abstract:Hesitant fuzzy linguistic term set (HFLTS) is defined as an ordered and consecutive subset of the linguistic term set for a linguistic variable. This paper carries out some states of the art review over the development of HFLTS theory. Firstly, we introduce the definition and originality of the HFLTS, and then conduct the review from four aspects, which are the hesitant fuzzy linguistic fusion theory, the hesitant fuzzy linguistic measurement theory, the hesitant fuzzy linguistic preference relation theory and the hesitant fuzzy linguistic decision making methodologies. Finally, we outline the future research directions on qualitative decision making with hesitant fuzzy linguistic information.
廖虎昌, 缑迅杰, 徐泽水. 基于犹豫模糊语言集的决策理论与方法综述[J]. 系统工程理论与实践, 2017, 37(1): 35-48.
LIAO Huchang, GOU Xunjie, XU Zeshui. A survey of decision making theory and methodologies of hesitant fuzzy linguistic term set. Systems Engineering - Theory & Practice, 2017, 37(1): 35-48.
[1] Zadeh L A. The concept of a linguistic variable and its application to approximate reasoning-Part I[J]. Information Sciences, 1975, 8(3): 199-249. [2] Rodríguez R M, Martínez L, Herrera F. Hesitant fuzzy linguistic terms sets for decision making[J]. IEEE Transactions on Fuzzy Systems, 2012, 20: 109-119. [3] Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8: 338-353. [4] Herrera F, Herrera-Viedma E. Linguistic decision analysis: Steps for solving decision problems under linguistic information[J]. Fuzzy Sets and Systems, 2000, 115: 67-82. [5] Rodríguez R M, Martínez L. An analysis of symbolic linguistic computing models in decision making[J]. International Journal of General Systems, 2013, 42: 121-136. [6] Xu Z S. Deviation measures of linguistic preference relations in group decision making[J]. Omega, 2005, 33: 249-254. [7] Liao H C, Xu Z S, Zeng X J. Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J]. Information Sciences, 2014, 271: 125-142. [8] Torra V. Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25: 529-539. [9] Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20: 87-96. [10] Atanassov K T, Gargov G. Interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1989, 31: 343-349. [11] Herrera F, Martínez L. A 2-tuple fuzzy linguistic representation model for computing with words[J]. IEEE Transactions on Fuzzy Systems, 2000, 8: 746-752. [12] Türkşen I B. Type 2 representation and reasoning for CWW[J]. Fuzzy Sets and Systems, 2002, 127: 17-36. [13] Xu Z S. A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J]. Information Sciences, 2004, 166: 19-30. [14] Wang J H, Hao J. A new version of 2-tuple fuzzy linguistic representation model for computing with words[J]. IEEE Transactions on Fuzzy Systems, 2006, 14: 435-445. [15] Liao H C, Xu Z S, Zeng X J, et al. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets[J]. Knowledge-Based Systems, 2015, 76: 127-138. [16] Rodríguez R M, Martínez L, Herrera F. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term set[J]. Information Sciences, 2013, 241: 28-42. [17] Wei C P, Zhao N, Tang X J. Operators and comparisons of hesitant fuzzy linguistic term sets[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(3): 575-585. [18] 冯向前, 谭倩云, 钱钢. 犹豫模糊语言的可能度排序方法[J]. 控制与决策, 2016, 31(4): 640-646.Feng X Q, Tan Q Y, Qian G. Possibility degree methods for ranking hesitant fuzzy linguistic sets[J]. Control and Decision, 2016, 31(4): 640-646. [19] Wang H. Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making[J]. International Journal of Computational Intelligence Systems, 2015, 8: 14-33. [20] Wang J Q, Wu J T, Wang J, et al. Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J]. Information Sciences, 2014, 288: 55-72. [21] Meng F Y, Chen X H, Zhang Q. Multi-attribute decision analysis under a linguistic hesitant fuzzy environment[J]. Information Sciences, 2014, 267: 287-305. [22] Wu J T, Wang J Q, Wang J, et al. Hesitant fuzzy linguistic multicriteria decision-making method based on generalized prioritized aggregation operator[J]. The Scientific World Journal, 2014: 1-16. [23] Zhang Z M, Wu C. Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making[J]. Journal of Intelligent, Fuzzy Systems, 2014, 26(5): 2185-2202. [24] Sahu S K, Sahu N, Thakur R S, et al. Hesitant fuzzy linguistic term set based document classification[C]//3rd International Conference on Communication Systems and Network Technologies (CSNT), Gwalior, INDIA, 2013: 586-590. [25] 杨尚洪, 鞠彦兵. 基于对偶犹豫模糊语言变量的多属性决策方法[J]. 运筹与管理, 2015, 24(5): 91-96.Yang S H, Ju Y B. Multi-attribute decision-making method based on dual hesitant fuzzy linguistic variables[J]. Operations Research and Management Science, 2015, 24(5): 91-96. [26] 徐泽水. 不确定多属性决策方法及应用[M]. 北京: 清华大学出版社, 2004. [27] Yager R R. Generalized OWA aggregation operators[J]. Fuzzy Optimization and Decision Making, 2004, 3: 93-107. [28] Fodor J, Marichal J L, Roubens M. Characterization of the ordered weighted averaging operators[J]. IEEE Transactions on Fuzzy Systems, 1995, 3: 236-240. [29] Yager R R, Filev D P. Induced ordered weighted averaging operators[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1999, 29: 141-150. [30] Xu Z S. Intuitionistic fuzzy aggregation operators[J]. IEEE Transactions on Fuzzy Systems, 2007, 15: 1179-1187. [31] Xu Z S, Yager R R. Some geometric aggregation operators based on intuitionistic fuzzy sets[J]. International Journal of General Systems, 2006, 35: 417-433. [32] Liao H C, Xu Z S. Intuitionistic fuzzy hybrid weighted aggregation operators[J]. International Journal of Intelligent Systems, 2014, 29(11): 971-993. [33] Xu Z S, Xia M M. Induced generalized intuitionistic fuzzy operators[J]. Knowledge-Based Systems, 2011, 24: 197-209. [34] Xia M M, Xu Z S. Generalized point operators for aggregating intuitionistic fuzzy information[J]. International Journal of Intelligent Systems, 2010, 25: 1061-1080. [35] Xu Z S, Cai X Q. Recent advances in intuitionistic fuzzy information aggregation[J]. Fuzzy Optimization and Decision Making, 2010, 9: 359-381. [36] Xu Z S, Yager R R. Intuitionistic fuzzy Bonferroni means[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 2011, 41: 568-578. [37] Xia M M, Xu Z S, Zhu B. Generalized intuitionistic fuzzy Bonferroni means[J]. International Journal of Intelligent Systems, 2012, 27: 23-47. [38] Xia M M, Xu Z S. Hesitant fuzzy information aggregation in decision making[J]. International Journal of Approximate Reasoning, 2011, 52: 395-407. [39] Liao H C, Xu Z S. Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment[J]. Journal of Intelligent & Fuzzy Systems, 2014, 26(4): 1601-1617. [40] Liao H C, Xu Z S. Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making[J]. Soft Computing, 2015, 19(9): 2551-2564. [41] Xia M M, Xu Z S, Chen N. Induced aggregation under confidence levels[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2011, 19: 201-227. [42] Zhu B, Xu Z S. Hesitant fuzzy Bonferroni means for multi-criteria decision making[J]. Journal of the Operational Research Society, 2013, 64(12): 1831-1840. [43] Zhang Z M. Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making[J]. Information Sciences, 2013, 234: 150-181. [44] Zhang J L, Qi X W. Research on Multiple attribute decision making under hesitant fuzzy linguistic environment with application to production strategy decision making[J]. Advanced Materials Research, 2013, 753-755: 2829-2836. [45] Zhang Y J, Wang Y Z, Wang J P. Hesitant fuzzy linguistic multiple attribute decision making[C]//16th International Conference on Information Fusion, Istanbul, Turkey, July 9-12, 2013. [46] Lee L W, Chen S M. Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators[J]. Information Sciences, 2015, 294: 513-529. [47] Xu Z S, Chen J. Ordered weighted distance measure[J]. Journal of Systems Science and Systems Engineering, 2008, 17: 432-445. [48] Burillo P, Bustince H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets[J]. Fuzzy Sets and Systems, 1996, 78: 305-316. [49] Szmidt E, Kacprzyk J. Distances between intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 2000, 114: 505-518. [50] Szmidt E, Kacprzyk J. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning[J]. Artificial Intelligence and Soft Computing-ICAISC 2004: Lecture Notes in Computer Science, 2004, 3070: 388-393. [51] Hung W L, Yang M S. Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance[J]. Pattern Recognition Letters, 2004, 25: 1603-1611. [52] Grzegorzewski P. Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric[J]. Fuzzy Sets and Systems, 2004, 148: 319-328. [53] Xu Z S, Chen J. An overview of distance and similarity measures of intuitionistic fuzzy sets[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2008, 16: 529-555. [54] Narukawa Y, Torra V. Non-monotonic fuzzy measures and intuitionistic fuzzy sets[J]. Lecture Notes in Computer Science, 2006, 3885: 150-160. [55] Xu Z S. Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making[J]. Fuzzy Optimization and Decision Making, 2007, 6: 109-121. [56] Xu Z S, Xia M M. Distance and similarity measures for hesitant fuzzy sets[J]. Information Sciences, 2011, 181: 2128-2138. [57] Murthy C A, Pal S K, Dutta-Majumder D. Correlation between two fuzzy membership functions[J]. Fuzzy Sets and Systems, 1985, 17: 23-38. [58] Chaudhuri B B, Bhattacharya A. On correlation between two fuzzy sets[J]. Fuzzy Sets and Systems, 2001, 118: 447-456. [59] Chiang D A, Lin N P. Correlation of fuzzy sets[J]. Fuzzy Sets and Systems, 1999, 102: 221-226. [60] Yu C H. Correlation of fuzzy numbers[J]. Fuzzy Sets and Systems, 1993, 55: 303-307. [61] Liu S T, Kao C. Fuzzy measures for correlation coefficient of fuzzy numbers[J]. Fuzzy Sets and Systems, 2002, 128: 267-275. [62] Hong D H. Fuzzy measures for a correlation coefficient of fuzzy numbers under (the weakest t-norm)-based fuzzy arithmetic operations[J]. Information Sciences, 2006, 176: 150-160. [63] Hung W L. Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets[J]. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2001, 9: 509-516. [64] Szmidt E, Kacprzyk J. Correlation of intuitionistic fuzzy sets[C]//Hüllermeier E, Kruse R, Hoffmann F. IPMU 2010, LNAI 6178, 2010: 169-177. [65] Mitchell H B. A correlation coefficient for intuitionistic fuzzy sets[J]. International Journal of Intelligent Systems, 2004, 19: 483-490. [66] Gerstenkorn T, Manko J. Correlation of intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1991, 44: 39-43. [67] Hong D H, Hwang S Y. Correlation of intuitionistic fuzzy sets in probability spaces[J]. Fuzzy Sets and Systems, 1995, 75: 77-81. [68] Xu Z S. On correlation measures of intuitionistic fuzzy sets[J]. Lecture Notes in Computer Science, 2006, 4224: 16-24. [69] Xu Z S, Xia M M. On distance and correlation measures of hesitant fuzzy information[J]. International Journal of Intelligent Systems, 2011, 26: 410-425. [70] Chen N, Xu Z S, Xia M M. Correlation coefficients of hesitant fuzzy sets and their application to clustering analysis[J]. Applied Mathematical Modelling, 2013, 37: 2197-2211. [71] Liao H C, Xu Z S, Zeng X J. Novel correlation coefficients between hesitant fuzzy sets and their application in decision making[J]. Knowledge-Based Systems, 2015, 82: 115-127. [72] Liao H C, Xu Z S. Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making[J]. Expert Systems with Applications, 2015, 42(12): 5328-5336. [73] Hesamian G, Shams M. Measuring similarity and ordering based on hesitant fuzzy linguistic term sets[J]. Journal of Intelligent & Fuzzy Systems, 2015, 28(2): 983-990. [74] Huang H C, Yang X J. Pairwise comparison and distance measure of hesitant fuzzy linguistic term sets[J]. Mathematical Problems in Engineering, 2014, 2014(3): 1-8. [75] Meng F Y, Chen X H. A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures[J]. Journal of Intelligent & Fuzzy Systems, 2015, 28(4): 1519-1531. [76] Orlovsky S A. Decision-making with a fuzzy preference relation[J]. Fuzzy Sets and Systems, 1978, 1: 155-167. [77] Saaty T L. The analytic hierarchy process[M]. New York, NY: McGraw-Hill, 1980. [78] Xu Z S. Intuitionistic preference relations and their application in group decision making[J]. Information Sciences, 2007, 177: 2363-2379. [79] Liao H C, Xu Z S, Xia M M. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making[J]. International Journal of Information Technology & Decision Making, 2014, 13(1): 47-76. [80] Herrera-Viedma E, Herrera F, Chiclana F, et al. Some issues on consistency of fuzzy preference relations[J]. European Journal of Operational Research, 2004, 154: 98-109. [81] Ma J, Fan Z P, Jiang Y P, et al. A method for repairing the inconsistency of fuzzy preference relations[J]. Fuzzy Sets and Systems, 2006, 157: 20-33. [82] Xu Z S. Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation[J]. International Journal of Approximate Reasoning, 2004, 36: 261-270. [83] Wang Y M, Fan Z P, Hua Z S. A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations[J]. European Journal of Operational Research, 2007, 182: 356-366. [84] Xu Z S, Da Q L. A least deviation method to obtain a priority vector of a fuzzy preference relation[J]. European Journal of Operational Research, 2005, 164: 206-216. [85] Fan Z P, Ma J, Jiang Y P, et al. A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations[J]. European Journal of Operational Research, 2006, 174: 311-321. [86] Lipovetsky S, Michael Conklin W. Robust estimation of priorities in the AHP[J]. European Journal of Operational Research, 2002, 137: 110-122. [87] Xu Z S, Wei C P. A consistency improving method in the analytic hierarchy process[J]. European Journal of Operational Research, 1999, 116: 443-449. [88] Xu Z S, Cai X Q, Szmidt E. Algorithms for estimating missing elements of incomplete intuitionistic preference relations[J]. International Journal of Intelligent Systems, 2011, 21: 787-813. [89] Xu Z S, Cai X Q. Group consensus algorithms based on preference relations[J]. Information Sciences, 2011, 181: 150-162. [90] Xu Z S. A method for estimating criteria weights from intuitionistic preference relations[J]. Fuzzy Information and Engineering, 2009, 1: 79-89. [91] Xu Z S. An error-analysis-based method for the priority of an intuitionistic fuzzy preference relation in decision making[J]. Knowledge-Based Systems, 2012, 33: 173-179. [92] Liao H C, Xu Z S. Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(6): 1669-1681. [93] Herrera-Viedma E, Herrera F, Chiclana F. A consensus model for multiperson decision making with different preference structures[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A, 2002, 32: 394-402. [94] Xu Z S. On consistency of the weighted geometric mean complex judgment matrix in AHP[J]. European Journal of Operational Research, 2002, 126: 683-687. [95] Xu Z S. Compatibility analysis of intuitionistic fuzzy preference relations in group decision making[J]. Group Decision and Negotiation, 2013, 22(3): 463-482. [96] Liao H C, Xu Z S, Zeng X J, et al. Framework of group decision making with intuitionistic fuzzy preference information[J]. IEEE Transactions on Fuzzy Systems, 2015, 23(4): 1211-1227. [97] Liao H C, Xu Z S, Zeng X J, et al. An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations[J]. Information Sciences, 2016, 329: 274-286. [98] Zhu B, Xu Z S. Consistency measures for hesitant fuzzy linguistic preference relations[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(1): 35-45. [99] Liu H B, Cai J F, Jiang L. On improving the additive consistency of the fuzzy preference relations based on comparative linguistic expressions[J]. International Journal of Intelligent Systems, 2014, 29: 544-559. [100] Zhang Z M, Wu C. On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations[J]. Knowledge-Based Systems, 2014, 72: 13-27. [101] Wang H, Xu Z S. Some consistency measures of extended hesitant fuzzy linguistic preference relations[J]. Information Sciences, 2015, 297: 316-331. [102] Dong Y C, Chen X, Herrera F. Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making[J]. Information Sciences, 2015, 297: 95-117. [103] Liu H B, Rodríguez R M. A fuzzy envelope of hesitant fuzzy linguistic term set and its application to multicriteria decision making[J]. Information Sciences, 2014, 258: 220-238. [104] 戴文战, 李昀. 基于梯形模糊隶属函数的复合语言多目标决策[J]. 控制与决策, 2015, 30(12): 2205-2211.Dai W Z, Li Y. Multi-target decision making method of composite linguistic expressions based on trapezoidal fuzzy membership function[J]. Control and Decision, 2015, 30(12): 2205-2211. [105] 杨恶恶, 王坚强, 马超群, 等. 基于云发生算法的犹豫语言多准则决策方法[J]. 控制与决策, 2015, 30(2): 371-374. Yang W E, Wang J Q, Ma C Q, et al. Hesitant linguistic multiple criteria decision making method based on cloud generating algorithm[J]. Control and Decision, 2015, 30(2): 371-374. [106] Chen S M, Hong J A. Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets[J]. Information Sciences, 2014, 286: 63-74. [107] 刘勇, 王成军, 杨威. 基于犹豫模糊语言信息的权重信息部分可知TOPSIS 方法[J]. 工程数学学报, 2016, 32(4): 497-506.Liu Y, Wang C J, Yang W. New hesitant fuzzy linguistic TOPSIS with partly known attribute weight information[J]. Chinese Journal of Engineering Mathematics, 2016, 32(4): 497-506. [108] 彭新东, 杨勇, 宋娟萍, 等. 基于组合权重的犹豫模糊语言决策方法[J]. 计算机工程, 2015, 41(9): 190-193, 198.Peng X D, Yang Y, Song J P, et al. Hesitant fuzzy linguistic decision method based on combination weight[J]. Computer Engineering, 2015, 41(9): 190-193, 198. [109] Beg I, Rashid T. TOPSIS for hesitant fuzzy linguistic term sets[J]. International Journal of Intelligent Systems, 2013, 28: 1162-1171. [110] Wei C P, Ren Z L, Rodriguez R M. A hesitant fuzzy linguistic TODIM method based on a score function[J]. International Journal of Computational Intelligence Systems, 2015, 8(4): 701-712. [111] Liao H C, Xu Z S, Zeng X J. Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2015, 23(5): 1343-1355. [112] Wang J Q, Wang J, Chen Q H, et al. An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets[J]. Information Sciences, 2014, 280: 338-351. [113] 王坚强, 吴佳亭. 基于优序关系的犹豫模糊语言多准则决策方法[J]. 控制与决策, 2015, 30(5): 887-891.Wang J Q, Wu J T. Method for multi-criteria decision-making with hesitant linguistic based on outranking relation[J]. Control and Decision, 2015, 30(5): 887-891. [114] 谭倩云, 冯向前, 张华荣. 基于可能度的犹豫模糊语言PROMETHEE 方法[J]. 统计与决策, 2016, 9: 82-85. [115] Wei C P, Zhao N, Tang X J. A novel linguistic group decision-making model based on extended hesitant fuzzy linguistic term sets[J]. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2015, 23(3): 379-398. [116] Yavuz M, Oztaysi B, Onar S C, et al. Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model[J]. Expert Systems with Applications, 2015, 42: 2835-2848.