Abstract:Defining distance measure and calculating attribute weight are two key points of multi-attribute decision making based on hesitant fuzzy distance. During the process of defining distance measure of two hesitant fuzzy numbers, the original meaning of the shorter hesitant fuzzy number is changed when some same elements are added to it. In this paper, two hesitant fuzzy numbers are extended to the same length simultaneously. Then, the conflict analysis model of hesitant fuzzy information system is established according to the conflict analysis theory by Pawlak, and the method for calculating attribute weights based on the degree of conflict is proposed. Finally, the specific method of multi-attribute decision-making under hesitant fuzzy information systems is presented. The effectiveness and the feasibility of the proposed method are exemplified on the basis of a case study on a enterprise development plan.
[1] ZADEL L A. Fuzzy Sets. Information Control, 1965, 8(3): 338-365. [2] TORRA V. Hesitant Fuzzy Sets. International Journal of Intelligent Systems, 2010, 25(6): 529-539. [3] XIA M M, XU Z S. Hesitant Fuzzy Information Aggregation in Decision Making. International Journal of Approximate Reasoning, 2011, 52(3): 395-407. [4] XU Z S, XIA M M. On Distance and Correlation Measures of Hesitant Fuzzy Information. International Journal of Intelligent Systems, 2011, 26(5): 410-425. [5] XU Z S, XIA M M. Distance and Similarity Measures for Hesitant Fuzzy Sets. Information Sciences, 2011, 181(11): 2128-2138. [6] FARHADINIA B. Information Measures for Hesitant Fuzzy Sets and Interval-Valued Hesitant Fuzzy Sets. Information Sciences, 2013, 240: 129-144. [7] LI D Q, ZENG W Y, LI J H. New Distance and Similarity Measures on Hesitant Fuzzy Sets and Their Applications in Multiple Criteria Decision Making. Engineering Applications of Artificial Intelligence, 2014, 40: 11-16. [8] LI D Q, ZENG W Y, ZHAO Y B. Note on Distance Measure of Hesitant Fuzzy Sets. Information Sciences, 2015, 321: 103-115. [9] ZHANG X L, XU Z S. Hesitant Fuzzy QUALIFLEX Approach with a Signed Distance-Based Comparison Method for Multiple Criteria Decision Analysis. Expert Systems with Applications, 2015, 42(2): 873-884. [10] FARHADINIA B, XU Z S. A Novel Distance-Based Multiple Attribute Decision-Making with Hesitant Fuzzy Sets. Soft Computing, 2020, 24(7): 5005-5017. [11] WEI G W, ZHAO X F, LIN R. Some Hesitant Interval-Valued Fuzzy Aggregation Operators and Their Applications to Multiple Attribute Decision Making. Knowledge-Based Systems, 2013, 46: 43-53. [12] QIAO J S. Hesitant Relations: Novel Properties and Applications in Three-Way Decisions. Information Sciences, 2019, 497: 165-188. [13] WEI C P, ZHAO N, TANG X J. Operators and Comparisons of Hesitant Fuzzy Linguistic Term Sets. IEEE Transactions on Fuzzy Systems, 2014, 22(3): 575-585. [14] LIAO H C, GOU X J, XU Z S, et al. Hesitancy Degree-Based Correlation Measures for Hesitant Fuzzy Linguistic Term Sets and Their Applications in Multiple Criteria Decision Making. Information Sciences, 2020, 508: 275-292. [15] 朱 丽,朱传喜,张小芝.基于粗糙集的犹豫模糊多属性决策方法.控制与决策, 2014, 29(7): 1335-1339. (ZHU L, ZHU C X, ZHANG X Z. Method for Hesitant Fuzzy Multi-attribute Decision Making Based on Rough Sets. Control and Decision, 2014, 29(7): 1335-1339.) [16] 刘小弟,朱建军,张世涛,等.一种新犹豫模糊符号距离及其应用.系统工程理论与实践, 2019, 39(2): 442-450. (LIU X D, ZHU J J, ZHANG S T, et al. A Novel Hesitant Fuzzy Signed Distance and Its Application. Systems Engineering-Theory & Practice, 2019, 39(2): 442-450.) [17] XU Z S, ZHANG X L. Hesitant Fuzzy Multi-attribute Decision Making Based on TOPSIS with Incomplete Weight Information. Knowledge-Based Systems, 2013, 52: 53-64. [18] PAWLAK Z. An Inquiry into Anatomy of Conflicts. Information Sciences, 1998, 109(1/2/3/4): 65-78. [19] 高俊山,谷冬元,徐章艳.一种新的基于粗糙集理论的冲突分析模型.管理学报, 2008, 5(6): 813-818. (GAO J S, GU D Y, XU Z Y. A New Conflict Analysis Model Based on Rough Set Theory. Chinese Journal of Management, 2008, 5(6): 813- 818.) [20] 高俊山,谷冬元,徐章艳,等.一个Pawlak粗糙集冲突分析模型的改进.中国管理科学, 2008, 16(2): 150-156. (GAO J S, GU D Y, XU Z Y, et al. New Conflict Analysis Model Based on Rough Set Theory. Chinese Journal of Management Science, 2008, 16(2): 150-156.) [21] SUN B Z, MA W M. Rough Approximation of a Preference Relation by Multi-decision Dominance for a Multi-agent Conflict Analysis Problem. Information Sciences, 2015, 315: 39-53. [22] LANG G M, MIAO D Q, CAI M J. Three-Way Decision Approaches to Conflict Analysis Using Decision-Theoretic Rough Set Theory. Information Sciences, 2017, 406/407: 185-207. [23] YAO Y Y. Three-Way Conflict Analysis: Reformulations and Extensions of the Pawlak Model. Knowledge-Based Systems, 2019, 180: 26-37. [24] 李小南,祁建军,孙秉珍,等.三支决策理论与方法.北京:科学出版社, 2019. (LI X N, QI J J, SUN B Z, et al. Three-Way Decision Theory and Methods. Beijing, China: Science Press, 2019.) [25] FARHADINIA B. Hesitant Fuzzy Set Lexicographical Ordering and Its Application to Multi-attribute Decision Making. Information Sciences, 2016, 327: 233-245. [26] ZHANG X L, XU Z S. The TODIM Analysis Approach Based on Novel Measure Functions under Hesitant Fuzzy Environment. Knowledge-Based Systems, 2014, 61: 48-58.