Factors Evaluation of Fog-Haze Weather Based on Hesitant Fuzzy Preference Relations
JIN Fei-Fei1,2, NI Zhi-Wei1,2
1.School of Management, Hefei University of Technology, Hefei 230009 2.Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education,Hefei University of Technology, Hefei 230009
Abstract:Aiming at group decision making problems under hesitant fuzzy environment, the concept of hesitant fuzzy preference relation is introduced. The additive consistency, multiplicative consistency and order consistency of the hesitant fuzzy preference relations are defined. A decision-making method of ranking alternative method is established based on the additive consistency and multiplicative consistency to obtain the priority weights. The consistency of hesitant fuzzy preference relations is improved effectively by the proposed method, and thus the improved preference relations can satisfy the need of additive consistency and multiplicative consistency. The optimization models are further developed to get the priority weight vector of the alternatives. Meanwhile, the preference information of the decision maker is retained in the decision process as much as possible, and the model is simplified. Therefore, the application of the hesitant fuzzy theory is greatly extended. The practicability and the effectiveness of the proposed method are verified through the experiment of affecting factors of fog-haze weather.
[1] Guo K H, Li W L. Combination Rule of D-S Evidence Theory Based on the Strategy of Cross Merging between Evidences. Expert Systems with Applications, 2011, 38(10): 13360-13366 [2] Xu Z S. A Survey of Preference Relations. International Journal of General Systems, 2007, 36(2): 179-203 [3] Xu Z S, Wei C P. A Consistency Improving Method in the Analytic Hierarchy Process. European Journal of Operational Research, 1999, 116(2): 443-449 [4] Xu G L, Liu F. An Approach to Group Decision Making Based on Interval Multiplicative and Fuzzy Preference Relations by Using Projection. Applied Mathematical Modelling, 2013, 37(6): 3929-3943 [5] Xu X H, Zhou S H, Zhou Y J, et al. A Multi-attribute Group Decision Method Based on Group Consistency Deviation Entropy of Multiplicative Preference Relation. Control and Decision, 2014, 29(2): 257-262 (in Chinese) (徐选华,周声海,周艳菊,等.基于乘法偏好关系的群一致性偏差熵多属性群决策方法.控制与决策, 2014, 29(2): 257-262) [6] Herrera F, Herrera-Viedma E. Choice Functions and Mechanisms for Linguistic Preference Relations. European Journal of Operational Research, 2000, 120(1): 144-161 [7] Zou L, Zhang Y X, Gao W. Linguistic-Valued Intuitionistic Fuzzy 2-Tuple Representation Model. Pattern Recognition and Artificial Intelligence, 2014, 27(5): 394-402 (in Chinese) (邹 丽,张云霞,高 伟.语言值直觉模糊二元组表示模型.模式识别与人工智能, 2014, 27(5): 394-402) [8] Wang H, Xu Z S. Some Consistency Measures of Extended Hesitant Fuzzy Linguistic Preference Relations. Information Sciences, 2015, 297: 316-331 [9] Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338-353 [10] Turksen I B. Interval Valued Fuzzy Sets Based on Normal Forms. Fuzzy Sets and Systems, 1986, 20(2): 191-210 [11] Atanassov K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96 [12] Wu L, Yang S L, Guo Q. Upper Approximation Reduction in Intuitionistic Fuzzy Object Information Systems with Dominance Relations. Pattern Recognition and Artificial Intelligence, 2014, 27(4): 300-304 (in Chinese) (吴 磊,杨善林,郭 庆.优势关系下直觉模糊目标信息系统的上近似约简.模式识别与人工智能, 2014, 27(4): 300-304) [13] Atanassov K, Gargov G. Interval-Valued Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1989, 31(3): 343-349 [14] Torra V. Hesitant Fuzzy Sets. International Journal of Intelligent Systems, 2010, 25(6): 529-539 [15] Liu X D, Zhu J J, Liu S F. Bidirectional Projection Method with Hesitant Fuzzy Information. Systems Engineering-Theory & Practice, 2014, 34(10): 2637-2644 (in Chinese) (刘小弟,朱建军,刘思峰.犹豫模糊信息下的双向投影决策方法.系统工程理论与实践, 2014, 34(10): 2637-2644) [16] Xu Z S. Consistency of Interval Fuzzy Preference Relations in Group Decision Making. Applied Soft Computing, 2011, 11(5): 3898-3909 [17] Wei G W. Maximizing Deviation Method for Multiple Attribute Decision Making in Intuitionistic Fuzzy Setting. Knowledge-Based Systems, 2008, 21(8): 833-836 [18] Xu Z S. Compatibility Analysis of Intuitionistic Fuzzy Preference Relations in Group Decision Making. Group Decision Making and Negotiation, 2013, 22(3): 463-482 [19] Gong Z W, Li L S, Forrest J, et al. The Optimal Priority Models of the Intuitionistic Fuzzy Preference Relation and Their Application in Selecting Industries with Higher Meteorological Sensitivity. Expert Systems with Applications, 2011, 38(4): 4394-4402 [20] Zhang Y, Ma H X, Liu B H, et al. Group Decision Making with 2-Tuple Intuitionistic Fuzzy Linguistic Preference Relations. Soft Computing, 2012, 16(8): 1439-1446 [21] Paternain D, Jurio A, Barrenechea E, et al. An Alternative to Fuzzy Methods in Decision-Making Problems. Expert Systems with Applications, 2012, 39(9): 7729-7735 [22] Behret H. Group Decision Making with Intuitionistic Fuzzy Prefe-rence Relations. Knowledge-Based Systems, 2014, 70: 33-43 [23] Xia M M, Xu Z S. Hesitant Fuzzy Information Aggregation in Decision Making. International Journal of Approximate Reasoning, 2011, 52(3): 395-407 [24] Xu Z S, Chen J. Some Models for Deriving the Priority Weights from Interval Fuzzy Preference Relations. European Journal of Operational Research, 2008, 184(1): 266-280 [25] Jin S J, Guo J K, Wheeler S, et al. Evaluation of Impacts of Trees on PM2.5 Dispersion in Urban Streets. Atmospheric Environment, 2014, 99: 277-287 [26] Zhu B, Xu Z S. Regression Methods for Hesitant Fuzzy Preference Relations. Technological and Economic Development of Economy, 2014, 19(z1): 5214-5227 [27] Zhu B, Xu Z S, Xu J P. Deriving a Ranking from Hesitant Fuzzy Preference Relations under Group Decision Making. IEEE Trans on Cybernetics, 2014, 44(8): 1328-1337 [28] Zhu B. Studies on Consistency Measure of Hesitant Fuzzy Prefe-rence Relations. Procedia Computer Science, 2013, 17: 457-464