基于新型符号距离的犹豫模糊多属性决策方法
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摘要
研究属性权重完全未知的犹豫模糊决策问题.针对犹豫模糊元中人为添加元素导致的主观性过强问题,提出一种基于新型符号距离的犹豫模糊决策方法.首先,根据犹豫模糊集元素之间的方差以及元素个数定义一种含有对数函数的新型犹豫度,并基于新型犹豫度定义新型犹豫模糊符号距离;然后,基于新型符号距离给出一种属性权重完全未知的数学规划模型得出属性权重,并利用加权符号距离对方案进行排序;最后,通过数值案例表明所提出方法区分度明显并且合理、有效.
This paper investigates the hesitant fuzzy decision making problem with unknown weight information. In order to solve the problem of subjectiveity caused by adding elements into a hesitant fuzzy element(HFE), a new type signed distance-based approach for the hesitant fuzzy multiple attribute decision making is proposed. Firstly, a new type hesitancy index with logarithmic function based on the number and variance of elements in a HFE is presented, and a new type hesitant fuzzy signed distance measure based on the new type hesitancy index is proposed. Then, based on the new type signed distance, a mathematical model is given to determine the attribute weights, and the priorities of alternatives can be obtained. Finally, a numerical example is given to illustrate that the discrimination of the proposed method is reasonable and effective.
This paper investigates the hesitant fuzzy decision making problem with unknown weight information. In order to solve the problem of subjectiveity caused by adding elements into a hesitant fuzzy element(HFE), a new type signed distance-based approach for the hesitant fuzzy multiple attribute decision making is proposed. Firstly, a new type hesitancy index with logarithmic function based on the number and variance of elements in a HFE is presented, and a new type hesitant fuzzy signed distance measure based on the new type hesitancy index is proposed. Then, based on the new type signed distance, a mathematical model is given to determine the attribute weights, and the priorities of alternatives can be obtained. Finally, a numerical example is given to illustrate that the discrimination of the proposed method is reasonable and effective.
引文
[1] Zadeh L A. Fuzzy sets[J]. Information and Control, 1965,8(3):338-353.
[2] Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[3] Yager R R. On the theory of bags[J]. Int J of General Systems, 1986, 13(1):23-37.
[4] Torra V. Hesitant fuzzy sets[J]. Int J of Intelligent Systems, 2010, 25(6):529-539.
[5] Torra V, Narukawa Y. On hesitant fuzzy sets and decision[C]. Proc of the 18th IEEE Int Conf on Fuzzy Systems. Jeju Island, 2009:1378-1382.
[6] 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 withApplications, 2015, 42(5):2835-2848.
[7] Wei G W, Zhao X F, Lin R. Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making[J]. Knowledge-Based Systems, 2013, 46(4):43-53.
[8] Rodriguez R M, Martinez L, Herrera F. A group decision making model dealing with comparative Linguistic expressions based on hesitant fuzzy linguistic term sets[J]. Information Science, 2013, 241(1):28-42.
[9] Beg I, Rashid T. TOPSIS for hesitant fuzzy linguistic term sets[J]. Int J of Intelligent Systems, 2013, 28(12):1162-1171.
[10] Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets[J]. Information Sciences, 2013, 240(10):129-144.
[11] Rodriguez R M, Martinez L, Torra V, et al. Hesitant fuzzy sets:State of the art and future directions[J]. Int J of Intelligent Systems, 2014, 29(6):495-524.
[12] Farhadinia B. A novel method of ranking hesitant fuzzy values for multiple attribute decision making problems[J].Int J of Intelligent Systems, 2013, 28(8):752-767.
[13] Farhadinia B. A series of score functions for hesitant fuzzy sets[J]. Information Sciences, 2014, 277(2):102-110.
[14] Yu D J. Some hesitant fuzzy information aggregation operators based on einstein operational laws[J]. Int J of Intelligent Systems, 2014, 29(4):320-340.
[15]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 G T. Method for multi-criteria decision-making with hesitant fuzzy linguistic based on outranking relation[J]. Control and Decision, 2015, 30(5):887-891.)
[16]阮传扬,杨建辉,韩莉娜,等.考虑可信度和属性优先级的犹豫模糊决策方法[J].运筹与管理, 2016, 25(3):125-131.(Ruan C Y, Yang J H, Han L N, et al. Hesitant fuzzy decision making method with confidence levels and preference relations on attributes[J]. Operations Research and Management Science, 2016, 25(3):125-131.)
[17] Ruan C Y, Yang J H. Hesitant fuzzy multi-attribute decision-making method considering the credibility[J].J of Computational Information Systems, 2015, 11(2):423-432.
[18] Xu Z S, Xia M M. Distance and similarity measures for hesitant fuzzy sets[J]. Information Sciences, 2011,181(11):2128-2138.
[19] Xu Z S. Hesitant fuzzy sets theory[M]. New York:Springer Publishing Company, 2014, 314:1-466.
[20]陈秀明,刘业政.多粒度犹豫模糊语言环境下未知权重的多属性群推荐方法[J].控制与决策, 2016, 31(9):1631-1637.(Chen X M, Liu Y Z. Method of group recommender systems with unknown attribute weights in a multi-granular hesitant fuzzy linguistic term environment[J]. Control and Decision, 2016, 31(9):1631-1637.)
[21] Li D Q, Zeng W Y, Zhao Y B. Note on distance measure of hesitant fuzzy sets[J]. Information Sciences, 2015,321(11):103-115.
[22] Hu J H, Zhang X L. Hesitant fuzzy information measures and their applications in multi-criteria decision making[J]. Int J of Systems Science, 2016, 47(1):62-76.
[23] Zhang X L, Xu Z S. Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis[J]. Expert Systems with Applications, 2015, 42(2):873-884.
[24]林松,刘小弟,朱建军,等.基于改进符号距离的权重未知犹豫模糊决策方法[J].控制与决策, 2018, 33(1):186-192.(Lin S, Liu X D, Zhu J J, et al. Hesitant fuzzy decision making method with unknown weight information based on an improved signed distance[J]. Control and Decision,2018, 33(1):186-192.)
[25] 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(7):115-127.
[26] Xu Z S, Zhang X L. Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J]. Knowledge-Based Systems, 2013,52(1):53-64.
[27] Liao H C, Xu Z S, Xia M M. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making[J]. Int J of Information Technology&Decision Making, 2014, 13(1):47-76.
[2] Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[3] Yager R R. On the theory of bags[J]. Int J of General Systems, 1986, 13(1):23-37.
[4] Torra V. Hesitant fuzzy sets[J]. Int J of Intelligent Systems, 2010, 25(6):529-539.
[5] Torra V, Narukawa Y. On hesitant fuzzy sets and decision[C]. Proc of the 18th IEEE Int Conf on Fuzzy Systems. Jeju Island, 2009:1378-1382.
[6] 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 withApplications, 2015, 42(5):2835-2848.
[7] Wei G W, Zhao X F, Lin R. Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making[J]. Knowledge-Based Systems, 2013, 46(4):43-53.
[8] Rodriguez R M, Martinez L, Herrera F. A group decision making model dealing with comparative Linguistic expressions based on hesitant fuzzy linguistic term sets[J]. Information Science, 2013, 241(1):28-42.
[9] Beg I, Rashid T. TOPSIS for hesitant fuzzy linguistic term sets[J]. Int J of Intelligent Systems, 2013, 28(12):1162-1171.
[10] Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets[J]. Information Sciences, 2013, 240(10):129-144.
[11] Rodriguez R M, Martinez L, Torra V, et al. Hesitant fuzzy sets:State of the art and future directions[J]. Int J of Intelligent Systems, 2014, 29(6):495-524.
[12] Farhadinia B. A novel method of ranking hesitant fuzzy values for multiple attribute decision making problems[J].Int J of Intelligent Systems, 2013, 28(8):752-767.
[13] Farhadinia B. A series of score functions for hesitant fuzzy sets[J]. Information Sciences, 2014, 277(2):102-110.
[14] Yu D J. Some hesitant fuzzy information aggregation operators based on einstein operational laws[J]. Int J of Intelligent Systems, 2014, 29(4):320-340.
[15]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 G T. Method for multi-criteria decision-making with hesitant fuzzy linguistic based on outranking relation[J]. Control and Decision, 2015, 30(5):887-891.)
[16]阮传扬,杨建辉,韩莉娜,等.考虑可信度和属性优先级的犹豫模糊决策方法[J].运筹与管理, 2016, 25(3):125-131.(Ruan C Y, Yang J H, Han L N, et al. Hesitant fuzzy decision making method with confidence levels and preference relations on attributes[J]. Operations Research and Management Science, 2016, 25(3):125-131.)
[17] Ruan C Y, Yang J H. Hesitant fuzzy multi-attribute decision-making method considering the credibility[J].J of Computational Information Systems, 2015, 11(2):423-432.
[18] Xu Z S, Xia M M. Distance and similarity measures for hesitant fuzzy sets[J]. Information Sciences, 2011,181(11):2128-2138.
[19] Xu Z S. Hesitant fuzzy sets theory[M]. New York:Springer Publishing Company, 2014, 314:1-466.
[20]陈秀明,刘业政.多粒度犹豫模糊语言环境下未知权重的多属性群推荐方法[J].控制与决策, 2016, 31(9):1631-1637.(Chen X M, Liu Y Z. Method of group recommender systems with unknown attribute weights in a multi-granular hesitant fuzzy linguistic term environment[J]. Control and Decision, 2016, 31(9):1631-1637.)
[21] Li D Q, Zeng W Y, Zhao Y B. Note on distance measure of hesitant fuzzy sets[J]. Information Sciences, 2015,321(11):103-115.
[22] Hu J H, Zhang X L. Hesitant fuzzy information measures and their applications in multi-criteria decision making[J]. Int J of Systems Science, 2016, 47(1):62-76.
[23] Zhang X L, Xu Z S. Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis[J]. Expert Systems with Applications, 2015, 42(2):873-884.
[24]林松,刘小弟,朱建军,等.基于改进符号距离的权重未知犹豫模糊决策方法[J].控制与决策, 2018, 33(1):186-192.(Lin S, Liu X D, Zhu J J, et al. Hesitant fuzzy decision making method with unknown weight information based on an improved signed distance[J]. Control and Decision,2018, 33(1):186-192.)
[25] 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(7):115-127.
[26] Xu Z S, Zhang X L. Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information[J]. Knowledge-Based Systems, 2013,52(1):53-64.
[27] Liao H C, Xu Z S, Xia M M. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making[J]. Int J of Information Technology&Decision Making, 2014, 13(1):47-76.