区间直觉模糊数环境下基于犹豫度和相关系数的多属性群决策模型研究

doi:10.16381/j.cnki.issn1003-207x.2019.0207

摘要/Abstract

摘要： 多属性群决策问题是当今复杂决策环境下的研究热点，而区间直觉模糊数可以从隶属度、非隶属度和犹豫度三方面描述不确定信息，具有很强的表现能力，因此学界基于区间直觉模糊数对多属性群决策问题进行了大量研究。但是现有研究一方面在处理共识达成问题时所广泛采用的"多数原则"策略会导致某些关键信息或知识被视为冲突意见而被修改或忽视；另一方面基于距离的区间直觉模糊数相似性测算方法忽略了犹豫度的影响，会造成评价信息损失。针对上述不足，提出区间直觉模糊数环境下基于犹豫度和相关系数的多属性群决策模型。首先，通过个体犹豫度和群体犹豫度的提出，保证了决策群体内部信息和知识的有效交流，使关键性决策信息或知识不会通过强制修改或删除的方式失效；其次，采用区间直觉模糊数相关系数测量相似度，避免基于距离测算而可能出现的错误结果；继而，将决策主体权重设置为区间直觉模糊数形式，通过计算不同决策者之间的相对优势值和劣势值进行主观赋值，保证了决策者权重的客观性和真实性；此外，结合TOPSIS和线性规划方法求解得到最优属性权重，保证了属性赋值的精确性，最后，通过具体的应用实例以及与当前学界主要研究成果的比较分析，进一步论证了所提模型的优势和创新性。

关键词: 犹豫度, 相关系数, 区间直觉模糊数, 多属性群决策

Abstract: A novel MAGDM method based on the correlation coefficient and hesitancy degrees under interval-valued intuitionistic fuzzy environmentis proposed. Firstly, the conceptions of individual hesitancy degree and group hesitancy degree are put forward to overcome the restrictions of the methodology of "majority rule". Secondly, the correlation coefficients of IVIFN are utilized to measure the similarity instead of distance functions in order to alleviate the drawbacks that donot consider the parameters of hesitancy. Thirdly, the subjective assignment methods are extended on utilizing the IVIFN values in order to better address the uncertainties in the MAGDM problem. Finally, TOPSIS and LP optimization method are used to calculate the optimal attribute weight, which ensures more optimal and accurate weights. A real-word application example has been presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison has been done with related existing works in order to show the validity of this methodology.

Key words: hesitancy degrees, correlation coefficients, similarity measurement, interval-value intuitionistic fuzzy Numbers, multi-attribute group decision making

中图分类号:

C934

彭友, 刘晓鹤, 孙健博. 区间直觉模糊数环境下基于犹豫度和相关系数的多属性群决策模型研究[J]. 中国管理科学, 2021, 29(8): 229-240.

PENG You, LIU Xiao-he, SUN Jian-bo. Interval-Valued Intuitionistic Fuzzy Multi-attribute Group Decision Making Approach Based on the Hesitancy Degrees and Correlation Coefficient[J]. Chinese Journal of Management Science, 2021, 29(8): 229-240.

参考文献

[1] 袁宇,关涛,闫相斌,等. 基于区间直觉模糊数相关系数的多准则决策模型[J].管理科学学报, 2014, 17(4):11-18. Yuan Yu, Guan Tao, Yan Xiangbin, et al.Multi-criteria decision making model based on interval-valued intuitionistic fuzzy number correlation coefficient[J].Journal of Management Sciences,2014,17(4):11-18.
[2] 赵萌,秦松松,谢佳恒,等. 考虑决策者风险偏好的区间直觉模糊多属性群决策方法[J]. 运筹与管理, 2018, 27(1):7-16. Zhao Meng, Qin Songsong,Xie Jiaheng, et al.Interval-valued intuitionistic fuzzy multi-attribute group decision makingconsidering risk preference of decision maker[J].Operations Research and Management Science,2018,27(1):7-16.
[3] Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and System, 1986(20):87-96.
[4] Atanassov K T,Gargov G. Interval-valued intuitionisticfuzzy sets[J]. Fuzzy Sets and System, 1989(31):343-349.
[5] Wan Shuping, Li Dengfeng.Atanassov's intuitionistic fuzzy programming method for heterogeneous multi-attribute group decision making with atanassov's intuitionistic fuzzy truthdegrees[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(2):300-312.
[6] Wan Shuping,Dong Jiuying. Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees[J]. Information Fusion, 2015, 26(C):49-65.
[7] 刘小弟,朱建军,张世涛,等.基于后悔理论与群体满意度的犹豫模糊随机多属性决策方法[J].中国管理科学, 2017, 25(10):171-178. Liu Xiaodi, Zhu Jianjun, Zhang Shitao, et al.Hesitant fuzzy stochastic multiple attribute decision making method based on regret theory and group satisfaction degree[J]. Chinese Journal of Management Science,2017,25(10):171-178.
[8] 余高锋,李登峰,吴坚,等.考虑决策者损失规避的异质信息多属性变权决策方法[J].中国管理科学, 2018,26(9):141-147. Yu Gaofeng, Li Dengfeng, Wu Jian, et al.Heterogeneous multi-attribute variable weight decision making method considering decision maker's loss aversion[J]. Chinese Journal of Management Science,2018,26(9):141-147.
[9] Yue Zhongliang, Jia Yuying. An application ofsoft computing technique in group decision making under interval-valued intuitionistic fuzzy environment[J]. Applied Soft Computing, 2013, 13(5):2490-2503.
[10] Wan Shuping, Xu Gaili,Dong Jiuying. A novel method for group decision makingwithinterval-valued Atanassov intuitionistic fuzzy preferencerelations[J]. Information Sciences, 2016, 372(1):53-71.
[11] Wan Shuping, Dong Jiuying. A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decisionmaking[J]. Journal of Computerand SystemSciences, 2014, 80(1):237-256.
[12] Zhang Xiaolu, Xu Zeshui.Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision-making[J]. Applied Soft Computing, 2015(26):42-56.
[13] Li Dengfeng, Cheng Chuntian. New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions[J]. Pattern Recognition Letters, 2002, 23(1-3):221-225.
[14] Szmidt E, Kacprzyk J. A new concept of a similarity measure of intuitionistic fuzzy sets and its use in group decision making[C]//Proceedings of the 2nd International Conference Modeling Decisions for Artificial Intelligence, Ukuba, Japan,July 25-27, 2005:272-282.
[15] Wan Shuping, Xu Jun, Dong Jiuying. Aggregating decision information into interval-valued intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making[J]. Knowledge-Based Systems, 2016(113):155-170.
[16] Pankaj G,Mukesh K M,Nishtha G,et al. Multi-attribute groupdecision making based on extended TOPSISmethod under interval-valued intuitionisticfuzzy environment[J]. Applied Soft Computing, 2018(69):554-567.
[17] Wan Shuping,Wang Feng, Dong Jiuying. A group decision-making method considering boththe groupconsensus and multiplicativeconsistency of interval-valuedintuitionistic fuzzy preference relations[J]. Information Sciences, 2018(466):109-128.
[18] 杜元伟,王素素,杨宁,等.考虑专家知识结构的不完备型多属性大群体决策方法[J].中国管理科学, 2017, 25(12):167-178. Du Yuanwei, Wang Susu, Yang Ning, et al.Multipleattribute large-group decision-making method with incomplete information by considering expert's knowledge structure[J]. Chinese Journal of Management Science,2017,25(12):167-178.
[19] Zhou Ligang, Tao Zhifu, Chen Huayou, et al. Continuous interval-valued intuitionisticfuzzy aggregation operators and their applications to group decision making[J]. AppliedMathematical Modeling, 2014, 38(7-8):2190-2205.
[20] 刘卫锋,常娟,杜迎雪.(语言)Heronian平均算子及其决策应用[J].中国管理科学, 2017,25(4):174-183. Liu Weifeng, Chang Juan, Du Xueying.(Linguistic) Heronianmean operators and applications in decision making[J]. Chinese Journal of Management Science,2017,25(4):174-183.
[21] Xu Zeshui. On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions[J]. Journal of Southeast University, 2007(1):139-143.
[22] Ye Jun. Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets[J]. Applied Mathematical Modelling, 2012(36):4466-4472.
[23] Cabrerizo F J, Alonso S, Herrera-Viedma E.A consensus model for group decision-makingproblems withunbalanced fuzzy linguistic information[J]. International Journal of Information Technology & Decision Making, 2009(8):109-131.
[24] Perez I, Cabrerizo F J, Herrera-Viedma E. A mobile decision support system for dynamic group decision-making problems[J].IEEE Transactions on Systems Man and Cybernetics-Part A:Systems and Humans, 2010, 40(6):1244-1256.
[25] Cabrerizo F J, Moreno J M, Perez I, et al. Analyzing consensus approaches in fuzzy group decision making:advantages and drawbacks[J]. Soft Computing, 2010, 14(5):451-463.
[26] Bustince H, Burillo P. Correlation of interval-valued intuitionistic fuzzy set[J]. Fuzzy Sets and System, 1995, 74(2):237-244.
[27] Park D, Kwun Y C, Park J H, et al. Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problem[J]. Mathematical and Computer Modeling, 2009(50):1279-1293.
[28] 陈岩, 金爽, 杨依宁. 区间直觉模糊信息的相容性测度和一致性群决策调整[J]. 数学的实践与认识, 2018, 48(1):231-239. Chen Yan, Jin Shuang, Yang Yining.A consensus adjustment method for group decision making based on compatibility of interval-valued intuitionistic fuzzy information[J]. Mathematics in Practice and Theory,2018, 48(1):231-239.
[29] Ye Jun. Multipleattributegroup decision-making methodswithcompletelyunknown weights in intuitionistic fuzzy setting and interval-valuedintuitionistic fuzzy setting[J].Group Decision and Negotiation,2013, 22(2):173-188.
[30] Wang Weize, Liu Xinwang. An extended LINMAP method for multi-attribute group decision making under interval-valuedintuitionistic fuzzy environment[C]//Proceedings of the 1st International Conference on Information Technology and Quantitative Management, Suzhou, China, May 16-18, 2013:490-497.
[31] Wan Shuping, Wang Feng, Dong Jiuying. A three-phase method for group decisionmakingwith interval-valued intuitionistic fuzzypreference relations[J]. IEEE Transactions on FuzzySystems, 2018, 26(2):998-1010.
[32] Wan Shuping, Wang Feng, Dong Jiuying. Additive consistent interval-valued Atanassov intuitionistic fuzzypreference relation and likelihood comparison algorithm based groupdecision-making[J]. European Journal of OperationalResearch, 2017, 263(2):571-582.
[33] Dong Yucheng, Zhang Hengjie, Herrera-Viedma E.Integrating experts' weights generated dynamically into the consensusreachingprocess and its applications in managingnon-cooperativebehaviors[J]. DecisionSupport Systems, 2016(84):1-15.