共识条件下最小最大妥协的直觉模糊数集结方法研究

doi:10.16381/j.cnki.issn1003-207x.2018.0976

摘要/Abstract

摘要： 直觉模糊集（IFS）理论是描述广泛模糊事物的重要工具。为减小决策过程中个体偏好值与群体偏好值的差异，协调个体与群体间矛盾，提升决策结果的执行效率，本文提出最小化最大妥协度（Minimize maximum compromise）的决策准则。给出直觉模糊环境下的，个体偏好值的集结算法及决策方法，并分别考虑了有无共识条件、有无决策主体权重的三类决策情景。最后给出算例，验证本文方法的有效性，结果表明，相较于I-IFOWG算子，本文方法能够有效降低群体决策中个体的妥协程度。

关键词: 群决策, 直觉模糊数, 集结, 最小最大妥协

Abstract: The intuitionistic fuzzy set (IFS) theory is an important tool for describing a wide range of fuzzy things and is widely used in group decision making theory. In this study, consensus decision making under intuitionistic fuzzy set is imvestigated, trying to minimize the maximum gap between individual preference and group preference. This investigation has practical meaning: A smaller gap means individuals are more satisfied with final decision, and the work efficiency will be higher when implement the decision. In this article, first, we define the concept of compromise degree and put forward three decision scenarios, which includes decision making without consensus constraints, with consensus constraints, and with weight. Second, a novel algorithm is developed to minimize the maximal compromise degree when aggregate individual decision information. At last, a numerical example is given to prove the validation of our algorithm and group decision method. The example shows, compared with Guiwu Wei's I-IFOWG operator, the compromise degree by our method is much lower. The study is expected to support intuitionistic fuzzy theory and consensus decision making theory.

Key words: group decision making, intuitionistic fuzzy number, aggregation, minimize maximum compromise

中图分类号:

C934

李磊, 张曙阳. 共识条件下最小最大妥协的直觉模糊数集结方法研究[J]. 中国管理科学, 2021, 29(2): 168-176.

LI Lei, ZHANG Shu-yang. Aggregation Method of Intuitionistic Fuzzy Numbers with Minimized Maximal Compromise under Consensus Condition[J]. Chinese Journal of Management Science, 2021, 29(2): 168-176.

参考文献

[1] Zadeh L A. Fuzzy sets[J]. Information & Control, 1965, 8(3):338-353.
[2] Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets & Systems, 1986, 20(1):87-96.
[3] Atanassov K T. More on intuitionistic fuzzy sets[J]. Fuzzy Sets & Systems, 1989, 33(1):37-45.
[4] Burillo P, Bustince H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets[J]. Fuzzy Sets & Systems, 1996, 78(3):305-316.
[5] 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.
[6] Szmidt E, Kacprzyk J. Distances between intuitionistic fuzzy sets[J]. Fuzzy Sets & Systems, 2000, 114(3):505-518.
[7] De S K, Biswas R, Roy A R. An application of intuitionistic fuzzy sets in medical diagnosis[J]. Fuzzy Sets & Systems, 2001, 117(2):209-213.
[8] Chen S M, Tan J M. Handling multi-criteria fuzzy decision-making problems based on vague set theory[J]. Fuzzy Sets & Systems, 1994, 67(2):163-172.
[9] Hong D H, Choi C H. Multi-criteria fuzzy decision-making problems based on vague set theory[J]. Fuzzy sets and systems, 2000, 114(1):103-113.
[10] Yager R R. On ordered weighted averaging aggregation operators in multi-criteria decision making[J]. Readings in Fuzzy Sets for Intelligent Systems, 1988, 18(1):80-87.
[11] Xu Zeshui, Ronald R. Yager. Some geometric aggregation operators based on intuitionistic fuzzy sets[J]. International Journal of General Systems, 2006, 35(4):417-433.
[12] Zeng Shouzhen, Su Weihua, Zhang Chonghui. Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making[J]. Technological & Economic Development of Economy, 2016, 22(2):177-193.
[13] Pan Tiejun, Zheng Leina, Zeng Shouzhen, et al. Induced generalized intuitionistic fuzzy aggregation distance operators and their application to decision making[C]//International Conference on Applications and Techniques in Cyber Security and Intelligence. Edizioni della Normale, Cham, 2017:493-500.
[14] Wei Jiang, Wei Boya, Liu Xiang, et al. Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making[J]. International Journal of Intelligent Systems, 2018, 33(1):49-67.
[15] Joshi R, Kumar S. A novel fuzzy decision-making method using entropy weights-based correlation coefficients under intuitionistic fuzzy environment[J]. International Journal of Fuzzy Systems, 2019, 21(1):232-242.
[16] 刘卫锋, 常娟, 何霞. 毕达哥拉斯模糊Hamacher集成算子及其决策应用[J]. 系统工程理论与实践, 2018, 38(6):1566-1574.
[17] 施明华, 肖庆宪. 直觉模糊幂Heronian平均算子及其在多属性决策中的应用[J]. 系统工程理论与实践, 2018, 38(4):971-982.
[18] Tao Zhifu, Han Bing, Chen Huayou. On intuitionistic fuzzy copula aggregation operators in multiple-attribute decision making[J]. Cognitive Computation, 2018, (1):1-15.
[19] Zeng Shouzhen, Llopis-Albert C, Zhang Yunhua. A novel induced aggregation method for intuitionistic fuzzy set and its application in multiple attribute group decision making[J]. International Journal of Intelligent Systems, 2018, 33(11):2175-2188.
[20] Qiu Junda, Li Lei. A new approach for multiple attribute group decision making with interval-valued intuitionistic fuzzy information[J]. Applied Soft Computing, 2017, (61):111-121.
[21] 刘东海, 刘原园, 陈晓红. 基于犹豫直觉模糊语言集均值-标准差偏好距离的多属性决策研究[J]. 中国管理科学, 2019, 27(1):177-186.
[22] 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):174-181.
[23] 曾守桢, 穆志民. 基于混合加权距离的毕达哥拉斯模糊TOPSIS多属性决策方法研究[J]. 中国管理科学, 2019, (3):198-205.
[24] Ngan R T, Son L H, Cuong B C, et al. H-max distance measure of intuitionistic fuzzy sets in decision making[J]. Applied Soft Computing, 2018:393-425.
[25] Yager R R, Kacprzyk J. The ordered weighted averaging operators:theory and applications[M] Kluwer Academic Publishers, Boston, 1997.
[26] Szmidt E, Kacprzyk J. Distances between intuitionistic fuzzy sets[J]. Fuzzy Sets & Systems, 2000, 114(3):505-518.
[27] Wei Guiwu. Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making[J]. Applied Soft Computing, 2010, 10(2):423-431.