基于Heronian平均算子的Pythagorean模糊不确定语言决策方法

doi:10.16381/j.cnki.issn1003-207x.2021.01.021

摘要/Abstract

摘要： 针对评价信息为Pythagorean模糊不确定语言数、属性权重未知且属性间相互影响的多属性决策问题，提出一种基于灰色关联法和Heronian平均算子的决策方法。首先，提出Pythagorean模糊不确定语言Heronian平均（PFULHM）算子和Pythagorean模糊不确定语言几何Heronian平均（PFULGHM）算子，并证明其满足幂等性、单调性、有界性及可交换性。考虑到属性权重之间重要程度的差异，定义了Pythagorean模糊不确定语言加权Heronian平均（PFULWHM）算子和Pythagorean模糊不确定语言加权几何Heronian平均（PFULWGHM）算子。其次，将灰色关联法运用到Pythagorean模糊不确定语言环境中求解属性权重。最后，提出基于PFULWHM算子和PFULWGHM算子的决策方法，并通过算例分析说明本文提出方法的有效性。

关键词: 多属性决策, Pythagorean模糊不确定语言集(PFULS), PFULWHM算子, 灰色关联

Abstract: Multiple attribute decision making method is one of the current hot research subjects and has been applied to a large amount of practical decision problems. With the development of society, owing to the lack of information or decision makers' hesitation, traditional crisp numbers are difficult to deal with this situation. Different types of uncertain numbers are proposed, such as fuzzy number, intuitionistic fuzzy number, linguistic term, Pythagorean fuzzy number. When decision makers evaluate some subjective information, they may feel comfortable to use linguistic terms. However, when they have some hesitation on their opinions with linguistic terms, they may use Pythagorean fuzzy uncertain linguistic numbers. Therefore, solving the multiple attribute decision making problems with Pythagorean fuzzy uncertain linguistic numbers is meaningful. In some cases, attribute weights may be unknown and attributes are interactional. To cope with this issue, a multiple attribute decision making method is proposed based on grey incidence analysis and Heronian mean (HM) operator. Firstly, the Pythagorean fuzzy uncertain linguistic Heronian mean (PFULHM) operator and the Pythagorean fuzzy uncertain linguistic geometric Heronian mean (PFULGHM) operator are proposed and their properties including idempotence, monotonicity, boundedness and commutativity are proved. Considering the attribute weights with different importance, based on the above two operators, the Pythagorean fuzzy uncertain linguistic weighted Heronian mean (PFULWHM) operator and the Pythagorean fuzzy uncertain linguistic weighted geometric Heronian mean (PFULWGHM) operator are defined. Furthermore, a novel grey incidence analysis formula for Pythagorean fuzzy uncertain linguistic numbers, and a new method are proposed to obtain attribute weights using grey incidence analysis. Finally, a decision model based on PFULWHM operator and PFULWGHM operator is constructed and an example is provided to illustrate the effectiveness of the proposed method. By means of the case study, we can draw the advantages of our method: (1)avoiding the loss of information; (2)solving decision making problem effectively with interactional attributes.

Key words: multiple attribute decision making, Pythagorean fuzzy uncertain linguistic set, Pythagorean fuzzy uncertain linguistic weighted Heronian mean operator, grey incidence analysis

中图分类号:

C934

李鹏, 沈志杰. 基于Heronian平均算子的Pythagorean模糊不确定语言决策方法[J]. 中国管理科学, 2021, 29(1): 217-225.

LI Peng, SHEN Zhi-jie. Pythagorean Fuzzy Uncertain Linguistic Decision Making Method Based on Heronian Mean Operator[J]. Chinese Journal of Management Science, 2021, 29(1): 217-225.

参考文献

[1] Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1): 87-96.
[2] Yager R R. Pythagorean fuzzy subsets[C]//IFSA World Congress and NAFIPS Meeting, Edmonton, Canada, June 24-28,2013.
[3] Yager R R. Pythagorean membership grades in multi-criteria decision making[J]. Fuzzy Systems IEEE Transactions on, 2014, 22(4):958-965.
[4] Ilbahar E, Karaşan A, Cebi S, Kahraman C. A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system[J]. Safety Science, 2018, 103:124-136.
[5] Liang Decui, Xu Zeshui, Liu Dun, et al. Method for three-way decisions using ideal TOPSIS solutions at pythagorean fuzzy information[J]. Information Sciences, 2018. DOI: 10.1016/j.ins.2018.01.015.
[6] Chen Tingyu. Remoteness index-based pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis[J]. Information Fusion, 2018,41:129-150.
[7] Mohagheghi V, Mousavi S M, Vahdani B. Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets[J]. Applied Soft Computing, 2017, 61. DOI: 10.1016/j.asoc.2017.08.003.
[8] Zhang Xiaolu. Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods[J]. Information Sciences, 2016, 330:104-124.
[9] Liu Chao, Tang Guolin, Liu Peide. An approach to multi-criteria group decision making with unknown weight information based on Pythagorean fuzzy uncertain linguistic aggregation operators[J]. Mathematical Problems in Engineering, 2017,(5):1-18.
[10] Liu Zhengmin, Liu Peide, Liu Weilong, et al. Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making[J]. Journal of Intelligent & Fuzzy Systems, 2017, 32(3):2779-2790.
[11] Teng Fei, Liu Zhengmin, Liu Peide. Some power maclaurin symmetric mean aggregation operators based on pythagorean fuzzy linguistic numbers and their application to group decision making[J]. International Journal of Intelligent Systems, 2018,33(9):1949-1985.
[12] 刘焕章, 裴道武. H-OWA算子及其在多属性决策中的应用[J]. 浙江理工大学学报, 2012, 29(1):138-142.
[13] 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,(4):174-183.
[14] 于倩,侯福均.犹豫模糊语言Heronian平均算子在多属性决策中的应用[J].运筹与管理,2016,25(2):90-97.
[15] Liu Peide, Liu Zhengmin, Zhang Xin. Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making[J]. Applied Mathematics & Computation, 2014, 230(12):570-586.
[16] Liu Peide, Chen Shyiming. Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers[J]. IEEE Transactions on Cybernetics,2017, 47(9):2514-2530.
[17] Liu P, Liu J, Merigó J M. Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making[J]. Applied Soft Computing, 2017. DOI: 10.1016/j.asoc.2017.10.017.
[18] Yu Dejian. Intuitionistic fuzzy geometric Heronian mean aggregation operators[J]. Applied Soft Computing Journal, 2013, 13(2):1235-1246.
[19] Bai Xiaoping, Liu Yanan. Reliability analysis on civil engineering project based on integrated adaptive simulation annealing and gray correlation method[J]. Frontiers of Structural & Civil Engineering, 2016, 10(4):462-471.
[20] Xu Zeshui. Induced uncertain linguistic OWA operators applied to group decision making[J]. Information Fusion, 2006, 7(2):231-238.
[21] Lin Rui, Zhao Xaiofei, Wang Hongjun, et al. Hesitant fuzzy linguistic aggregation operators and their application to multiple attribute decision making[J]. Journal of Intelligent & Fuzzy Systems, 2014, 36(11):49-63.
[22] 刘政敏, 刘培德, 刘位龙. 基于Pythagorean不确定语言的扩展VIKOR多属性群决策方法[J]. 控制与决策, 2017, 32(12):2145-2152.