Vector-Type Two-Tuple Semantic Density Weighted Operator and Its Application

doi:10.12068/j.issn.1005-3026.2020.10.018

Abstract

Abstract: Aiming at the problem of multi-attribute decision making， two-tuple semantic information in the form of vector is integrated and an information aggregation method of vector-type two-tuple semantic density weighted averaging (V-TDWA) operator is proposed. Firstly， the basic idea of the vector-type two-tuple semantic weighted operator and its synthetic operators are introduced， and then their properties are analyzed. Secondly， based on the density of information distribution， the clustering problem of the vector-type two-tuple semantic information is discussed， and a clustering method based on vector similarity is given. Based on the clustering group， the maximum entropy value method is used to solve the density weight of different clustering groups. Finally， an example is given to briefly explain the application of the vector-type two-tuple semantic density aggregation operator.

Key words: multi-attribute decision making, two-tuple semantic information, density weighted operator, vector similarity, density weight

CLC Number:

C934

YI Ping-tao， WANG Lu， LI Wei-wei. Vector-Type Two-Tuple Semantic Density Weighted Operator and Its Application[J]. Journal of Northeastern University Natural Science, 2020, 41(10): 1483-1490.

References

[1]Yager R R.On ordered weighted averaging aggregation operators in multi-criteria decision making［J］.Readings in Fuzzy Sets for Intelligent Systems，1993，18(1):80-87.
[2]Mahmooda T，Liu P，Yec J，et al.Several hybrid aggregation operators for triangular intuitionistic fuzzy set and their application in multi-criteria decision making［J］.Granular Computing，2018，3(2):1-16.
[3]Wan S，Wang F，Dong J.A group decision making method with interval valued fuzzy preference relations based on the geometric consistency［J］.Information Fusion，2018，40:87-100.
[4]Herrera F，Herrera-Viedma E，Martínez L.A fusion approach for managing multi-granularity linguistic term sets in decision making［J］.Fuzzy Sets & Systems，2000，114(1):43-58.
[5]Zhong X Y，Xu X H.Clustering-based method for large group decision making with hesitant fuzzy linguistic information:integrating correlation and consensus［J］.Applied Soft Computing Journal，2020.DOI:10.1016/j.asoc.2019.105973.
[6]Mi X M，Liao H C，Wu X L，et al.Probabilistic linguistic information fusion:a survey on aggregation operators in terms of principles，definitions，classifications，applications，and challenges［J］.International Journal of Intelligent Systems，2020，35(3):529-556.
[7]Peng H G，Wang J Q，Zhang H Y.Multi-criteria outranking method based on probability distribution with probabilistic linguistic information［J］.Computers & Industrial Engineering，2020.DOI:10.1016/j.cie.2020.106318.
[8]Liu P，You X.Probabilistic linguistic TODIM approach for multiple attribute decision making［J］.Granular Computing，2017，2 (4):333-342.
[9]刘春龙，廖朝辉，郑义平.基于二元语义多属性综合决策方法研究与应用［J］.计算机应用研究，2014，31(6):1669-1672，1676.(Liu Chun-long，Liao Zhao-hui，Zheng Yi-ping.Research and application on multi-attribute comprehensive decision-making method based on two-tuple linguistic［J］.Application Research of Computers，2014，31(6):1669-1672，1676.)
[10]余高锋，刘文奇，石梦婷.二元语义粗算子及其语言多属性决策中的应用［J］.计算机工程与应用，2014，50(9):249-253.(Yu Gao-feng，Liu Wen-qi，Shi Meng-ting.Two-tuple linguistic rough operator and application in linguistic multi-attribute decision making［J］.Computer Engineering and Applications，2014，50(9):249-253.)
[11]韩二东，郭鹏，赵静.二元语义处理不同偏好评价信息的群决策方法［J］.计算机工程与应用，2015，51(4):35-40.(Han Er-dong，Guo Peng，Zhao Jing.Group decision making method based on two-tuple linguistic with different forms of preference evaluation information［J］.Computer Engineering and Applications，2015，51(4):35-40.)
[12]张茂竹.两类不确定性二元语义Bonferroni集成算子及其决策应用［D］.合肥:安徽大学，2017.(Zhang Mao-zhu.Two types of uncertain 2-tuple linguistic Bonferroni aggregation operators and their applications to decision making［D］.Hefei:Anhui University，2017.)
[13]葛淑娜，魏翠萍.基于二元语义的犹豫模糊语言决策方法［J］.运筹与管理，2017，26(3):108-114.(Ge Shu-na，Wei Cui-ping.Hesitant fuzzy language decision making method based on 2-tuple［J］.Operations Research and Management Science，2017，26(3):108-114.)
[14]冯向前，刘琦，魏翠萍.基于犹豫模糊二元语义的多属性决策方法［J］.运筹与管理，2018，27(1):17-22.(Feng Xiang-qian，Liu Qi，Wei Cui-ping.Hesitant fuzzy 2-tuple linguistic multiple attribute decision making method［J］.Operations Research and Management Science，2018，27(1):17-22.)
[15]王洪强，张梦情，张英婕，等.基于二元语义与价值工程的PPP项目私人合作伙伴的选择［J］.数学的实践与认识，2018，48(12):59-69.(Wang Hong-qiang，Zhang Meng-qing，Zhang Ying-jie，et al.The choice of the private partner of PPP project based on two tuple semantics and value engineering［J］.Mathematics in Practice and Theory，2018，48(12):59-69.)
[16]Chen Z S，Chin K S，Tsui K L.Constructing the geometric Bonferroni mean from the generalized Bonferroni mean with several extensions to linguistic 2-tuples for decision-making［J］.Applied Soft Computing Journal，2019，78:595-613.
[17]于婷，张发明，何意雄.二元语义信息下的动态激励群体评价方法及应用［J］.计算机工程与应用，2017，53(18):263-270.(Yu Ting，Zhang Fa-ming，He Yi-xiong.Method of dynamic incentive group evaluation based on two-tuple linguistic information and its application［J］.Computer Engineering and Applications，2017，53(18):263-270.)
[18]Liu P D，Chen S M.Multi-attribute group decision making based on intuitionistic 2-tuple linguistic information［J］.Information Sciences，2018，430/431:599-619.
[19]易平涛，郭亚军，张丹宁.密度加权平均中间算子及其在多属性决策中的应用［J］.控制与决策，2007，22(5):515-519.(Yi Ping-tao，Guo Ya-jun，Zhang Dan-ning.Density weighted averaging middle operator and application multi-attribute decision making［J］.Control and Decision，2007，22(5):515-519.)
[20]易平涛，李伟伟，郭亚军.二元语义密度算子及其在多属性决策中的应用［J］.控制与决策，2012，27(5):757-760.(Yi Ping-tao，Li Wei-wei，Guo Ya-jun.Two-tuple linguistic density operator and its application in multi-attribute decision making［J］.Control and Decision，2012，27(5):757-760.)
[21]Herrera F，Martinez L.A 2-tuple fuzzy linguistic representation model for computing with words［J］.IEEE Transactions on Fuzzy Systems，2000，8(6):746-752.
[22]张宇，刘雨东，计钊.向量相似度测度方法［J］.声学技术，2009，28(4):532-536.(Zhang Yu，Liu Yu-dong，Ji Zhao.Vector similarity measurement method［J］.Technical Acoustics，2009，28(4):532-536.)
[15]关守平，房少纯.一种新型的区间-粒子群优化算法［J］.东北大学学报(自然科学版)，2012，33(10):1381-1384.(Guan Shou-ping，Fang Shao-chun.A new interval particle swarm optimization algorithm［J］.Journal of Northeastern University(Natural Science)，2012，33(10):1381-1384.)(上接第1482页)
[10]滕子浩，廖敦明，吴圣川，等.基于XFEM与自适应网格的非均质材料裂纹扩展模拟［J］.固体力学学报，2019，40(3):238-247.(Teng Zi-hao，Liao Dun-ming，Wu Sheng-chuan，et al.Crack growth simulation in heterogeneous material based on XFEM and the adaptively-refined mesh［J］.Chinese Journal of Solid Mechanics，2019，40(3):238-247.)
[11]杨绿峰，徐华，李冉，等.广义参数有限元法计算应力强度因子［J］.工程力学，2009，26(3):48-54.(Yang Lu-feng，Xu Hua，Li Ran，et al.The finite element with generalized coefficients for stress intensity factor［J］.Journal of Engineering Mechanics，2009，26(3):48-54.)
[12]徐华，蓝淞耀，杨绿峰，等.复杂荷载作用下带裂纹薄板SIFs的快速解法［J］.华中科技大学学报(自然科学版)，2019，47(4):73-79.(Xu Hua，Lan Song-yao，Yang Lu-feng，et al.Quick solution to SIFs of thin plate with cracks under complex loads［J］.Journal of Huazhong University of Science and Technology，(Natural Science Edition)，2019，47(4):73-79.)
[13]杨欢欢.功能梯度材料静动态断裂力学参量研究及有限元程序设计［D］.南京:南京理工大学，2015.(Yang Huan-huan.Study on static and dynamic fracture mechanics parameters of functionally graded materials and finite element programming［D］.Nanjing:Nanjing University of Sinence and Technology，2015.)
[14]Erdogan F，Wu B.The surface crack problem for a plate with functionally graded properties［J］.Journal of Applied Mechanics，1997，64(3):449-456.
[15]石久波.非均匀材料的裂纹尖端场［D］.南京:南京航空航天大学，2007.(Shi Jiu-bo.Crack-tip fields for inhomogeneous materials［D］.Nanjing:Nanjing University of Aeronautics and Astronautics，2007.)
[15]关守平，房少纯.一种新型的区间-粒子群优化算法［J］.东北大学学报(自然科学版)，2012，33(10):1381-1384.(Guan Shou-ping，Fang Shao-chun.A new interval particle swarm optimization algorithm［J］.Journal of Northeastern University(Natural Science)，2012，33(10):1381-1384.)