基于TOPSIS的语言真值直觉模糊多属性决策
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摘要
针对具有模糊语言值信息的多属性决策问题,结合传统的TOPSIS方法,提出了基于TOPSIS的语言真值直觉模糊多属性决策方法。在语言真值直觉模糊代数的基础上,用语言真值直觉模糊对来表达既有可比的又有不可比的模糊语言值信息,给出了语言真值直觉模糊对之间的归一化距离算法,并讨论了其相关性质。提出了语言真值直觉模糊正、负理想点,通过计算各方案属性值与正、负理想点之间的距离,得到各方案与理想点之间的相对贴近度,并根据相对贴近度的排序结果得到最优方案。实例说明该决策方法的合理性和有效性。
For multi-attribute decision making problems with fuzzy linguistic-valued information,in this paper,we propose a linguistic truth-valued intuitionistic fuzzy multi-attribute decision making approach based on the technique for order performance by similarity to ideal solution( TOPSIS),in combination with the traditional TOPSIS approach. On the basis of linguistic truth-valued intuitionistic fuzzy algebra,in our approach,we used linguistic truth-valued intuitionistic fuzzy pairs to express fuzzy linguistic-valued information that is both comparable and incomparable. We define the normalized distance algorithm for linguistic truth-valued intuitionistic fuzzy pairs and discuss its related properties. We propose linguistic truth-valued intuitionistic fuzzy positive and negative ideal points by calculating the distances between the attribute values of every scheme with positive and negative ideal points to obtain their relative degree of closeness. From the ranking result of the relative degree of closeness,we can determine the best scheme. We give an example to illustrate the reasonability and effectiveness of our proposed decision-making approach.
For multi-attribute decision making problems with fuzzy linguistic-valued information,in this paper,we propose a linguistic truth-valued intuitionistic fuzzy multi-attribute decision making approach based on the technique for order performance by similarity to ideal solution( TOPSIS),in combination with the traditional TOPSIS approach. On the basis of linguistic truth-valued intuitionistic fuzzy algebra,in our approach,we used linguistic truth-valued intuitionistic fuzzy pairs to express fuzzy linguistic-valued information that is both comparable and incomparable. We define the normalized distance algorithm for linguistic truth-valued intuitionistic fuzzy pairs and discuss its related properties. We propose linguistic truth-valued intuitionistic fuzzy positive and negative ideal points by calculating the distances between the attribute values of every scheme with positive and negative ideal points to obtain their relative degree of closeness. From the ranking result of the relative degree of closeness,we can determine the best scheme. We give an example to illustrate the reasonability and effectiveness of our proposed decision-making approach.
引文
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[8]牛强.基于区间直觉集的互联网金融模式择优方法[J].统计与决策,2016(1):66-68.NIU Qiang.Internet financial model optimizing method based on interval intuitionistic sets[J].Statistics and decision,2016(1):66-68.
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[11]邹丽.基于语言真值格蕴涵代数的格值命题逻辑及其归结自动推理研究[D].成都:西南交通大学,2010:1-160.ZOU Li.Studies on lattice-valued propositional logic and its resolution-based automatic reasoning based on linguistic truth-valued lattice implication algebra[D].Cheng Du:Southwest Jiaotong University,2010:1-160.
[12]HWANG C L,YOON K.Multiple attribute decision making:methods and applications[M].New York:SpringerVerlag,1981.
[13]JOSHI D,KUMAR S.Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making[J].Egyptian informatics journal,2014,15(2):97-104.
[14]CHEN S M,CHENG S H,LAN T C.Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values[J].Information sciences,2016,367:279-295.
[15]BISWAS P,PRAMANIK S,GIRI B C.TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment[J].Neural computing and applications,2016,27(3):727-737.
[16]CHEN C T.Extensions of the TOPSIS for group decisionmaking under fuzzy environment[J].Fuzzy sets and systems,2000,114(1):1-9.
[17]MAHDAVI I,HEIDARZADE A,SADEGHPOURGILDEH B,et al.A general fuzzy TOPSIS model in multiple criteria decision making[J].The international journal of advanced manufacturing technology,2009,45(3/4):406-420.
[2]王跃,杨燕,王红军,等.一种基于少量标签的改进迁移模糊聚类[J].智能系统学报,2016,11(3):1-8.WANG Yue,YANG Yan,WANG Hongjun,et al.An improved transfer fuzzy clustering with few labels[J].CAAI transactions on intelligent systems,2016,11(3):310-317.
[3]李滔,王士同.适合大规模数据集的增量式模糊聚类算法[J].智能系统学报,2016,11(2):188-199.LI Tao,WANG Shitong.Incremental fuzzy(c+p)-means clustering for large data[J].CAAI transactions on intelligent systems,2016,11(2):188-199.
[4]ATANASSOV K.Intuionistic fuzzy sets[J].Fuzzy sets and systems,1986,20(1):87-96.
[5]ATANASSOV K.More on intuionistic fuzzy sets[J].Fuzzy sets and systems,1989,33(1):37-45.
[6]SZMIDT E,KACPRZYK J.Entropy for intuitionistic fuzzy sets[J].Fuzzy sets and systems,2011(118):467-477.
[7]WANG Y,WEN X,ZOU L.10-Elements linguistic truthvalued intuitionistic fuzzy first-order logic system[M].Springer Berlin Heidelberg,2015:407-417.
[8]牛强.基于区间直觉集的互联网金融模式择优方法[J].统计与决策,2016(1):66-68.NIU Qiang.Internet financial model optimizing method based on interval intuitionistic sets[J].Statistics and decision,2016(1):66-68.
[9]XU Y,LI X,LIU J,et al.Determination ofα-resolution for lattice-valued first-order logic based on lattice implication algebra[C]//2007 International conference on Intelligent Systems and Knowledge Engineering.2007:1567-1574.
[10]XU Yang,MA Jun.Linguistic truth-valued lattice implication algebra and its properties[C]//The Proceedings of the IMACS Multi-conference on Computational Engineering in Systems Applications.Beijing,2006:1413-1418.
[11]邹丽.基于语言真值格蕴涵代数的格值命题逻辑及其归结自动推理研究[D].成都:西南交通大学,2010:1-160.ZOU Li.Studies on lattice-valued propositional logic and its resolution-based automatic reasoning based on linguistic truth-valued lattice implication algebra[D].Cheng Du:Southwest Jiaotong University,2010:1-160.
[12]HWANG C L,YOON K.Multiple attribute decision making:methods and applications[M].New York:SpringerVerlag,1981.
[13]JOSHI D,KUMAR S.Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making[J].Egyptian informatics journal,2014,15(2):97-104.
[14]CHEN S M,CHENG S H,LAN T C.Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values[J].Information sciences,2016,367:279-295.
[15]BISWAS P,PRAMANIK S,GIRI B C.TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment[J].Neural computing and applications,2016,27(3):727-737.
[16]CHEN C T.Extensions of the TOPSIS for group decisionmaking under fuzzy environment[J].Fuzzy sets and systems,2000,114(1):1-9.
[17]MAHDAVI I,HEIDARZADE A,SADEGHPOURGILDEH B,et al.A general fuzzy TOPSIS model in multiple criteria decision making[J].The international journal of advanced manufacturing technology,2009,45(3/4):406-420.