基于相对熵的区间Pythagorean模糊多属性AQM决策方法及其应用
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摘要
针对决策信息为区间Pythagorean模糊数,属性权重不完全确定的多属性决策问题,提出了一种基于相对熵的AQM决策方法。首先,提出区间Pythagorean模糊数的相对熵,计算了各方案与区间Pythagorean模糊正理想方案和负理想方案间的相对熵,据此构建了基于方案相对满意度最大的非线性规划属性权重确定模型;其次,针对每个属性,利用新的区间Pythagorean模糊数得分函数计算方案的0-1优先关系矩阵,依据AQM方法对所有0-1优先关系矩阵进行融合得到合成0-1优先关系矩阵,并确定了方案的综合度,由此获得方案的排序。最后,以软件开发项目的选取为实例说明了该方法的可行性和有效性。
For the problem of multi-attribute decision making,in which the attribute values are the intervalvalued Pythagorean fuzzy numbers and the information about criteria weights is incomplete,a decision making method is proposed based on relative entropy and AQM method. Firstly,the relative entropy of interval-valued Pythagorean fuzzy numbers is defined,the relative entropy between alternative and ideal( critical) alternative is obtained,and an optimization model is established to obtain the criteria weights. Then,the 0-1 precedence relationship matrix for each alternative on each attribute is given by using a new score function,and according to AQM method,the combination 0-1 precedence relationship matrix of alternatives is composed. Furthermore,the comprehensive scale is obtained and a ranking of alternatives can be determined by using the comprehensive scale. Finally,the method is used to select a software development project so as to verify the effectiveness and feasibility.
For the problem of multi-attribute decision making,in which the attribute values are the intervalvalued Pythagorean fuzzy numbers and the information about criteria weights is incomplete,a decision making method is proposed based on relative entropy and AQM method. Firstly,the relative entropy of interval-valued Pythagorean fuzzy numbers is defined,the relative entropy between alternative and ideal( critical) alternative is obtained,and an optimization model is established to obtain the criteria weights. Then,the 0-1 precedence relationship matrix for each alternative on each attribute is given by using a new score function,and according to AQM method,the combination 0-1 precedence relationship matrix of alternatives is composed. Furthermore,the comprehensive scale is obtained and a ranking of alternatives can be determined by using the comprehensive scale. Finally,the method is used to select a software development project so as to verify the effectiveness and feasibility.
引文
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[17] Zhang X L. Multicriteria Pythagorean fuzzy decision analysis:a hierarchical QUALIFLEX approach with the closeness index-based ranking methods[J]. Information Sciences,2016,330(2):104-124.
[18]刘卫锋,常娟,何霞.广义毕达哥拉斯模糊集成算子及其决策应用[J].控制与决策,2016,31(12):2280-2286.
[19] Peng X D,Yang Y. Fundamental properties of intervalvalued pythagorean fuzzy aggregation operators[J].International Journal of Intelligent Systems,2015,31(5):444-487.
[20] Liang W,Zhang X L,Liu M F. The maximizing deviation method based on interval-valued pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis[J]. Discrete Dynamics in Nature and Society,Article ID 746572,2015,15pp.
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[22] Gou X J,Xu Z S,Liao H C. Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information[J]. Information Sciences,2016,357(8):144-160.
[2]赵萌,邱菀华,刘北上.基于相对熵的多属性决策排序方法[J].控制与决策,2010,25(7):1098-1100.
[3] Navarrete N,Fukushima M,Mine H. A new ranking method based on relative position estimate and its extensions[J]. IEEE Transactions on Systems Man&Cybernetics,1979,9(11):681-689.
[4] Zadeh L A. Fuzzy sets[J]. information and control,1965,8(3):338-356.
[5] Atanassov K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1986,20(1):87-96.
[6] Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1989,31(3):343-349.
[7]王坚强.信息不完全确定的多准则区间直觉模糊决策方法[J].控制与决策,2006,21(11):1253-1256.
[8]徐泽水.区间直觉模糊信息的集成方法及其在决策中的应用[J].控制与决策,2007,22(2):215-219.
[9]卫贵武.一种区间直觉模糊数多属性决策的TOPSIS方法[J].统计与决策,2008,1:149-150.
[10]高建伟,刘慧晖,谷云东.基于前景理论的区间直觉模糊多准则决策方法[J].系统工程理论与实践,2014,34(12):3175-3181.
[11]邵良杉,赵琳琳.区间直觉模糊信息下的双向投影决策模型[J].控制与决策,2016,31(3):571-576.
[12] Yager R R. Pythagorean membership grades in multicriteria decision making[J]. IEEE Transactions on Fuzzy Systems,2014,22(4):958-965.
[13] Yager R R,Abbasov A M. Pythagorean membership grades,complex numbers,and decision making[J].International Journal of Intelligent Systems,2014,28(5):436-452.
[14] Zhang X L,Xu Z S. Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets[J].International Journal of Intelligent Systems,2014,29(12):1061-1078.
[15] Garg H. A new generalized pythagorean fuzzy information aggregation using einstein operations and its application to decision making[J]. International Journal of Intelligent Systems,2016,3(2):161-172.
[16] Ren P J,Xu Z S,Gou X J. Pythagorean fuzzy TODIM approach to multi-criteria decision making[J]. Applied Soft Computing,2016,42(3):246-259.
[17] Zhang X L. Multicriteria Pythagorean fuzzy decision analysis:a hierarchical QUALIFLEX approach with the closeness index-based ranking methods[J]. Information Sciences,2016,330(2):104-124.
[18]刘卫锋,常娟,何霞.广义毕达哥拉斯模糊集成算子及其决策应用[J].控制与决策,2016,31(12):2280-2286.
[19] Peng X D,Yang Y. Fundamental properties of intervalvalued pythagorean fuzzy aggregation operators[J].International Journal of Intelligent Systems,2015,31(5):444-487.
[20] Liang W,Zhang X L,Liu M F. The maximizing deviation method based on interval-valued pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis[J]. Discrete Dynamics in Nature and Society,Article ID 746572,2015,15pp.
[21] Cover T M,Thomas Joy A. Elements of information theory[M]. New York:John Wiley and Sons,2006.
[22] Gou X J,Xu Z S,Liao H C. Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information[J]. Information Sciences,2016,357(8):144-160.