广义Pythagorean模糊软集及其在医疗诊断中的应用
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摘要
由于多属性决策问题中属性本身具有不确定性的特性,在不考虑属性本身的不确定性情形下,决策者所做的决策存在准确率偏低的情况,从而影响决策结果的效果。针对此问题,本文首先在Pythagorean模糊软集的基础上,将属性进行量化,引出一种广义Pythagorean模糊软集,并讨论了其基本性质。其次,给出了一种广义Pythagorean模糊软关系并利用Pythagorean模糊软集的得分函数,设计出一种决策失误降低的决策方法。最后,提出一种广义Pythagorean模糊软集的相似测度方法,将该方法应用于医疗诊断,并通过一个实例说明了该方法的有效性。
Due to the uncertainty of attributes in multi-attribute decision making problems, decision makers make decisions with low accuracy without considering itself of the uncertainty of attributes, which affects the effectiveness of the decision result.Given that a degree is attached with the parametrization of fuzzy sets while defining a Pythagorean fuzzy soft set, we first propose a generalized Pythagorean fuzzy soft set and investigate its basic properties. Then a decision method to reduce decision errors is introduced using a generalized Pythagorean fuzzy soft relation and Pythagorean fuzzy soft scoring function. Moreover, an approach to similarity measure of the generalized Pythagorean fuzzy soft set is established and applied to medical diagnosis. Finally, the efficiency of the approach is examined by an example.
Due to the uncertainty of attributes in multi-attribute decision making problems, decision makers make decisions with low accuracy without considering itself of the uncertainty of attributes, which affects the effectiveness of the decision result.Given that a degree is attached with the parametrization of fuzzy sets while defining a Pythagorean fuzzy soft set, we first propose a generalized Pythagorean fuzzy soft set and investigate its basic properties. Then a decision method to reduce decision errors is introduced using a generalized Pythagorean fuzzy soft relation and Pythagorean fuzzy soft scoring function. Moreover, an approach to similarity measure of the generalized Pythagorean fuzzy soft set is established and applied to medical diagnosis. Finally, the efficiency of the approach is examined by an example.
引文
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[6] 刘卫锋,何霞.毕达哥拉斯犹豫模糊集[J].模糊系统与数学,2016,30(4):107～115.
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[11] Yang X B,et al.Combination of interval-valued fuzzy set and soft set[J].Computers and Mathematics with Applications,2009,58(3):521～527.
[12] Alkhazaleh S,Salleh A R,Hassan N.Possibility fuzzy soft set[J].Advances in Decision Sciences,2011,2011:1～18..
[13] 彭新东,杨勇,宋娟萍,蒋芸.毕达哥拉斯模糊软集及其应用[J].计算机工程,2015,41(7):224～229.
[14] Muthukumar P,Sai Sundara Krishnan G.A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis[J].Applied Soft Computing,2016,41:148～156.
[15] Majumdar P,Samanta S K.Generalized fuzzy soft sets[J].Computers and Mathematics with Applications,2010,59(4):1425～1432.
[16] Agarwal M,Biswas K K,Hanmandlu M.Generalized intuitionistic fuzzy soft sets with applications indecision-making[J].Applied Soft Computing,2013,13(8):3552～3566.
[17] Garg H.Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process[J].International Journal of Intelligent Systems,2017,32(6):597～630.
[2] Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy sets and Systems,1986,20(1):87～96.
[3] Yager R R.Pythagorean membership grades in multi-criteria decision making[J].IEEE Transaction on Fuzzy Systems,2014,22(4):958～965.
[4] 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.
[5] Zhang X L.Multicriteria Pythagorean fuzzy decision analysis:A hierarchical QUALIFLEX approach with the closeness index-based ranking methods[J].Information Sciences,2016,330:104～124.
[6] 刘卫锋,何霞.毕达哥拉斯犹豫模糊集[J].模糊系统与数学,2016,30(4):107～115.
[7] Molodtsov D A.Soft set theory-First results[J].Computers and Mathematics with Applications,1999,37(4):19～31.
[8] Maji P K,Biswas R,Roy A R.Fuzzy soft set[J].Journal of Fuzzy Mathematics,2001,9(3):589～602.
[9] Maji P K,Biswas R,Roy A R.Intuitionistic fuzzy soft set[J].Journal of Fuzzy Mathematics,2001,9(3):677～692.
[10] Majumdar P,et al.Generalized fuzzy soft sets[J].Computers and Mathematics with Applications,2010,59(4):1425～1432.
[11] Yang X B,et al.Combination of interval-valued fuzzy set and soft set[J].Computers and Mathematics with Applications,2009,58(3):521～527.
[12] Alkhazaleh S,Salleh A R,Hassan N.Possibility fuzzy soft set[J].Advances in Decision Sciences,2011,2011:1～18..
[13] 彭新东,杨勇,宋娟萍,蒋芸.毕达哥拉斯模糊软集及其应用[J].计算机工程,2015,41(7):224～229.
[14] Muthukumar P,Sai Sundara Krishnan G.A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis[J].Applied Soft Computing,2016,41:148～156.
[15] Majumdar P,Samanta S K.Generalized fuzzy soft sets[J].Computers and Mathematics with Applications,2010,59(4):1425～1432.
[16] Agarwal M,Biswas K K,Hanmandlu M.Generalized intuitionistic fuzzy soft sets with applications indecision-making[J].Applied Soft Computing,2013,13(8):3552～3566.
[17] Garg H.Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process[J].International Journal of Intelligent Systems,2017,32(6):597～630.