犹豫模糊最优加权Bonferroni几何平均算子及其在多属性决策中的应用
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摘要
Bonferroni几何平均算子是信息集结问题的研究热点,其主要优点是能捕获变量间的关联性。在Bonferroni几何平均算子基础上提出犹豫模糊最优加权Bonferroni几何平均算子、广义犹豫模糊最优加权Bonferroni几何平均算子。新算子能体现变量同余下变量整体间的加权平均、余下变量相互间的加权平均,并具有退化性。验证了新算子具有幂等性、单调性、有界性等优良性质。以此为基础,提出一种犹豫模糊多属性决策方法,并通过算例验证了方法的实用性。
The geometric Bonferroni mean can capture the interrelationship between input arguments, and has been a hot research topic in information aggregation problem. In this paper, based on the geometric Bonferroni mean, we develop the hesitant fuzzy optimized weighted geometric Bonferroni mean operator and the generalized hesitant fuzzy optimized weighted geometric Bonferroni mean operator. New operators reflect the weighted mean between the individual criterion and other criteria, and the internal weighted mean of other criteria. Then we study their desirable properties, such as reducibility, idempotency, monotonicity and boundedness, etc. Finally, based on the new operators, we propose an approach to multiple attribute decision making under the hesitant fuzzy environment, and a practical example is provided to illustrate our results.
The geometric Bonferroni mean can capture the interrelationship between input arguments, and has been a hot research topic in information aggregation problem. In this paper, based on the geometric Bonferroni mean, we develop the hesitant fuzzy optimized weighted geometric Bonferroni mean operator and the generalized hesitant fuzzy optimized weighted geometric Bonferroni mean operator. New operators reflect the weighted mean between the individual criterion and other criteria, and the internal weighted mean of other criteria. Then we study their desirable properties, such as reducibility, idempotency, monotonicity and boundedness, etc. Finally, based on the new operators, we propose an approach to multiple attribute decision making under the hesitant fuzzy environment, and a practical example is provided to illustrate our results.
引文
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[2] Trillas E,García-Honrado I.A Short Reflection on the Word ‘Probable’ in Language[M].The Mathematics of the Uncertain,Berlin:Springer,2018.
[3] Garg H ,Kumar K .An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making[J].Soft Computing,2018,22(15):4959–4970.
[4] Yi Z H,Li H Q.Triangular norm‐based cuts and possibility characteristics of triangular intuitionistic fuzzy numbers for decision making[J].International Journal of Intelligent Systems,2018,33(1):1165-1179.
[5] Zeng W ,Li D ,Yin Q .Weighted Interval-Valued Hesitant Fuzzy Sets and Its Application in Group Decision Making[J].International Journal of Fuzzy Systems,2019,12:1-12.
[6] Liu P ,Liu J .Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making[J].International Journal of Intelligent Systems,2018,33(2):315-347.
[7] Maali F,Campinas S,Decker S.Gagg:A Graph Aggregation Operator[M].The Semantic Web.Latest Advances and New Domains.2015.
[8] Liang D ,Zhang Y ,Xu Z ,et al.Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading[J].International Journal of Intelligent Systems,2018(2):615-633.
[9] Beliakov G,James S,Mordelová J,et al.Generalized Bonferroni mean operators in multi-criteria aggregation[J].Fuzzy Sets and Systems,2010,161(17):2225-2245.
[10] Shi H N ,Wu S H .Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities[J].Journal of Inequalities and Applications,2018,2018(1):1-12.
[11] Zhou W,He J.Intuitionistic fuzzy geometric Bonferroni means and their application in multicriteria decision making[J].International Journal of Intelligent Systems,2012,27(12):995-1019.