Pythagorean fuzzy BM operators with reducibility and applications in decision making

LIU Weifeng, DU Yingxue, LIU Wanli

Systems Engineering - Theory & Practice ›› 2020, Vol. 40 ›› Issue (2) : 499-509.

PDF(502 KB)
中国科学院数学与系统科学研究院期刊网
PDF(502 KB)
Systems Engineering - Theory & Practice ›› 2020, Vol. 40 ›› Issue (2) : 499-509. DOI: 10.12011/1000-6788-2018-0997-11

Pythagorean fuzzy BM operators with reducibility and applications in decision making

  • LIU Weifeng, DU Yingxue, LIU Wanli
Author information +
History +

Abstract

Reducibility is an important property of aggregation operator. Aiming at Pythagorean fuzzy weighted Bonferroni mean (BM) operator without reducibility in related references, the Pythagorean fuzzy reducible weighted BM operators and their applications in decision making are discussed. Pythagorean fuzzy reducible weighted BM operator (PFRWBM) is defined, and the mathematical expression of this operator is obtained by derivation and some properties of this operator are discussed. Almost immediately generalized Pythagorean fuzzy reducible weighted BM operator (GPFRWBM) is proposed, and its mathematical expression is given and some properties are also discussed. Then, Pythagorean fuzzy reducible weighted BGM operator (PFRWBGM) and generalized Pythagorean fuzzy reducible weighted BGM operator (GPFRWBGM) are also defined, and their mathematical expression are given and some properties of these operators are discussed. Finally, an approach to multiple attribute decision making based on PFRWBM operators is proposed, and a practical example is given to illustrate our results.

Key words

Pythagorean fuzzy set / Bonferroni mean operator / reducibility / aggregation operator / decision making

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations
LIU Weifeng , DU Yingxue , LIU Wanli. Pythagorean fuzzy BM operators with reducibility and applications in decision making. Systems Engineering - Theory & Practice, 2020, 40(2): 499-509 https://doi.org/10.12011/1000-6788-2018-0997-11

References

[1] Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[3] Atanassov K. New operators defined over the intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1994, 61(2):137-142.
[4] De S K, Biswas R, Roy A R. Some operators on the intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 2000, 114(3):477-484.
[5] Xu Z S. Intuitionistic fuzzy aggregation operators[J]. IEEE Transactions on Fuzzy Systems, 2007, 15(6):1179-1187.
[6] Xu Z S, Yager R R. Some geometric aggregation operators based on intuitionistic fuzzy sets[J]. International Journal of General Systems, 2006, 35(4):417-433.
[7] Zhao H, Xu Z S, Ni M F, et al. Generalized aggregation operators for intuitionistic fuzzy sets[J]. International Journal of intelligent Systems, 2010, 25(1):1-30.
[8] Tan C Q, Chen X H. Intuitionistic fuzzy Choquet integral operators for multi-criteria decision making[J]. Expert Systems with Applications, 2010, 37(7):149-157.
[9] Xu Z S, Yager R R. Intuitionistic fuzzy Bonferroni means[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics, 2011, 41(2):568-578.
[10] Xia M M, Xu Z S, Zhu B. Generalized intuitionistic fuzzy Bonferroni means[J]. International Journal of Intelligent Systems, 2012, 27(1):23-47.
[11] Zhou W, He J M. Intuitionistic fuzzy Geometric Bonferroni means and their application in multicriteria decision making[J]. International Journal of Intelligent Systems, 2012, 27(12):995-1019.
[12] Zhou W, He J M. Intuitionistic fuzzy normalized weighted Bonferroni means and its application in multicriteria decision making[J]. Journal of Applied Mathematics, 2012, 2012:1-22. doi:10.1155/2012/136254.
[13] Gerstenkorn T, Manko J. Correlation of intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 2007, 44(1):39-43.
[14] Xu Z S, Chen J, Wu J J. Clustering algorithm for intuitionistic fuzzy sets[J]. Information Sciences, 2008, 178(19):3775-3790.
[15] Yager R R. Abbasov A M. Pythagorean membership grades, complex numbers and decision making[J]. International Journal of Intelligent Systems, 2013, 28(5):436-452.
[16] Yager R R. Pythagorean membership grades in multicriteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(4):958-965.
[17] 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.
[18] Xue W T, Xu Z S, Zhang X L, et al. Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making[J]. International Journal of Intelligent Systems, 2018, 33(1):93-125.
[19] Ren P J, Xu Z S, Gou X J. Pythagorean fuzzy TODIM approach to multi-criteria decision making[J]. Applied Soft Computing, 2016, 42:246-259.
[20] Liang D C, Xu Z S, Darko A P. Projection model for fusing the information for Pythagorean fuzzy multicriteria group decision making based on geometric Bonferroni mean[J]. International Journal of Intelligent Systems, 2017, 32(9):966-987.
[21] 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. Liu W F, Chang J, He X. Generalized Pythagorean fuzzy aggregation operators and applications in decision making[J]. Control and Decision, 2016, 31(12):2280-2286.
[22] 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, 31(9):886-920.
[23] 刘卫锋,常娟,何霞. 毕达哥拉斯模糊Hamacher集成算子及其决策应用[J]. 系统工程理论与实践, 2018, 38(6):1566-1574.Liu W F, Chang J, He X. Pythagorean fuzzy Hamacher aggregation operators and its application to decision making[J]. Systems Engineering-Theory & Practice, 2018, 38(6):1566-1574.
[24] Ma Z M, Xu Z S. Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision making problems[J]. International Journal of Intelligent Systems, 2016, 31(12):1198-1219.
[25] Wei G W, Lu M. Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making[J]. International Journal of Intelligent Systems, 2018, 33(5):1043-1070.
[26] 刘卫锋,杜迎雪,常娟.毕达哥拉斯模糊交叉影响集成算子及其决策应用[J].控制与决策, 2017, 32(6):1033-1040.Liu W F, Du Y X, Chang J. Pythagorean fuzzy interaction aggregation operators and applications in decision making[J]. Control and Decision, 2017, 32(6):1033-1040.
[27] Gao H, Lu M, Wei G W, et al. Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making[J]. Fundamenta Informaticae, 2018, 159(4):385-428.
[28] Peng X D, Yang Y. Pythagorean fuzzy Choquet integral based MMBAC method for multiple attribute group decision making[J]. International Journal of Intelligent Systems, 2016, 31(10):989-1020.
[29] 何霞,杜迎雪,刘卫锋.毕达哥拉斯模糊幂平均算子[J].模糊系统与数学, 2016, 30(6):116-124.He X, Du Y X, Liu W F. Pythagorean fuzzy power average operators[J]. Fuzzy Systems and Mathematics, 2016, 30(6):116-124.
[30] Wei G W, Lu M. Pythagorean fuzzy power aggregation operators in multiple attribute decision making[J]. International Journal of Intelligent Systems, 2018, 33(1):169-186.
[31] Wang J, Zhang R T, Shang X P, et al. Pythagorean fuzzy Bonferroni mean operators with their application to supply chain management[C]//2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Banff Center, Banff, Canada, 2017. doi:10.1109/SMC.2017.8122695.
[32] Liang D C, Zhang Y R J, Xu Z S, et al. Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading[J]. International Journal of Intelligent Systems, 2018, 33(3):615-633.
[33] 李德清,曾文艺,尹乾.勾股模糊集的距离测度及其在多属性决策中的应用[J]. 控制与决策, 2017, 32(10):1817-1823.Li D Q, Zeng W Y, Yin Q. Distance measures of Pythagorean fuzzy sets and their applications in multiattribute decision making[J]. Control and Decision, 2017, 32(10):1817-1823.
[34] Garg H. A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes[J]. International Journal of Intelligent Systems, 2016, 31(12):1234-1252.
[35] Wei G W, Wei Y. Similarity measures of Pythagorean fuzzy sets based on consine function and their applications[J]. International Journal of Intelligent Systems, 2018, 33(3):634-652.
[36] 彭新东,杨勇,宋娟萍,等.毕达哥拉斯模糊软集及其应用[J].计算机工程, 2015, 41(7):224-229.Peng X D, Yang Y, Song J P, et al. Pythagorean fuzzy soft sets and its application[J]. Computer Engineering, 2015, 41(7):224-229.
[37] 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.Liu W F, He X. Pythagorean hesitant fuzzy set[J]. Fuzzy Systems and Mathematics, 2016, 30(4):107-115.
[38] 张超,李德玉.勾股模糊粗糙集及其在多属性决策中的应用[J].小型微型计算机系统, 2016, 37(7):1531-1535.Zhang C, Li D Y. Pythagorean fuzzy rough sets and its applications in multi-attribute decision making[J]. Journal of Chinese Computer Systems, 2016, 37(7):1531-1535.
[39] Yager R R. On generalized Bonferroni mean operators for multi-criteria aggregation[J]. International Journal of Approximate Reasoning, 2009, 50(8):1279-1286.
[40] Beliakov G, James S, Mordelva J, et al. Generalized Bonferroni mean operators in multi-criteria aggregation[J]. Fuzzy Sets and Systems, 2010, 161(17):2227-2242.
[41] Xu Z S. Uncertain Bonferroni means operators[J]. International Journal of Intelligent Systems, 2010, 3(6):761-769.
[42] Xia M M, Xu Z S, Zhu B. Geometric Bonferroni means with their application in multi-criteria decision making[J]. Knowledge-Based Systems, 2013, 40(1):88-100.

Funding

National Natural Science Foundation of China (11501525); Key Scientific Research Projects in Colleges and Universities of Henan Province (18A110032, 20A110035)
PDF(502 KB)

497

Accesses

0

Citation

Detail
Sections
Recommended

/

〈 〉