Pythagorean Fuzzy Hamacher Power Aggregation Operators in Multiple Attribute Decision Making

• Autorzy: Wei, Gui-Wu
• Języki publikacji: EN

Abstrakty

EN

In this paper, we utilize Hamacher operations and power aggregation operators to develop some Pythagorean fuzzy Hamacher power aggregation operators: Pythagorean fuzzy Hamacher power average (PFHPA) operator, Pythagorean fuzzy Hamacher power geometric (PFHPG) operator, Pythagorean fuzzy Hamacher power weighted average (PFHPWA) operator, Pythagorean fuzzy Hamacher power weighted geometric (PFHPWG) operator, Pythagorean fuzzy Hamacher power ordered weighted average (PFHPOWA) operator, Pythagorean fuzzy Hamacher power ordered weighted geometric (PFHPOWG) operator, Pythagorean fuzzy Hamacher power hybrid average (PFHPHA) operator and Pythagorean fuzzy Hamacher power hybrid geometric (PFHPHG) operator. The prominent characteristic of these proposed operators are studied. Then, we utilize these operators to develop some approaches to solve the multiple attribute decision making problems with Pythagorean fuzzy numbers (PFNs). Finally, a practical example is given to verify the developed approach and deliver a comparative analysis.

Słowa kluczowe

EN

Hamacher aggregation operators; multiple attribute decision making; MADM; Pythagorean fuzzy Hamacher power hybrid average operator; PFHPHA; Pythagorean fuzzy Hamacher power hybrid geometric operator; PFHPHG; Pythagorean fuzzy numbers; PFNs

• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 166, nr 1
• Strony: 57--85
• Opis fizyczny: Bibliogr. 82 poz., tab.

Twórcy

autor

Wei, Gui-Wu

• School of Business, Sichuan Normal University, Chengdu, 610101, P.R. China,

Bibliografia

• [1] Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986. 20(1):87-96. URL https://doi.org/10.1016/S0165-0114(86)80034-3.
• [2] Atanassov KT. Two theorems for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 2000. 110(2):267-269. URL https://doi.org/10.1016/S0165-0114(99)00112-8.
• [3] Zadeh L. Fuzzy sets. Information and Control, 1965. 8(3):338-353.
• [4] Zhu YJ, Li DF. A new definition and formula of entropy for intuitionistic fuzzy sets. Journal of Intelligent & Fuzzy Systems, 2016. 30(6):3057-3066. doi:10.3233/IFS-152031.
• [5] Li Z, Wei G, Gao H. Methods for Multiple Attribute Decision Making with Interval-Valued Pythagorean Fuzzy Information. Mathematics, 2018. 6(11). doi:10.3390/math6110228.
• [6] Wang J, Wei G, Gao H. Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information. Mathematics, 2018. 6(10). URL https://doi.org/10.3390/math6100201.
• [7] Deng X, Wei G, Gao H, Wang J. Models for Safety Assessment of Construction Project With Some 2-Tuple Linguistic Pythagorean Fuzzy Bonferroni Mean Operators. IEEE Access, 2018. 6:52105-52137. doi:10.1109/ACCESS.2018.2869414.
• [8] Wei G. MInterval-valued dual hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 2017. 33(3):1881-1893.
• [9] Huang YH, Wei GW. TODIM method for Pythagorean 2-tuple linguistic multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 2018. 35(1):901-915. doi:10.3233/JIFS-171636.
• [10] Wang J, Wei G, Lu M. An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers. Symmetry, 2018. 10(10):497. doi:10.3390/sym10100497.
• [11] Deng X, Wang J, Wei G, Lu M. Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators. Mathematics, 2018. 6(11):236. URL https://doi.org/10.3390/math6110236.
• [12] Li Z, Gao H, Wei G. Methods for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Dombi Hamy Mean Operators. Symmetry, 2018. 10(11):574. URL https://doi.org/10.3390/sym10110574.
• [13] Wei GW. TODIM method for picture fuzzy multiple attribute decision making. Informatica, 2018. 29(3):555-566. URL http://dx.doi.org/10.15388/Informatica.2018.181.
• [14] Wei G. Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. International Journal of Machine Learning & Cybernetics, 2016. 7(6):1093-1114. doi:10.1007/s13042-015-0433-7.
• [15] Wei G, Alsaadi FE, Hayat T, Alsaedi A. A Linear Assignment Method for Multiple Criteria Decision Analysis with Hesitant Fuzzy Sets Based on Fuzzy Measure. International Journal of Fuzzy Systems, 2016. 19(3):1-8. doi:10.1007/s40815-016-0177-x.
• [16] Gao H, Wei G, Huang Y. Dual Hesitant Bipolar Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making. IEEE Access, 2017. PP(99):1-1.
• [17] Wei G, Wei C, Gao H. Multiple Attribute Decision Making with Interval-Valued Bipolar Fuzzy Information and Their Application to Emerging Technology Commercialization Evaluation. IEEE Access. PP(99):1-1.
• [18] Wang J, Wei G, Lu M. TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment. Symmetry, 2018. 10(10). doi:10.3390/sym10100486.
• [19] Wei G, Wei Y. Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 2018. 35(2):2001-2013. doi:10.3233/JIFS-171741.
• [20] Wei GW. Some similarity measures for picture fuzzy sets and their applications. Iranian Journal of Fuzzy Systems, 2018. 15(1):77-89. doi:10.22111/IJFS.2018.3579.
• [21] Yager RR. Pythagorean fuzzy subsets. In: Ifsa World Congress and Nafips Meeting. 2013 pp. 57-61. doi:10.1109/IFSA-NAFIPS.2013.6608375.
• [22] Yager RR. Pythagorean Membership Grades in Multicriteria Decision Making. IEEE Transactions on Fuzzy Systems, 2014. 22(4):958-965. doi:10.1109/TFUZZ.2013.2278989.
• [23] Zhang X, Xu Z. Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets. International Journal of Intelligent Systems, 2015. 29(12):1061-1078. doi:10.1002/int.21676.
• [24] Peng X, Yang Y. Some Results for Pythagorean Fuzzy Sets. International Journal of Intelligent Systems, 2015. 30(11):1133-1160. URL https://doi.org/10.1002/int.21738.
• [25] Ren P, Xu Z, Gou X. Pythagorean fuzzy TODIM approach to multi-criteria decision making. Applied Soft Computing, 2016. 42:246-259. URL https://doi.org/10.1016/j.asoc.2015.12.020.
• [26] Zeng S, Chen J, Li X. A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making. International Journal of Information Technology & Decision Making, 2016. 15(02):403-422. URL https://doi.org/10.1142/S0219622016500012.
• [27] Garg H. A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making. International Journal of Intelligent Systems, 2016. 31(9):886-920. URL https://doi.org/10.1002/int.21809.
• [28] Garg H. Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment. International Journal of Intelligent Systems, 2018. 33(4):687-712. URL https://doi.org/10.1002/int.21949.
• [29] Wei G, Lu M. Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making: PYTHAGOREAN FUZZY MACLAURIN SYMMETRIC MEAN OPERATORS. International Journal of Intelligent Systems, 2018. 33(5):1043-1070. URL https://doi.org/10.1002/int.21911.
• [30] Wei G, Lu M. Pythagorean fuzzy power aggregation operators in multiple attribute decision making. International Journal of Intelligent Systems, 2018. 33(1):169-186. URL https://doi.org/10.1002/int.21946.
• [31] Yager RR. The power average operator. Systems Man & Cybernetics Part A Systems & Humans IEEE Transactions on, 2001. 31(6):724-731. doi:10.1109/3468.983429.
• [32] Wei G. Some linguistic power aggregating operators and their application to multiple attribute group decision making. IOS Press, 2013. 25(3):695-707. doi:10.3233/IFS-120676.
• [33] Wei G, Zhao X, Wang H, Lin R. Fuzzy power aggregating operators and their application to multiple attribute group decision making. Technological and Economic Development of Economy, 2013. 19(3):377-396. URL https://doi.org/10.3846/20294913.2013.821684.
• [34] Gao H, Lu M, Wei G, Wei Y. Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fundamenta Informaticae, 2018. 159(4):385-428. doi:10.3233/FI-2018-1669.
• [35] Liang D, Zhang Y, Xu Z, Darko AP. Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading. International Journal of Intelligent Systems, 2018. (2):615-633. URL https://doi.org/10.1002/int.21960.
• [36] Liang D, Xu Z, Darko AP. Projection Model for Fusing the Information of Pythagorean Fuzzy Multicriteria Group Decision Making Based on Geometric Bonferroni Mean: PYTHAGOREAN FUZZY MULTICRITERIA GDM BASED ON GBM. International Journal of Intelligent Systems, 2017. 32(9):966-987. URL https://doi.org/10.1002/int.21879.
• [37] Garg H. A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision-Making Processes. International Journal of Intelligent Systems, 2016. 31(12):1234-1252. URL https://doi.org/10.1002/int.21827.
• [38] Garg H. Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Computational & Mathematical Organization Theory, 2017. 23(4):1-26. doi:10.1007/s10588-017-9242-8.
• [39] Garg H. Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t-Norm and t-Conorm for Multicriteria Decision-Making Process. International Journal of Intelligent Systems, 2017. 32(6):597-630. URL https://doi.org/10.1002/int.21860.
• [40] Wei G, Wei Y. Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 2018. 33(3):634-652. URL https://doi.org/10.1002/int.21965.
• [41] Li Z, Wei G, Lu M. Pythagorean Fuzzy Hamy Mean Operators in Multiple Attribute Group Decision Making and Their Application to Supplier Selection. Symmetry, 2018. 10(10):505. URL https://doi.org/10.3390/sym10100505.
• [42] Gao H. Pythagorean Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making. Journal of Intelligent and Fuzzy Systems, 2018. 35(2):2229-2245. doi:10.3233/JIFS-172262.
• [43] Hamachar H. Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione Trappl, Klir, Riccardi (Eds.). Progress in Cybernatics and systems research, 1978. (3):276-288.
• [44] LY Zhou GW XF Zhao. Hesitant Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making. International Journal of Intelligent Systems, 2014. 26(6):26892699. doi:10.3233/IFS-130939.
• [45] Liu P. Some Hamacher Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making. IEEE Transactions on Fuzzy Systems, 2014. 22(1):83-97. doi:10.1109/TFUZZ.2013.2248736.
• [46] GW Wei, Lu M, Tang X, Wei Y. Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making. International Journal of Intelligent Systems, 2018. 33(6):1197-1233. URL https://doi.org/10.1002/int.21978.
• [47] Gou X, Xu Z, Ren P. The Properties of Continuous Pythagorean Fuzzy Information. International Journal of Intelligent Systems, 2016. 31(5):401-424. URL https://doi.org/10.1002/int.21788.
• [48] Marek Reformat RRY. Suggesting Recommendations Using Pythagorean Fuzzy Sets illustrated Using Netflix Movie Data. IPMU, 2014. (1):546-556. doi:10.1007/978-3-319-08795-5_56.
• [49] Deschrijver G, Cornelis C, Kerre EE. On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems, 2004. 12(1):45-61. doi:10.1109/TFUZZ.2003.822678.
• [50] Roychowdhury S, Wang BH. On generalized Hamacher families of triangular operators. International Journal of Approximate Reasoning, 1998. 19(3-4):419-439.
• [51] Deschrijver G, Kerre EE. A generalisation of operators on intuitionistic fuzzy sets using triangular norms and conorms. Notes on Instuitionistic Fuzzy Sets, 2002. 1(1):19-27. URL http://ifigenia.org/wiki/issue:nifs/8/1/19-27.
• [52] Wang W, Liu X. Intuitionistic Fuzzy Geometric Aggregation Operators Based on Einstein Operations. International Journal of Intelligent Systems, 2011. 26(11):1049-1075. URL https://doi.org/10.1002/int.20498.
• [53] Zhao X, Wei G. Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowledge-Based Systems, 2013. 37:472-479. URL https://doi.org/10.1016/j.knosys.2012.09.006.
• [54] Gao H, Wei G, Huang Y. Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE Access, 2018. 6(1):11508-11522. doi:10.1109/ACCESS.2017.2784963.
• [55] Lu M, GW Wei, Alsaadi FE, Hayat T, Alsaedi A. Hesitant Pythagorean Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making. Journal of Intelligent and Fuzzy Systems, 2017. 33(2):1105-1117. doi:10.3233/JIFS-16554.
• [56] Wei G, Alsaadi FE, Hayat T, Alsaedi A. Bipolar Fuzzy Hamacher Aggregation Operators in Multiple Attribute Decision Making. International Journal of Fuzzy Systems, 2017. 33(6):1-12. doi:10.1007/s40815-017-0338-6.
• [57] Wei G, Gao H, Wang J, Huang Y. Research on Risk Evaluation of Enterprise Human Capital Investment with Interval-valued bipolar 2-tuple linguistic Information. IEEE Access, 2018. (6):35697-35712. doi:10.1109/ACCESS.2018.2836943.
• [58] Wei G, Gao H, Wei Y. Some q-Rung Orthopair Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making. International Journal of Intelligent Systems, 2017. 33(7):713-724. doi:10.3233/JIFS-161798.
• [59] Tang X, Wei G. Models for Green Supplier Selection in Green Supply Chain Management with Pythagorean 2-Tuple Linguistic Information. IEEE Access, 2018. 6:18042-18060. doi:10.1109/ACCESS.2018.2817551.
• [60] Wei G. Picture fuzzy aggregation operators and their application to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 2017. 33(2):713-724. doi:10.3233/JIFS-161798.
• [61] Lu M, GW Wei, Alsaadi FE, Hayat T, Alsaedi A. Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making, 2017. 33(2):1197-1207. doi:10.3233/JIFS-16946.
• [62] Wu S, Wang J, Wei G, Wei Y. Research on Construction Engineering Project Risk Assessment with Some 2-Tuple Linguistic Neutrosophic Hamy Mean Operators. Sustainability, 2018. 10(5):1536. doi:10.3390/su10051536.
• [63] Garg H. Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple attribute decision making. 2017. 8(3):267-289. doi:10.1615/Int.J.UncertaintyQuantification.2018020979.
• [64] Garg H. Linguistic Pythagorean fuzzy sets and its applications in multi-attribute decision-making process. International Journal of Intelligent Systems, 2018. 33(1):1234-1263. URL https://doi.org/10.1002/int.21979.
• [65] Wei G. Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Applied Soft Computing, 2010. 10(2):423-431. URL https://doi.org/10.1016/j.asoc.2009.08.009.
• [66] Wei G, Alsaadi FE, Hayat T, Alsaedi A. Picture 2-tuple linguistic aggregation operators in multiple attribute decision making. Soft Computing, 2016. 33(2):1-14. doi:10.1007/s00500-016-2403-8.
• [67] Wei G. Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making. Kybernetes, 2017. 46(10):1777-1800. URL https://doi.org/10.1108/K-01-2017-0025.
• [68] Xu Z, Yager RR. Power-Geometric Operators and Their Use in Group Decision Making. IEEE Transactions on Fuzzy Systems, 2010. 18(1):94-105. doi:10.1109/TFUZZ.2009.2036907.
• [69] Ma Z, Xu Z. Symmetric Pythagorean Fuzzy Weighted Geometric/Averaging Operators and Their Application in Multicriteria Decision-Making Problems: PYTHAGOREAN FUZZY WEIGHTED GEOMETRIC/AVERAGING OPERATORS. International Journal of Intelligent Systems, 2016. 31(12):1198-1219. URL https://doi.org/10.1002/int.21823.
• [70] Garg H. New exponential operational laws and their aggregation operators for interval valued Pythagorean fuzzy multicriteria decision making. International Journal of Intelligent Systems, 2018. 33(3):653-683. URL https://doi.org/10.1002/int.21966.
• [71] Arqub OA, Al-Smadi M, Momani S, Hayat T. Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Computing, 2016. 20(8):3283-3302. doi:10.1007/s00500-015-1707-4.
• [72] Arqub OA, Al-Smadi M, Momani S, Hayat T. Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Computing, 2017. 21(23):7191-7206. doi:10.1007/s00500-016-2262-3.
• [73] Abu Arqub O. Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integro-differential equations. Neural Computing and Applications, 2017. 28(7):1591-1610. doi:10.1007/s00521-015-2110-x.
• [74] Wang J, Wei G, Wei Y. Models for Green Supplier Selection with Some 2-Tuple Linguistic Neutrosophic Number Bonferroni Mean Operators. Symmetry, 2018. 10(5):131. doi:10.3390/sym10050131.
• [75] Tai WS, Chen CT. A new evaluation model for intellectual capital based on computing with linguistic variable. Expert Systems with Applications, 2009. 36(2):3483-3488. URL https://doi.org/10.1016/j.eswa.2008.02.017.
• [76] Wei G, Gao H. The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica, 2018. 29(1):1-8.
• [77] Kuo MS, Liang GS. A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers. Applied Soft Computing, 2012. 12(1):476-485. URL https://doi.org/10.1016/j.asoc.2011.08.020.
• [78] Wei G, Wang J. A comparative study of robust efficiency analysis and Data Envelopment Analysis with imprecise data. Expert Systems with Applications, 2017. 81:28-38. URL https://doi.org/10.1016/j.eswa.2017.03.043.
• [79] Wang WP. Evaluating new product development performance by fuzzy linguistic computing. Expert Systems with Applications, 2009. 36(6):9759-9766. URL https://doi.org/10.1016/j.eswa.2009.02.034.
• [80] Wei G. Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 2017. 28(3):547-564.
• [81] Wei Y, Liu J, Lai X, Hu Y. Which determinant is the most informative in forecasting crude oil market volatility: Fundamental, speculation, or uncertainty? Energy Economics, 2017. 68:141-150. URL https://doi.org/10.1016/j.eneco.2017.09.016.
• [82] Wei Y, Q Yu, Liu J, Cao Y. Hot money and Chinas stock market volatility: Further evidence using the GARCH-MIDAS model. Physica A: Statistical Mechanics and its Applications, 2018. (492):923-930. URL https://doi.org/10.1016/j.physa.2017.11.022.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Identyfikatory

DOI

10.3233/FI-2019-1794