Picture Fuzzy Hamacher Aggregation Operators and their Application to Multiple Attribute Decision Making

• Autorzy: Wei G.

Identyfikatory

DOI

10.3233/FI-2018-1628

• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic, geometric aggregation operators and Hamacher operations with picture fuzzy information. Then, motivated by the ideal of traditional arithmetic, geometric aggregation operators and Hamacher operations, we have developed some aggregation operators for aggregating picture fuzzy information: picture fuzzy Hamacher aggregation operators, picture fuzzy Hamacher geometric aggregation operators, picture fuzzy Hamacher correlated aggregation operators, induced picture fuzzy Hamacher aggregation operators, induced picture fuzzy Hamacher correlated aggregation operators, picture fuzzy Hamacher prioritized aggregation operators, picture fuzzy Hamacher power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Słowa kluczowe

EN

multiple attribute decision making; Hamacher aggregation operators; picture fuzzy Hamacher aggregation operators; picture fuzzy Hamacher geometric aggregation operators; picture fuzzy set; power aggregation; prioritized aggregation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2018
• Tom: Vol. 157, nr 3
• Strony: 271--320
• Opis fizyczny: Bibliogr. 90 poz., tab.

Twórcy

autor

Wei G.

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

Bibliografia

• [1] Atanassov K. 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 K. More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 1989;33(1):37-46. URL https://doi.org/10.1016/0165-0114(89)90215-7.
• [3] Zadeh LA. Fuzzy sets, Information and Control 1965;8(3):338-356. URL https://doi.org/10.1016/S0019-9958(65)90241-X.
• [4] Bustince H, and Burillo P. Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 1995;74(2):237-244. URL https://doi.org/10.1016/0165-0114(94)00343-6.
• [5] Atanassov K, Pasi G, Yager R. Intuitionistic fuzzy interpretations of multi-criteria multi-person and multimeasurement tool decision making. International Journal of Systems Science 2005;36(14):859-868. URL http://dx.doi.org/10.1080/00207720500382365.
• [6] Chen TY. Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets. Information Sciences 2011;181:2139-2165. URL https://doi.org/10.1016/j.ins.2011.01.036.
• [7] Chen TY, and Li CH. Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis. Information Sciences 2010;180(21):4207-4222. URL https://doi.org/10.1016/j.ins.2010.07.009.
• [8] Chen T-Y. Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Information Sciences 2014;261:149-169. URL https://doi.org/10.1016/j.ins.2013.08.054.
• [9] Wei GW. Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision making with incomplete weight information, International Journal of Fuzzy Systems, 2015;17(3):484-489. URL https://doi.org/10.1007/s40815-015-0060-1.
• [10] Chen S-M, and Chiou C-H. Multiattribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Sets, PSO Techniques, and Evidential Reasoning Methodology. IEEE Trans. Fuzzy Systems 2015;23(6):1905-1916. doi:10.1109/TFUZZ.2014.2370675.
• [11] Garg H. A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Applied Soft Computing 2016;38:988-999. URL https://doi.org/10.1016/j.asoc.2015.10.040.
• [12] Liu HW, and Wang GJ. Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research 2007;179(1):220-233. URL https://doi.org/10.1016/j.ejor.2006.04.009.
• [13] Li DF. Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Applied Soft Computing 2011;11(4):3402-3418. URL https://doi.org/10.1016/j.asoc.2011.01.011.
• [14] Li D-F, and Ren H-P. Multi-attribute decision making method considering the amount and reliability of intuitionistic fuzzy information. Journal of Intelligent and Fuzzy Systems 2015;28(4):1877-1883. doi:10.3233/IFS-141475.
• [15] Wei GW. GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowledge-Based Systems 2010;23(3):243-247. URL https://doi.org/10.1016/j.knosys.2010.01.003.
• [16] Wei GW. Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Applied Soft Computing 2010;10(2):423-431. doi:10.1016/j.asoc.2009.08.009.
• [17] Wei GW, Wang HJ, and Lin R. Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowledge and Information Systems 2011;26(2):337-349. URL https://doi.org/10.1007/s10115-009-0276-1.
• [18] Wei GW, and Zhao XF. Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making, Expert Systems with Applications, 2012;39(2):2026-2034. URL https://doi.org/10.1016/j.eswa.2011.08.031.
• [19] Wei GW. Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making. Expert Systems with Applications 2011;38(9):11671-11677. URL https://doi.org/10.1016/j.eswa.2011.03.048.
• [20] Park JH, Park Y, Young CK, Xue T. Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems, Mathematical and Computer Modeling 2009;50(9-10):1279-1293. URL https://doi.org/10.1016/j.mcm.2009.06.010.
• [21] Yager RR. A note on measuring fuzziness for intuitionistic and interval-valued fuzzy sets. International Journal of General Systems 2015;44(7-8):889-901. URL http://dx.doi.org/10.1080/03081079. 2015.1029472.
• [22] Wan S-P, and Li D-F. Atanassov’s Intuitionistic Fuzzy Programming Method for Heterogeneous Multiattribute Group Decision Making With Atanassov’s Intuitionistic Fuzzy Truth Degrees. IEEE Trans. Fuzzy Systems 2014;22(2):300-312. doi:10.1109/TFUZZ.2013.2253107.
• [23] Wan S-P, and Li D-F. Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees. Inf. Sci. 2015;325(2):484-503. URL https://doi.org/10.1016/j.ins.2015.07.014.
• [24] Wang J-q, Wang P, Wang J, Zhang H-y, Chen X-h. Atanassov’s Interval-Valued Intuitionistic Linguistic Multicriteria Group Decision-Making Method Based on the Trapezium Cloud Model. IEEE Trans. Fuzzy Systems 2015;23(3):542-554. doi:10.1109/TFUZZ.2014.2317500.
• [25] Wei GW, and Merig JM. Methods for strategic decision making problems with immediate probabilities in intuitionistic fuzzy setting, Scientia Iranica 2012;19(6):1936-1946. URL https://doi.org/10.1016/j.scient.2012.07.017.
• [26] Zhano XF, and Wei GW. 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.
• [27] Tang Y, Wei LL, Wei GW. Approaches to multiple attribute group decision making based on the generalized Dice similarity measures with intuitionistic fuzzy information, International Journal of Knowledge-based and Intelligent Engineering Systems, 2017;21(2):85-95. doi:10.3233/KES-170354.
• [28] Xu ZS. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems 2007;15(6):1179-1187. doi:10.1109/TFUZZ.2006.890678.
• [29] Xu ZS, and Yager RR. Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems 2006;35:417-433. URL http://dx.doi.org/10.1080/03081070600574353.
• [30] Cuong B. Picture fuzzy sets-first results. part 1, in: Seminar ”Neuro-Fuzzy Systems with Applications”, Institute of Mathematics, Hanoi, 2013.
• [31] Singh P. Correlation coefficients for picture fuzzy sets, Journal of Intelligent & Fuzzy Systems 2014;27:2857-2868. doi:10.3233/IFS-141338.
• [32] Son L. DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets, Expert System with Applications 2015;2:51-66. doi:10.1016/j.eswa.2014.07.026.
• [33] Thong PH, and Son LH. A new approach to multi-variables fuzzy forecasting using picture fuzzy clustering and picture fuzzy rules interpolation method, in: 6th International Conference on Knowledge and Systems Engineering, Hanoi, Vietnam, 2015, pp. 679-690. URL https://doi.org/10.1007/978-3-319-11680-8_54.
• [34] Thong NT. HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis, Expert Systems with Applications 2015;42(7):3682-3701. URL https://doi.org/10.1016/j.eswa.2014.12.042.
• [35] Wei GW. Picture fuzzy cross-entropy for multiple attribute decision making problems Journal of Business Economics and Management, 2016;17(4):491-502. URL http://dx.doi.org/10.3846/16111699. 2016.1197147.
• [36] Wei GW. 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.
• [37] Wei GW, Alsaadi FE, Tasawar H, Alsaedi A. Projection models for multiple attribute decision making with picture fuzzy information, International Journal of Machine Learning and Cybernetics, 2016. doi:10.1007/s13042-016-0604-1.
• [38] Beliakov G, Pradera A, and Calvo T. Aggregation Functions: A Guide For Practitioners. Heidelberg, Germany: Springer, 2007. ISBN: 3540737200, 9783540737209.
• [39] Wei GW. Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, International Journal of Machine Learning and Cybernetics 2016;7(6):1093-1114. URL https://doi.org/10.1007/s13042-015-0433-7.
• [40] Yager RR. On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems Man and Cybernetics 1988;18(1):183-190. doi:10.1109/21.87068.
• [41] Yager RR, and Filev DP. Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics- Part B 1999;29(2):141-150. doi:10.1109/3477.752789.
• [42] Chiclana F, Herrera F, Herrera-Viedma E. The ordered weighted geometric operator: Properties and application. In: Proc of 8th Int Conf on Information Processing and Management of Uncertainty in Knowledge-based Systems, Madrid, 2000. pp 985991. URI http://hdl.handle.net/2086/1201.
• [43] Xu ZS, and Da QL. An overview of operators for aggregating information. International Journal of Intelligent System, 2003;18:953-969. doi:10.1002/int.10127.
• [44] Zhou LY, Zhao XF, Wei GW. Hesitant Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making, Journal of Intelligent and Fuzzy Systems, 2014;26(6):2689-2699. 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] Lu M, Wei GW, 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.
• [47] Wu SJ, and Wei GW. Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, International Journal of Knowledge-based and Intelligent Engineering Systems, 2017;21(3):189-201. doi:10.3233/KES-170363.
• [48] Wei GW, and Lu M. Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making, Archives of Control Sciences, 2017;27(3):365-395. URL https://doi.org/10.1515/acsc-2017-0024.
• [49] Tan C, Yi W, Chen X. Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making. Applied Soft Computing 2015;26:325-349. URL https://doi.org/10.1016/j.asoc.2014.10.007.
• [50] Gl L, Lovassy R, Rudas IJ, Kczy LT. Learning the optimal parameter of the Hamacher t-norm applied for fuzzy-rule-based model extraction. Neural Computing and Applications 2014;24(1):133-142. URL https://doi.org/10.1007/s00521-013-1499-3.
• [51] Chen SM, and Tan JM. Handling multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets Systems 1994;67:163-172. URL https://doi.org/10.1016/0165-0114(94) 90084-1Getrightsandcontent.
• [52] Deschrijver G, Cornelis C, and Kerre EE. On the representation of intuitionistic fuzzy t-norms and tconorms, IEEE Transactions on Fuzzy Systems 2004;12(1):45-61. doi:10.1109/TFUZZ.2003.822678.
• [53] Roychowdhury S, and Wang BH. On generalized Hamacher families of triangular operators, International Journal of Approximate Reasoning, 1998;19(3-4):419-439. URL https://doi.org/10.1016/S0888-613X(98)10018-X.
• [54] Deschrijver G, and Kerre EE. A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, Notes on Intuitionistic Fuzzy Sets, 2002;8:19-27. URL https://lib.ugent.be/catalog/pug01:161876.
• [55] Hamachar H. Uber logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione, in: Trappl, Klir, Riccardi (Eds.), Progress in Cybernatics and systems research, vol. 3, Hemisphere, Washington DC, 1978, pp. 276-288.
• [56] Keeney RL, and Raiffa H. Decision with multiple objectives. New York: Wiley, 1976. ISBN:0471465100, 9780471465102.
• [57] Wakker P. Additive representations of preferences. Kluwer Academic Publishers, 1999.
• [58] Wang Z, and Klir G. Fuzzy Measure Theory, Plenum Press, New York, 1992. ISBN:0306442604, 9780306442605.
• [59] Grabisch M, Murofushi T, and Sugeno M. Fuzzy Measure and Integrals. New York: Physica-Verlag, 2000. ISBN:3790812587, 9783790812589.
• [60] Choquet G. Theory of capacities, Annales de l’institut Fourier, 1954:5:131-295. doi:10.5802/aif.53.
• [61] Yager RR. Induced aggregation operators, Fuzzy Sets and Systems 2003;137(1):59-69. URL https://doi.org/10.1016/S0165-0114(02)00432-3.
• [62] Yager RR. Prioritized aggregation operators, International Journal of Approximate Reasoning 2008;48(1):263-274. URL https://doi.org/10.1016/j.ijar.2007.08.009.
• [63] Yager RR. Prioritized OWA aggregation, Fuzzy Optimization Decision Making, 2009;8(3):245-262. URL https://doi.org/10.1007/s10700-009-9063-4.
• [64] Yager RR. The power average operator, IEEE Transactions on Systems, Man, and Cybernetics-Part A, 2001;31(6):724-731. doi:10.1109/3468.983429.
• [65] Liao X, Li Y, and Lu B. A model for selecting an ERP system based on linguistic information processing, Information Systems 2007;32(7):1005-1017. URL https://doi.org/10.1016/j.is.2006.10.005.
• [66] Singh P. Correlation coefficients for picture fuzzy sets. Journal of Intelligent and Fuzzy Systems 2015;28(2):591-604. doi:10.3233/IFS-141338.
• [67] Wei GW, Alsaadi FE, Hayat T, Alsaedi A. Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making, Iranian Journal of Fuzzy Systems, 2016;13(4):1-16. doi:10.22111/IJFS.2016.2592.
• [68] Lu M, Wei GW, Alsaadi FE, Hayat T, Alsaedi A. Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 2017;33(2):1197-1207. doi:10.3233/JIFS-16946.
• [69] Wei GW, 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, 2017;19(3):607-614. URL https://doi.org/10.1007/s40815-016-0177-x.
• [70] Wei GW, and Wang JM. 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.
• [71] Wei GW. Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making, Informatica, Lithuanian Academy of Sciences, 2017;28(3):547-564.
• [72] Wei GW, Lu M, Alsaadi FE, Hayat T, Alsaedi A. Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 2017;33(2):1129-1142. doi:10.3233/JIFS-16715.
• [73] Wei GW. Picture 2-tuple linguistic Bonferroni mean operators and their application to multiple attribute decision making, International Journal of Fuzzy System, 2017;19(4):997-1010. URL https://doi.org/10.1007/s40815-016-0266-x.
• [74] Wei GW. Interval-valued dual hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 2017;33(3):1881-1893. doi:10.3233/JIFS-161811.
• [75] Wei GW, Zhao XF, Wang HJ, and Lin R. Hesitant Fuzzy Choquet Integral Aggregation Operators and Their Applications to Multiple Attribute Decision Making, Information: An International Interdisciplinary Journal 2012;15(2):441-448.
• [76] Wei GW. Some harmonic averaging operators with 2-tuple linguistic assessment information and their application to multiple attribute group decision making, International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems, 2011;19(6):977-998. URL https://doi.org/10.1142/S0218488511007428.
• [77] Wei GW, and Zhao XF. Minimum Deviation Models for Multiple Attribute Decision Making in Intuitionistic Fuzzy Setting. International Journal of Computational Intelligence Systems 2011;4(2):174-183. doi:10.2991/ijcis.2011.4.2.6.
• [78] Zhou LY, Lin R, Zhao XF, and Wei GW. Uncertain linguistic prioritized aggregation operators and their application to multiple attribute group decision making, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2013;21(4):603-627. URL https://doi.org/10.1142/S0218488513500293.
• [79] Wei GW, Alsaadi FE, Hayat T, Alsaedi A. Hesitant bipolar fuzzy aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 2017;33(2):1119-1128. doi:10.3233/JIFS-16612.
• [80] Lu M, and Wei GW. Pythagorean uncertain linguistic aggregation operators for multiple attribute decision making, International Journal of Knowledge-based and Intelligent Engineering Systems, 2017;21(3):165-179. doi:10.3233/KES-170361.
• [81] Zhang N, and Wei GW. Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling 2013;37(7):4938-4947. URL https://doi.org/10.1016/j.apm.2012.10.002.
• [82] Wei GW, Alsaadi FE, Hayat T, Alsaedi A. Picture 2-tuple linguistic aggregation operators in multiple attribute decision making, Soft Computing, 2016. doi:10.1007/s00500-016-2403-8.
• [83] Garg H. Generalized Intuitionistic Fuzzy Multiplicative Interactive Geometric Operators and their application to multiple criteria decision making, International Journal of Machine Learning and Cybernetics, 2015, doi:10.1007/s13042-015-0432-8.
• [84] Garg H, Agarwal N, Tripathi A. Generalized intuitionistic fuzzy entropy measure of order α and degree β and its applications to multi-criteria decision making problem, International Journal of Fuzzy System Applications, 2017;6(1):89-110.
• [85] Wei GW, Wang JM, and Chen J. Potential optimality and robust optimality in multiattribute decision analysis with incomplete information: A comparative study, Decision Support Systems, 2013;55(3):679-684. URL https://doi.org/10.1016/j.dss.2013.02.005.
• [86] 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. doi:10.1002/int.21809.
• [87] Wei GW, and Lu M. Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in multiple attribute decision making, International Journal of Intelligent Systems, 2017. doi:10.1002/int.21911.
• [88] Garg H. Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making, Computer and Industrial Engineering, 2016;101:53-69. URL https://doi.org/10.1016/j.cie.2016.08.017.
• [89] Garg H. Some series of intuitionistic fuzzy interactive averaging aggregation operators, SpringerPlus, Springer, 2016;5(1):1-27. doi: 10.1186/s40064-016-2591-9.
• [90] Xu XR, and Wei GW. Dual hesitant bipolar fuzzy aggregation operators in multiple attribute decision making, International Journal of Knowledge-based and Intelligent Engineering Systems, 2017;21(3):155-164. doi:10.3233/KES-170360.

Uwagi

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