Banzhaf-Choquet-copula-based aggregation operators for managing q-rung orthopair fuzzy information. (English) Zbl 1498.91145
Summary: Information fusion of fuzzy numbers has played a vital role in the decision support systems under the environment of q-rung orthopair fuzzy set (q-ROFS), which is an effective extension of intuitionistic fuzzy set and fuzzy set. The goals of the present work are to build a family of new aggregation operators (AOs) under q-ROF environment and apply them to MADM problems. First, the extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) are proposed to handle q-ROF information; consequently, the operational law of q-ROFNs is defined based on EAC and EACC. In order to comprehensively consider the relationship between attributes, the q-rung orthopair fuzzy Banzhaf-Choquet-copula AOs \((BCCA^q)\) and q-rung orthopair fuzzy Banzhaf-Choquet-copula geometric operators \((BCCG^q)\) are introduced on the basis of the operation of q-rung orthopair fuzzy numbers (q-ROFNs); consequently, some special cases of \(BCCA^q/BCCG^q\) operators are investigated when the generators of copula take different functions which satisfy the condition of the generators of copulas. In addition, to determine the fuzzy measure (FM) of attribute sets objectively, the improved maximum deviation method and Banzhaf function model are built. Finally, the corresponding decision-making approaches are constructed based on the proposed AOs and proposed models. Proposed approaches can effectively address the some decision-making problems (DMPs), in which the weights of attributes are incompletely unknown (completely unknown), and the correlation also exists among all attribute sets.
MSC:
| 91B06 | Decision theory |
| 91B86 | Mathematical economics and fuzziness |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62H86 | Multivariate analysis and fuzziness |
Keywords:
q-rung orthopair fuzzy set (q-ROFS); extended Archimedean copula and extended Archimedean co-copula; Banzhaf function; fuzzy measure; aggregation operators; multiattribute decision makingReferences:
| [1] | Atanassov, KT, Intuitionistic fuzzy sets, Fuzzy Sets Syst, 20, 87-96 (1986) · Zbl 0631.03040 |
| [2] | Banzhaf, J., Weighed voting does not work: a methamtical analysis, Rutgers Law Rev, 19, 317-343 (1965) |
| [3] | Bustince, H.; Galar, M.; Bedregal, B.; Kolesarova, A.; Mesiar, R., A new approach to interval-valued choquet integrals and the problem of ordering in interval-valued fuzzy set applications, IEEE Transactions on Fuzzy systems, 21, 1150-1162 (2013) |
| [4] | Chen, K.; Luo, YD, Generalized orthopair linguistic Muirhead mean operators and their application in multi-criteria decision making, J Intell Fuzzy Syst, 37, 797-809 (2019) |
| [5] | Chen, SM; Cheng, SH; Chiou, CH, Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasioning methodology, Inf Fusion, 27, 215-227 (2016) |
| [6] | Chen, T.; He, SS; Wang, JQ; Li, L.; Luo, HY, Novel operations for linguistic neutrosophic sets on the basis of Archimedean copulas and co-copulas and their application in multi-criteria decision-making problems, J Intell Fuzzy Syst, 72, 2887-2912 (2019) |
| [7] | Du, WS, Minkowski-type distance measures for generalized orthopair fuzzy sets, Int J Intell Syst, 33, 802-817 (2018) |
| [8] | Du, WS, Weighted power means of q-rung orthopair fuzzy information and their applications in multiattribute decision making, Int J Intell Syst, 34, 2835-2862 (2019) |
| [9] | Du, WS, Correlation and correlation coefficient of generalized orthopair fuzzy sets, Int J Intell Syst, 34, 564-583 (2019) |
| [10] | Fahmi, A.; Amin, F.; Niaz, S., Decision making based on linguistic interval-valued intuitionistic neutrosophic Dombi fuzzy hybrid weighted geometric operator, Soft Comput, 24, 21, 15907-15925 (2020) |
| [11] | Fu, Q.; Song, YF; Fan, CL; Lei, L.; Wang, XD, Evidential model for intuitionistic fuzzy multi-attribute group decision making, Soft Comput, 24, 10, 7615-7635 (2020) · Zbl 1490.91063 |
| [12] | Gao, J.; Xu, Z., Differential calculus of interval-valued q-rung orthopair fuzzy functions and their applications, Int J Intell Syst, 34, 3190-3219 (2019) |
| [13] | Gao, J.; Liang, ZL; Shang, J.; Xu, ZS, Continuities, derivatives, and differentials of q-Rung orthopair fuzzy functions, IEEE Trans Fuzzy Syst, 27, 1687-1699 (2019) |
| [14] | Garg, H., A new generalized Pythagorean fuzzy information aggregation using einstein operations and its application to decision making, Int J Intell Syst, 31, 886-920 (2016) |
| [15] | Garg, H., Novel neutrality operation-based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis, Int J Intell Syst, 34, 2459-2489 (2019) |
| [16] | Genest, C.; Mackay, RJ, Copulas Archimediennes et familles delois bidimensionanelles dont les marges sont donness, Can J Statis, 14, 145-159 (1986) · Zbl 0605.62049 |
| [17] | Huang, WW; Zhang, FW; Xu, SH, A complete ranking method for interval-valued intuitionistic fuzzy numbers and its applications to multicriteria decision making, Soft Comput (2020) · Zbl 1491.03048 · doi:10.1007/s00500-020-05324-6 |
| [18] | Jana, C.; Muhiuddin, G.; Pal, M., Some Dombi aggregation of q-rung orthopair fuzzy numbers in multiple-attribute decision making, Int J Intell Syst, 34, 3220-3240 (2019) |
| [19] | Joshi, BP; Gegov, A., Confidence levels q-rung orthopair fuzzy aggregation operators and its applications to MCDM problems, Int J Intell Syst, 35, 125-149 (2020) |
| [20] | Ju, YB; Luo, C.; Ma, J.; Wang, AH, A novel multiple-attribute group decision-making method based on q-rung orthopair fuzzy generalized power weighted aggregation operators, Int J Intell Syst, 34, 2077-2103 (2019) |
| [21] | Ju, YB; Wang, AH; Ma, J.; Gao, HX; Gonzalez, E., Some q-rung orthopair fuzzy 2-tuple linguistic Muirhead mean aggregation operators and their applications to multiple-attribute group decision making, Int J Intell Syst, 35, 184-213 (2020) |
| [22] | Khan, MSA, Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making, Soft Comput, 23, 251-267 (2018) · Zbl 1415.91092 |
| [23] | Khan, MSA, The Pythagorean fuzzy Einstein Choquet integral operators and their application in group decision making, Comput Appl Math, 38, 1-35 (2019) · Zbl 1463.91041 |
| [24] | Li, L.; Zhang, RT; Wang, J.; Shang, XP, Some q-rung orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making, Arch Control Sci, 28, 551-583 (2018) · Zbl 1443.91113 |
| [25] | Li, HX; Yin, SY; Yang, Y., Some preference relations based on q-rung orthopair fuzzy sets, Int J Intell Syst, 34, 2920-2936 (2019) |
| [26] | Liang, DC; Zhang, YRJ; Cao, W., q-Rung orthopair fuzzy Choquet integral aggregation and its application in heterogeneous multicriteria two-sided matching decision making, Int J Intell Syst, 34, 3275-3301 (2019) |
| [27] | Liu, YN; Jiang, W., A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making, Soft Comput, 24, 9, 6987-7003 (2020) · Zbl 1490.03031 |
| [28] | Liu, PD; Liu, JL, Some q-Rung Orthopair Fuzzy Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making, International Journal of Intelligent Systems, 33, 315-347 (2018) |
| [29] | Liu, PD; Liu, WQ, Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers, Int J Intell Syst, 34, 652-689 (2019) |
| [30] | Liu, PD; Liu, WQ, Multiple-attribute group decision-making method of linguistic q-rung orthopair fuzzy power Muirhead mean operators based on entropy weight, Int J Intell Syst, 34, 1755-1794 (2019) |
| [31] | Liu, PD; Wang, P., Some q-Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple-Attribute Decision Making, International Journal of Intelligent Systems, 33, 259-280 (2018) |
| [32] | Liu, PD; Wang, P., Multiple-attribute decision-making based on archimedean bonferroni operators of q-rung orthopair fuzzy numbers, IEEE Trans Fuzzy Syst, 27, 834-848 (2019) |
| [33] | Liu, ZM; Wang, S.; Liu, PD, Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators, Int J Intell Syst, 33, 2341-2363 (2018) |
| [34] | Liu, DH; Chen, XH; Peng, D., Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets, Int J Intell Syst, 34, 1572-1587 (2019) |
| [35] | Liu, ZM; Li, L.; Li, JQ, q-Rung orthopair uncertain linguistic partitioned Bonferroni mean operators and its application to multiple attribute decision-making method, Int J Intell Syst, 34, 2490-2520 (2019) |
| [36] | Liu, ZM; Xu, HX; Yu, YN; Li, JQ, Some q-rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making, Int J Intell Syst, 34, 2521-2555 (2019) |
| [37] | Liu, Y.; Wei, G.; Liu, B.; Xu, L., Group decision making for internet public opinion emergency based upon linguistic intuitionistic fuzzy information, Int J Mach Learn Cybern (2021) · doi:10.1007/s13042-020-01262-9 |
| [38] | Marichal, JL, The influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making, Discrete Appl Math, 168, 139-164 (2000) · Zbl 1005.91012 |
| [39] | Meng, F.; Zhang, Q.; Zhan, J., The interval-valued intuitionistic fuzzy geometric choquet aggregation operator based on the generalized banzhaf index and 2-additive measure, Technol Econ Dev Econ, 21, 186-215 (2015) |
| [40] | Nelsen, RB, An introduction to copula (2013), Berlin: Springer Science Business Media, Berlin |
| [41] | Pasi, G., A multi-criteria decision making approach based on the choquet integral for assessing the credibility of user-generated content, Inf Sci, 503, 574-588 (2019) |
| [42] | Peng, XD; Liu, L., Information measures for q-rung orthopair fuzzy sets, Int J Intell Syst, 34, 1795-1834 (2019) |
| [43] | Peng, XD; Dai, JG; Garg, H., Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function, Int J Intell Syst, 33, 2255-2282 (2018) |
| [44] | Qin, YC; Qi, QF; Scott, PJ; Jiang, X., Multiple criteria decision making based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades, Soft Comput, 24, 16, 12329-12355 (2020) · Zbl 1491.91063 |
| [45] | Shu, XQ; Ai, ZH; Xu, ZS; Ye, JM, Integrations of q-Rung Orthopair Fuzzy Continuous Information, IEEE Trans Fuzzy Syst, 27, 1974-1985 (2019) |
| [46] | Sklar, M., Fonctions de répartition àn dimensions et leurs marges, Université Paris, 8, 229-231 (1959) · Zbl 0100.14202 |
| [47] | Sugeno M (1974) Theory of fuzzy integral and its application. Doctorial dissertation. Tokyo Institute of Technology, Tokyo, Japan |
| [48] | Tan, C., Atanassov’s intuitionistic fuzzy Quasi-Choquet geometric operators and their applications to multicriteria decision making, Fuzzy Optim Decis Making, 14, 139-172 (2014) · Zbl 1428.03068 |
| [49] | Tan, C.; Chen, X., Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making, Expert Syst Appl, 37, 149-157 (2010) |
| [50] | Tan, C.; Chen, X., Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making, Int J Intell Syst, 26, 659-686 (2011) |
| [51] | Tao, Z., On Intuitionistic Fuzzy Copula Aggregation Operators in Multiple- Attribute Decision Making, Cognitive Computation, 10, 610-624 (2018) |
| [52] | Tao, Z., The novel computational model of unbalanced linguistic variables based on archimedean copula, Int J Uncertain Fuzziness Knowl-Based Syst, 26, 601-631 (2018) · Zbl 1469.68116 |
| [53] | Verma, R.; Merigo, JM, Multiple attribute group decision making based on 2-dimension linguistic intuitionistic fuzzy aggregation operators, Soft Comput, 24, 22, 17377-17400 (2020) · Zbl 1491.91066 |
| [54] | Wang, F.; Wan, SP, A comprehensive group decision-making method with interval-valued intuitionistic fuzzy preference relations, Soft Comput (2020) · Zbl 1491.91068 · doi:10.1007/s00500-020-05145-7 |
| [55] | Wang, J.; Wei, GW; Lu, JP; Alsaadi, FE; Hayat, T.; Wei, C., Some q-rung orthopair fuzzy Hamy mean operators in multiple attribute decision-making and their application to enterprise resource planning systems selection, Int J Intell Syst, 34, 2429-2458 (2019) |
| [56] | Wang, J.; Zhang, RT; Zhu, XM; Zhou, Z.; Shang, XP; Li, WZ, Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making, J Intell Fuzzy Syst, 36, 1599-1614 (2019) |
| [57] | Wang, P.; Wang, J.; Wei, GW; Wei, C., Similarity measures of q-Rung orthopair fuzzy sets based on cosine function and their applications, Mathematics, 7, 340 (2019) |
| [58] | Wang, J.; Wei, GW; Wang, R.; Alsaadi, FE; Hayat, T.; Wei, C., Some q-rung interval-valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making, Int J Intell Syst, 34, 2769-2806 (2019) |
| [59] | Wang, HH; Ju, YB; Liu, PD, Multi-attribute group decision-making methods based on q-rung orthopair fuzzy linguistic sets, Int J Intell Syst, 34, 1129-1157 (2019) |
| [60] | Wei, GW; Gao, H.; Wei, Y., Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making, Int J Intell Syst, 33, 1426-1458 (2018) |
| [61] | Wei, GW; Wei, C.; Wang, J.; Gao, H.; Wei, Y., Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization, Int J Intell Syst, 34, 50-81 (2019) |
| [62] | Wei, AP; Li, DF; Lin, PP; Jiang, BQ, An information-based score function of interval-valued intuitionistic fuzzy sets and its application in multiattribute decision making, Soft Comput (2020) · Zbl 1491.03070 · doi:10.1007/s00500-020-05265-0 |
| [63] | Xing, Y., q-Rung orthopair fuzzy uncertain linguistic choquet integral operators and their application to multi-attribute decision making, J Intell Fuzzy Syst, 37, 1123-1139 (2019) |
| [64] | Xing, YP; Zhang, RT; Wang, J.; Zhu, XM, Some new Pythagorean fuzzy Choquet-Frank aggregation operators for multi-attribute decision making, Int J Intell Syst, 33, 2189-2215 (2018) |
| [65] | Xing, YP; Zhang, RT; Zhou, Z.; Wang, J., Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making, Soft Comput, 23, 11627-11649 (2019) · Zbl 1436.91053 |
| [66] | Xu, ZS, Intuitionsitic fuzzy aggregation operators, IEEE Trans Fuzzy Syst, 15, 1179-1187 (2007) |
| [67] | Yager, RR, Pythagorean membership grades in multicriteria decision making, IEEE Trans Fuzzy Syst, 22, 958-965 (2014) |
| [68] | Yager, RR, Generalized orthopair fuzzy sets, IEEE Trans Fuzzy Syst, 25, 1222-1230 (2017) |
| [69] | Yang, W.; Pang, YF, New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making, Int J Intell Syst, 34, 439-476 (2019) |
| [70] | Zadeh, LA, Fuzzy sets, Inf Control, 8, 338-353 (1965) · Zbl 0139.24606 |
| [71] | Zhang, Z.; Guo, C., Luis Martínez, Managing multigranular linguistic distribution assessments in large-scale multiattribute group decision making, IEEE Trans Syst Man Cybern Syst, 47, 3063-3076 (2017) |
| [72] | Zhang, C.; Liao, HC; Luo, L., Additive consistency-based priority-generating method of q-rung orthopair fuzzy preference relation, Int J Intell Syst, 34, 2151-2176 (2019) |
| [73] | Zhang, C.; Liao, HC; Luo, L.; Xu, ZS, Multiplicative consistency analysis for q-rung orthopair fuzzy preference relation, Int J Intell Syst, 35, 38-71 (2020) |
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