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Multiattribute decision making based on interval-valued intuitionistic fuzzy values, score function of connection numbers, and the set pair analysis theory. (English) Zbl 1483.68406

Summary: This paper proposes a new multiattribute decision making (MADM) method based on the proposed score function of connection numbers (CNs) and the set pair analysis (SPA) theory in the interval-valued intuitionist fuzzy (IVIF) context. Firstly, we develop a score function for ranking CNs. The various notable characteristics of the proposed score function of CNs are also presented. Then, we propose a new MADM method based on interval-valued intuitionist fuzzy values (IVIFVs), the proposed score function of CNs and the SPA theory, where we convert IVIFVs into CNs and the optimal weights of attributes are calculated from the IVIF weights of attributes. Finally, the proposed MADM method is applied for MADM in the IVIF context, where the preference orders (POs) of the alternatives obtained by the proposed MADM method are compared with the ones obtained by the existing MADM methods. The proposed MADM method can overcome the drawbacks of the existing MADM methods.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
91B06 Decision theory
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[1] Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, 1, 87-96 (1986) · Zbl 0631.03040
[2] Atanassov, K.; Gargov, G., Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31, 3, 343-349 (1989) · Zbl 0674.03017
[3] Cao, Y. X.; Zhou, H.; Wang, J. Q., An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis, Int. J. Mach. Learn. Cyber., 9, 4, 629-640 (2018)
[4] Chen, S. M.; Chang, C. H., Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators, Inf. Sci., 352-353, 133-149 (2016) · Zbl 1398.68532
[5] Chen, S. M.; Chiou, C. H., Multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and evidential reasoning methodology, IEEE Trans. Fuzzy Syst., 23, 6, 1905-1916 (2015)
[6] Chen, S. M.; Chu, Y. C., Multiattribute decision making based on U-quadratic distribution of intervals and the transformed matrix in interval-valued intuitionistic fuzzy environments, Inf. Sci., 537, 30-45 (2020) · Zbl 1475.91058
[7] Chen, S. M.; Fan, K. Y., Multiattribute decision making based on probability density functions and the variances and standard deviations of largest ranges of evaluating interval-valued intuitionistic fuzzy values, Inf. Sci., 490, 329-343 (2019)
[8] Chen, S. M.; Han, W. H., An improved MADM method using interval-valued intuitionistic fuzzy values, Inf. Sci., 467, 489-505 (2018)
[9] Chen, S. M.; Han, W. H., A new multiattribute decision making method based on multiplication operations of interval-valued intuitionistic fuzzy values and linear programming methodology, Inf. Sci., 429, 421-432 (2018) · Zbl 1437.91139
[10] Chen, S. M.; Huang, Z. C., Multiattribute decision making based on interval-valued intuitionistic fuzzy values and linear programming methodology, Inf. Sci., 381, 341-351 (2017)
[11] Chen, S. M.; Cheng, S. H.; Lan, T. C., Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values, Inf. Sci., 367-368, 279-295 (2016)
[12] Chunfeng, L.; Zhang, L.; Yang, A., The fundamental operation on connection number and its application, J. Theoret. Appl. Inf. Technol., 49, 2, 618-623 (2013)
[13] Ejegwa, P. A., Improved composite relation for pythagorean fuzzy sets and its application to medical diagnosis, Granul. Comput., 5, 2, 277-286 (2020)
[14] Fu, S.; Zhou, H., Triangular fuzzy number multi-attribute decision-making method based on set-pair analysis, J. Software Eng., 11, 1, 116-122 (2016)
[15] Garg, H.; Kaur, G., Novel distance measures for cubic intuitionistic fuzzy sets and their applications to pattern recognitions and medical diagnosis, Granul. Comput., 5, 2, 169-184 (2020)
[16] Garg, H.; Kumar, K., A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application, Scientia Iranica, 25, 4, 2373-2388 (2017)
[17] 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, Soft Comput, 22, 15, 4959-4970 (2018) · Zbl 1398.03177
[18] Garg, H.; Kumar, K., Distance measures for connection number sets based on set pair analysis and its applications to decision-making proces, Appl. Intell., 48, 10, 3346-3359 (2018)
[19] Garg, H.; Kumar, K., Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making, Granul. Comput., 4, 2, 237-247 (2019)
[20] Garg, H.; Kumar, K., Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis, Arab. J. Sci. Eng., 43, 6, 3213-3227 (2018) · Zbl 1390.90608
[21] Garg, H.; Kumar, K., A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory, Artif. Intell. Rev., 53, 1, 595-624 (2020)
[22] Garg, H.; Kumar, K., A novel possibility measure to interval-valued intuitionistic fuzzy set using connection number of set pair analysis and its applications, Neural. Comput. Appl., 32, 8, 3337-3348 (2020)
[23] Jiang, Y. L.; Xu, C. F.; Yao, Y.; Zhao, K. Q., Systems Information in Set Pair Analysis and Its Applications, 1717-1722 (2004), Proceedings of 2004 International Conference on Machine Learning and Cybernetics: Proceedings of 2004 International Conference on Machine Learning and Cybernetics Shanghai, China
[24] Khan, M. S.A.; Abdullah, S.; Ali, A.; Amin, F., An extension of VIKOR method for multi-attribute decision-making under Pythagorean hesitant fuzzy setting, Granul. Comput., 4, 3, 421-434 (2019)
[25] Kumar, K.; Garg, H., Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making, Appl. Intell., 48, 8, 2112-2119 (2018)
[26] Kumar, K.; Garg, H., TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment, Comp. Appl. Math., 37, 2, 1319-1329 (2018) · Zbl 1394.90351
[27] Li, D. F., TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets, IEEE Trans. Fuzzy Syst., 18, 2, 299-311 (2010)
[28] Liu, X.; Wang, L.i., An extension approach of TOPSIS method with OWAD operator for multiple criteria decision-making, Granul. Comput., 5, 1, 135-148 (2020)
[29] Ma, Z. M.; Xu, Z. S., Computation of generalized linguistic term sets based on fuzzy logical algebras for multi-attribute decision making, Granul. Comput., 5, 1, 17-28 (2020)
[30] Manna, S.; Basu, T. M.; Mondal, S. K., Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making, Granul. Comput., 4, 3, 585-599 (2019)
[31] Mishra, A. R.; Rani, P.; Pardasani, K. R., Multiple-criteria decision-making for service quality selection based on Shapley COPRAS method under hesitant fuzzy sets, Granul. Comput., 4, 3, 435-449 (2019)
[32] Mishra, A. R.; Singh, R. K.; Motwani, D., Multi-criteria assessment of cellular mobile telephone service providers using intuitionistic fuzzy WASPAS method with similarity measures, Granul. Comput., 4, 3, 511-529 (2019)
[33] Mishra, A. R.; Chandel, A.; Motwani, D., Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets, Granul. Comput., 5, 1, 97-117 (2020)
[34] Newbold, P.; Carlson, W.; Thorne, B., Statistics for Business and Economics (2013), Pearson, Boston: Pearson, Boston U.S.A Massachusetts
[35] Rahman, K.; Abdullah, S.; Ali, A., Some induced aggregation operators based on interval-valued Pythagorean fuzzy numbers, Granul. Comput., 4, 1, 53-62 (2019)
[36] Rani, P.; Jain, D.; Hooda, D. S., Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision making method based on shapley weighted divergence measure, Granul. Comput., 4, 3, 407-420 (2019)
[37] Surhone, L. M.; Timpledon, M. T.; Marseken, S. F., U-Quadratic Distribution, VDM Publ. (2010)
[38] Tang, J.; Meng, F., Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making, Granul. Comput., 4, 1, 109-124 (2019)
[39] Wang, C. Y.; Chen, S. M., Multiple attribute decision making based on interval-valued intuitionistic fuzzy sets, linear programming methodology, and the extended TOPSIS method, Inf. Sci., 397-398, 155-167 (2017)
[40] Wang, C. Y.; Chen, S. M., An improved multiattribute decision making method based on new score function of interval-valued intuitionistic fuzzy values and linear programming methodology, Inf. Sci., 411, 176-184 (2017) · Zbl 1431.91125
[41] Wang, C. Y.; Chen, S. M., A new multiple attribute decision making method based on linear programming methodology and novel score function and novel accuracy function of interval-valued intuitionistic fuzzy values, Inf. Sci., 438, 145-155 (2018) · Zbl 1440.91016
[42] Xu, Z., Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control Decision, 22, 2, 215-219 (2007), (in Chinese)
[43] Zadeh, L. A., Fuzzy sets, Inf. Control, 8, 3, 338-353 (1965) · Zbl 0139.24606
[44] Zeng, S.; Chen, S. M.; Kuo, L. W., Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method, Inf. Sci., 488, 76-92 (2019)
[45] Zeng, S.; Chen, S. M.; Fan, K. Y., Interval-valued intuitionistic fuzzy multiple attribute decision making based on nonlinear programming methodology and TOPSIS method, Inf. Sci., 506, 424-442 (2020)
[46] Zhang, Z., Maclaurin symmetric means of dual hesitant fuzzy information and their use in multi-criteria decision making, Granul. Comput., 5, 2, 251-275 (2020)
[47] Zhao, K. Q., Set Pair Analysis and Its Preliminary Application (2000), Zhejiang Science and Technology Press: Zhejiang Science and Technology Press Hangzhou, China, (in Chinese)
[48] Zhitao, Z.; Yingjun, Z., Multiple attribute decision making method in the frame of interval-valued intuitionistic fuzzy sets, 192-196 (2011), Proceedings of the 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery: Proceedings of the 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery Shanghai, China
[49] Zou, X. Y.; Chen, S. M.; Fan, K. Y., Multiple attribute decision making using improved intuitionistic fuzzy weighted geometric operators of intuitionistic fuzzy values, Inf. Sci., 535, 242-253 (2020) · Zbl 1459.68210
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