×

Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. (English) Zbl 1479.91079

Summary: In this paper, we propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers for multi-criteria decision-making (MCDM). Aimed at the best-to-others vector and the others-to-worst vector in the form of triangular fuzzy numbers, this paper regards consistency equations as fuzzy equations. The derivation of optimal fuzzy weights of criteria is formulated as a fuzzy decision-making problem, where a mathematical programming model is constructed to derive optimal fuzzy weights of criteria to build a normalized triangular fuzzy weight vector. Then, we propose four linear programming models based on the obtained mathematical programming model for the optimistic decision maker, the pessimistic decision maker and the neutral decision maker, respectively. Through a proper selection of the values of tolerance parameters, each of the linear programming models certainly has a unique global optimal solution. Moreover, this paper proposes the concept of fuzzy consistency index and the concept of fuzzy consistency ratio. Several application examples are used to validate the proposed fuzzy BWM. The proposed fuzzy BWM provides us with a very useful way for MCDM in fuzzy environments.

MSC:

91B06 Decision theory
91B86 Mathematical economics and fuzziness
90B50 Management decision making, including multiple objectives
90C05 Linear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aboutorab, H.; Saberi, M.; Asadabadi, M. R.; Hussain, O.; Chang, E., ZBWM: The Z-number extension of Best Worst method and its application for supplier development, Expert Syst. Appl., 107, 115-125 (2018)
[2] Ahmed, F.; Kilic, K., Fuzzy analytic hierarchy process: A performance analysis of various algorithms, Fuzzy Sets Syst., 362, 110-128 (2019)
[3] Ahmad, W. N.K. W.; Rezaei, J.; Sadaghiani, S.; Tavasszy, L. A., Evaluation of the external forces affecting the sustainability of oil and gas supply chain using best worst method, J. Clear. Prod., 153, 242-252 (2017)
[4] Bas, E.; Egrioglu, E.; Yolcu, U.; Grosan, C., Type 1 fuzzy function approach based on ridge regression for forecasting, Granular Comput., 4, 4, 629-637 (2019)
[5] Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Manage. Sci., 17, 4, 141-164 (1970) · Zbl 0224.90032
[6] Castillo, O.; Cervantes, L.; Melin, P.; Pedrycz, W., A new approach to control of multivariable systems through a hierarchical aggregation of fuzzy controllers, Granular Comput., 4, 1, 1-13 (2019)
[7] Chang, J. R.; Yu, P. Y., Weighted-fuzzy-relations time series for forecasting information technology maintenance cost, Granular Comput., 4, 4, 687-697 (2019)
[8] S.J. Chen, S.M. Chen, A new method to measure the similarity between fuzzy numbers, In: Proceedings of the 2001 10th IEEE International Conference on Fuzzy Systems, Melbourne, Australia, vol. 3, pp. 1123-1126, 2001.
[9] Chen, S. M.; Chen, S. W., Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships, IEEE Trans. Cybern., 45, 3, 391-403 (2014)
[10] Chen, S. M.; Chu, H. P.; Sheu, T. W., TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors, IEEE Trans. Syst. Man Cyber. Part A Syst. Hum., 42, 6, 1485-1495 (2012)
[11] Chiang, H. S.; Chen, M. Y.; Wu, Z. W., Applying fuzzy Petri nets for evaluating the impact of bedtime behaviors on sleep quality, Granular Comput., 3, 4, 321-332 (2018)
[12] Dantzig, G. B., Linear Programming 2: Theory and Extensions (2003), Springer: Springer New York · Zbl 1029.90037
[13] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press · Zbl 0444.94049
[14] Garg, H., Some arithmetic operations on the generalized sigmoidal fuzzy numbers and its application, Granular Comput., 3, 1, 9-25 (2018)
[15] Guo, S.; Zhao, H., Fuzzy best-worst multi-criteria decision-making method and its applications, Knowl.-Based Syst., 121, 23-31 (2017)
[16] Hafezalkotob, A., A novel approach for combination of individual and group decisions based on fuzzy best-worst method, Appl. Soft Comput., 59, 316-325 (2017)
[17] Herman, M. W.; Koczkodaj, W. W., A Monte Carlo study of pairwise comparison, Inf. Process. Lett., 57, 25-29 (1996) · Zbl 1004.68550
[18] Ibrahim, A. M.; William-West, T. O., Induction of shadowed sets from fuzzy sets, Granular Comput., 4, 1, 27-38 (2019)
[19] Kaa, G. V.D.; Fens, T.; Rezaei, J.; Kaynak, D.; Hatun, Z.; Tsilimeni-archangelidi, A., Realizing smart meter connectivity: Analyzing the competing technologies Power line communication, mobile telephony, and radio frequency using the best worst method, Renew. Sustain. Energy Rev., 103, 320-327 (2019)
[20] Kaur, R.; Singh, S.; Kumar, H., AuthCom: Authorship verification and compromised account detection in online social networks using AHP-TOPSIS embedded profiling based technique, Expert Syst. Appl., 113, 397-414 (2018)
[21] Khanmohammadi, E.; Zandieh, M.; Tayebi, T., Drawing a strategy canvas using the fuzzy best-worst method, Global J. Flexible Syst. Manage., 20, 57-75 (2019)
[22] Lagunes, M. L.; Castillo, O.; Soria, J.; Garcia, M.; Valdez, F., Optimization of granulation for fuzzy controllers of autonomous mobile robots using the Firefly algorithm, Granular Comput., 4, 2, 185-195 (2019)
[23] Lai, Y. F.; Chen, M. Y.; Chiang, H. S., Constructing the lie detection system with fuzzy reasoning approach, Granular Comput., 3, 2, 169-176 (2018)
[24] Li, J.; Wang, J. Q.; Hu, J. H., Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information, Int. J. Mach. Learn. Cybern., 10, 7, 1671-1685 (2019)
[25] Liao, M. S.; Liang, G. S.; Chen, C. Y., Fuzzy grey relation method for multiple criteria decision-making problems, Qual. Quant., 47, 6, 3065-3077 (2013)
[26] Liu, H.; Zhang, L., Fuzzy rule-based systems for recognition-intensive classification in granular computing context, Granular Comput., 3, 4, 355-365 (2018)
[27] Liu, S.; Xu, Z.; Gao, J., A fuzzy compromise programming model based on the modified S-curve membership functions for supplier selection, Granular Comput., 3, 4, 275-283 (2018)
[28] Liu, Y.; Li, F. Y.; Wang, Y.; Yu, X.; Yuan, J.; Wang, Y., Assessing the environmental impact caused by power grid projects in high altitude areas based on BWM and Vague sets techniques, Sustainability, 10, 6, 1768 (2018)
[29] Mi, X.; Tang, M.; Liao, H.; Shen, W.; Lev, B., The state-of-the-art survey on integrations and applications of the best worst method in decision making: Why, what, what for and what’s next, Omega, 87, 205-225 (2019)
[30] Mou, Q.; Xu, Z.; Liao, H., An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making, Inf. Sci., 374, 224-239 (2016)
[31] Nafari, J.; Arab, A.; Ghaffari, S., Through the looking glass: Analysis of factors influencing Iranian student’s study abroad motivations and destination choice, SAGE Open, 7, 1-19 (2017)
[32] Nawaz, F.; Asadabadi, M. R.; Janjua, N. K.; Hussain, O. K.; Chang, E.; Saberi, M., An MCDM method for cloud service selection using a Markov Markov chain and the best-worst method, Knowl.-Based Syst., 159, 120-131 (2018)
[33] Pamucar, D.; Chatterjee, K.; Zavadskas, E. K., Assessment of third-party logistics provider using multi-criteria decision making approach based on interval rough numbers, Comput. Ind. Eng., 127, 383-407 (2019)
[34] Pamucar, D.; Petrovic, I.; Cirovi, G., Modification of the best-worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers, Expert Syst. Appl., 91, 89-106 (2018)
[35] Raj, A.; Srivastava, S. K., Sustainability performance assessment of an aircraft manufacturing firm, Benchmarking Int. J., 25, 1500-1527 (2018)
[36] Rezaei, J., Best-worst multi-criteria decision-making method, Omega, 53, 49-57 (2015)
[37] Rezaei, J., Best-worst multi-criteria decision-making method: Some properties and a linear, Omega, 64, 126-130 (2016)
[38] Rezaei, J.; Nispeling, T.; Sarkis, J.; Tavasszy, L., A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method, J. Clearner Prod., 135, 577-588 (2016)
[39] Rezaei, J.; Wang, J.; Tavasszy, L., Linking supplier development to supplier segmentation using best worst method, Expert Syst. Appl., 42, 23, 9152-9164 (2015)
[40] Saaty, T. L., The Analytic Hierarchy Process (1980), McGraw-Hill: McGraw-Hill New York · Zbl 0587.90002
[41] Safarzadeh, S.; Khansefid, S.; Rasti-Barzoki, M., A group multi-criteria decision-making based on best-worst method, Comput. Ind. Eng., 126, 111-121 (2018)
[42] Sahebi, I. G.; Arab, A.; Moghadam, M. R.S., Analyzing the barriers to humanitarian supply chain management: a case study of the Tehran Red Crescent societies, Int. J. Disaster Risk Reduct., 24, 232-241 (2017)
[43] Salimi, N.; Rezaei, J., Evaluating firms’ R & D performance using best worst method, Eval. Progr. Plan., 66, 147-155 (2018)
[44] Torbati, A. R.; Sayadi, M. K., A new approach to investigate the performance of insurance branches in Iran using best-worst method and fuzzy inference system, J. Soft Comput. Decis. Support Syst., 5, 4, 13-28 (2018)
[45] Wan, S.; Dong, J., Decision Making Theories and Methods Based on Interval-Valued Intuitionistic Fuzzy Sets (2020), Springer: Springer Singapore · Zbl 1470.91005
[46] Wan, S.; Wang, F.; Dong, J., Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making, Eur. J. Oper. Res., 263, 2, 571-582 (2017) · Zbl 1380.90296
[47] Wan, S. P.; Wang, F.; Dong, J. Y., A preference degree for intuitionistic fuzzy values and application to multi-attribute group decision making, Inf. Sci., 370-371, 127-146 (2016) · Zbl 1428.68303
[48] Wang, Y. M.; Elhag, T. M.S., On the normalization of interval and fuzzy weights, Fuzzy Sets Syst., 157, 2456-2471 (2006) · Zbl 1171.68764
[49] Wu, Q.; Zhou, L.; Chen, Y.; Chen, H., An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods, Inf. Sci., 502, 394-417 (2019)
[50] Zadeh, L. A., Fuzzy sets, Inf. Control, 8, 3, 338-353 (1965) · Zbl 0139.24606
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.