Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation
Abstract
The financial risk evaluation is critically vital for enterprises to identify the potential financial risks, provide decision basis for financial risk management, and prevent and reduce risk losses. In the case of considering financial risk assessment, the basic problems that arise are related to strong fuzziness, ambiguity and inaccuracy. q-rung orthopair fuzzy set (q-ROFS), portrayed by the degrees of membership and non-membership, is a more resultful tool to seize fuzziness. In this article, the novel q-rung orthopair fuzzy score function is given for dealing the comparison problem. Later, the 
and 
operations are explored and their interesting properties are discussed. Then, the objective weights are calculated by CRITIC (Criteria Importance Through Inter-criteria Correlation). Moreover, we present combined weights that reflects both subjective preference and objective preference. In addition, the q-rung orthopair fuzzy MCDM (multi-criteria decision making) algorithm based on CoCoSo (Combined Compromise Solution) is presented. Finally, the feasibility of algorithm is stated by a financial risk evaluation example with corresponding sensitivity analysis. The salient features of the proposed algorithm are that they have no counter-intuitive case and have a stronger capacity in differentiating the best alternative.
First published online 03 March 2020
Keyword : financial risk evaluation, q-rung orthopair fuzzy set, CoCoSo, combined weights, score function, CRITIC
How to Cite
Peng, X. ., & Huang, H. . (2020). Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation. Technological and Economic Development of Economy, 26(4), 695-724. https://doi.org/10.3846/tede.2020.11920
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: A guide for practitioners (1th ed.). Berlin: Springer.
Bonferroni, C. (1950). Sulle medie multiple di potenze. Bollettino Unione Matematica Italiana, 5(3–4), 267–270. http://eudml.org/doc/196058
Chen, S. M., & Tan, J. M. (1994). Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 67(2), 163–172. https://doi.org/10.1016/0165-0114(94)90084-1
Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763–770. https://doi.org/10.1016/0305-0548(94)00059-H
Du, W. S. (2018). Minkowski-type distance measures for generalized orthopair fuzzy sets. International Journal of Intelligent Systems, 33(4), 802–817. https://doi.org/10.1002/int.21968
Du, W. S. (2019). Correlation and correlation coefficient of generalized orthopair fuzzy sets. International Journal of Intelligent Systems, 34(4), 564–583. https://doi.org/10.1002/int.22065
Duan, J. (2019). Financial system modeling using Deep Neural Networks (DNNs) for effective risk assessment and prediction. Journal of the Franklin Institute, 356(8), 4716–4731. https://doi.org/10.1016/j.jfranklin.2019.01.046
Gao, J., Liang, Z., Shang, J., & Xu, Z. (2019). Continuities, derivatives and differentials of q-rung orthopair fuzzy functions. IEEE Transactions on Fuzzy Systems, 27(8), 1687–1699. https://doi.org/10.1109/TFUZZ.2018.2887187
Gerrard, R., Hiabu, M., Kyriakou, I., & Nielsen, J. P. (2019). Communication and personal selection of pension saver’s financial risk. European Journal of Operational Research, 274(3), 1102–1111. https://doi.org/10.1016/j.ejor.2018.10.038
Goda, K., & Tesfamariam, S. (2019). Financial risk evaluation of non-ductile reinforced concrete buildings in eastern and western Canada. International Journal of Disaster Risk Reduction, 33, 94–107. https://doi.org/10.1016/j.ijdrr.2018.09.013
Hong, D. H., & Choi, C. H. (2000). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114(1), 103–113. https://doi.org/10.1016/S0165-0114(98)00271-1
Huang, H. H., & Liang, Y. (2019). An integrative analysis system of gene expression using self-paced learning and SCAD-Net. Expert Systems with Applications, 135, 102–112. https://doi.org/10.1016/j.eswa.2019.06.016
Liu, D., Chen, X., & Peng, D. (2019). Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets. International Journal of Intelligent Systems, 34(7), 1572–1587. https://doi.org/10.1002/int.22108
Liu, P., & Liu, J. (2018). Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. International Journal of Intelligent Systems, 33(2), 315–347. https://doi.org/10.1002/int.21933
Liu, P., & Wang, P. (2018a). Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems, 33(2), 259–280. https://doi.org/10.1002/int.21927
Liu, P., & Wang, P. (2018b). Multiple-attribute decision making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Transactions on Fuzzy Systems, 27(5), 834–848. https://doi.org/10.1109/TFUZZ.2018.2826452
Liu, P., Chen, S. M., & Wang, P. (2018a). Multiple-attribute group decision-making based on q-rung orthopair fuzzy power Maclaurin symmetric mean operators. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 16 p. https://doi.org/10.1109/TSMC.2018.2852948
Liu, Z., Liu, P., & Liang, X. (2018b). Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment. International Journal of Intelligent Systems, 33(9), 1900–1928. https://doi.org/10.1002/int.22001
Liu, Z., Wang, S., & Liu, P. (2018c). Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators. International Journal of Intelligent Systems, 33(12), 2341–2363. https://doi.org/10.1002/int.22032
MacLaurin, C. IV. (1730). A second letter from Mr. Colin McLaurin, Professor of Mathematicks in the University of Edinburgh and F. R. S. to Martin Folkes, Esq; concerning the roots of equations, with the demonstration of other rules in algebra; being the continuation of the letter published in the Philosophical Transactions, N°394. Philosophical Transactions of the Royal Society of London, 36(408), 59–96. https://doi.org/10.1098/rstl.1729.0011
Muirhead, R. F. (1902). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21, 144–162. https://doi.org/10.1017/S001309150003460X
Peng, X., & Dai, J. (2019). Research on the assessment of classroom teaching quality with q‐rung orthopair fuzzy information based on multiparametric similarity measure and combinative distancebased assessment. International Journal of Intelligent Systems, 34(7), 1588–1630. https://doi.org/10.1002/int.22109
Peng, X., & Liu, L. (2019). Information measures for q-rung orthopair fuzzy sets. International Journal of Intelligent Systems, 34(8), 1795–1834. https://doi.org/10.1002/int.22115
Peng, X., & Selvachandran, G. (2019). Pythagorean fuzzy set: state of the art and future directions. Artificial Intelligence Review, 52(3), 1873–1927. https://doi.org/10.1007/s10462-017-9596-9
Peng, X., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 30(11), 1133–1160. https://doi.org/10.1002/int.21738
Peng, X., Dai, J., & Garg, H. (2018). Exponential operation and aggregation operator for q‐rung orthopair fuzzy set and their decision-making method with a new score function. International Journal of Intelligent Systems, 33(11), 2255–2282. https://doi.org/10.1002/int.22028
Peng, X., Krishankumar, R., & Ravichandran, K. S. (2019). Generalized orthopair fuzzy weighted distance‐ based approximation (WDBA) algorithm in emergency decision‐making. International Journal of Intelligent Systems, 34(10), 2364–2402. https://doi.org/10.1002/int.22140
Shu, X., Ai, Z., Xu, Z., & Ye, J. (2019). Integrations of q-Rung orthopair fuzzy continuous information. IEEE Transactions on Fuzzy Systems, 24(10), 1974–1985. https://doi.org/10.1109/TFUZZ.2019.2893205
Wang, J., Zhang, R., Li, L., Shang, X., Li, W., & Xu, Y. (2018, November). Some q-rung orthopair fuzzy dual Maclaurin symmetric mean operators with their application to multiple criteria decision making. In International Symposium on Knowledge and Systems Sciences. Springer, Singapore https://doi.org/10.1007/978-981-13-3149-7_19
Wang, J., Zhang, R., Zhu, X., Zhou, Z., Shang, X., & Li, W. (2019). Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. Journal of Intelligent & Fuzzy Systems, 36(2), 1599–1614. https://doi.org/10.3233/JIFS-18607
Wang, R., & Li, Y. (2018). A novel approach for green supplier selection under a q-rung orthopair fuzzy environment. Symmetry, 10(12), 687. https://doi.org/10.3390/sym10120687
Wei, G., Gao, H., & Wei, Y. (2018). Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(7), 1426–1458. https://doi.org/10.1002/int.21985
Wei, G., Wei, C., Wang, J., Gao, H., & Wei, Y. (2019). Some q‐rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. International Journal of Intelligent Systems, 34(1), 50–81. https://doi.org/10.1002/int.22042
Xing, Y., Zhang, R., Zhou, Z., & Wang, J. (2019). Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making. Soft Computing, 23(22), 11627–11649. https://doi.org/10.1007/s00500-018-03712-7
Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222– 1230. https://doi.org/10.1109/TFUZZ.2016.2604005
Yang, W., & Pang, Y. (2019). New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making. International Journal of Intelligent Systems, 34(3), 439–476. https://doi.org/10.1002/int.22060
Yazdani, M., Zarate, P., Zavadskas, E. K., & Turskis, Z. (2018). A Combined Compromise Solution (CoCoSo) method for multi-criteria decision-making problems. Management Decision, 57(9), 25012519. https://doi.org/10.1108/MD-05-2017-0458
Ye, J., Ai, Z., & Xu, Z. (2019). Single variable differential calculus under q-rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application. International Journal of Intelligent Systems, 34(7), 1387–1415. https://doi.org/10.1002/int.22100
Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. https://doi.org/10.1002/int.21676
Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: A guide for practitioners (1th ed.). Berlin: Springer.
Bonferroni, C. (1950). Sulle medie multiple di potenze. Bollettino Unione Matematica Italiana, 5(3–4), 267–270. http://eudml.org/doc/196058
Chen, S. M., & Tan, J. M. (1994). Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 67(2), 163–172. https://doi.org/10.1016/0165-0114(94)90084-1
Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763–770. https://doi.org/10.1016/0305-0548(94)00059-H
Du, W. S. (2018). Minkowski-type distance measures for generalized orthopair fuzzy sets. International Journal of Intelligent Systems, 33(4), 802–817. https://doi.org/10.1002/int.21968
Du, W. S. (2019). Correlation and correlation coefficient of generalized orthopair fuzzy sets. International Journal of Intelligent Systems, 34(4), 564–583. https://doi.org/10.1002/int.22065
Duan, J. (2019). Financial system modeling using Deep Neural Networks (DNNs) for effective risk assessment and prediction. Journal of the Franklin Institute, 356(8), 4716–4731. https://doi.org/10.1016/j.jfranklin.2019.01.046
Gao, J., Liang, Z., Shang, J., & Xu, Z. (2019). Continuities, derivatives and differentials of q-rung orthopair fuzzy functions. IEEE Transactions on Fuzzy Systems, 27(8), 1687–1699. https://doi.org/10.1109/TFUZZ.2018.2887187
Gerrard, R., Hiabu, M., Kyriakou, I., & Nielsen, J. P. (2019). Communication and personal selection of pension saver’s financial risk. European Journal of Operational Research, 274(3), 1102–1111. https://doi.org/10.1016/j.ejor.2018.10.038
Goda, K., & Tesfamariam, S. (2019). Financial risk evaluation of non-ductile reinforced concrete buildings in eastern and western Canada. International Journal of Disaster Risk Reduction, 33, 94–107. https://doi.org/10.1016/j.ijdrr.2018.09.013
Hong, D. H., & Choi, C. H. (2000). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114(1), 103–113. https://doi.org/10.1016/S0165-0114(98)00271-1
Huang, H. H., & Liang, Y. (2019). An integrative analysis system of gene expression using self-paced learning and SCAD-Net. Expert Systems with Applications, 135, 102–112. https://doi.org/10.1016/j.eswa.2019.06.016
Liu, D., Chen, X., & Peng, D. (2019). Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets. International Journal of Intelligent Systems, 34(7), 1572–1587. https://doi.org/10.1002/int.22108
Liu, P., & Liu, J. (2018). Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. International Journal of Intelligent Systems, 33(2), 315–347. https://doi.org/10.1002/int.21933
Liu, P., & Wang, P. (2018a). Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems, 33(2), 259–280. https://doi.org/10.1002/int.21927
Liu, P., & Wang, P. (2018b). Multiple-attribute decision making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Transactions on Fuzzy Systems, 27(5), 834–848. https://doi.org/10.1109/TFUZZ.2018.2826452
Liu, P., Chen, S. M., & Wang, P. (2018a). Multiple-attribute group decision-making based on q-rung orthopair fuzzy power Maclaurin symmetric mean operators. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 16 p. https://doi.org/10.1109/TSMC.2018.2852948
Liu, Z., Liu, P., & Liang, X. (2018b). Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment. International Journal of Intelligent Systems, 33(9), 1900–1928. https://doi.org/10.1002/int.22001
Liu, Z., Wang, S., & Liu, P. (2018c). Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators. International Journal of Intelligent Systems, 33(12), 2341–2363. https://doi.org/10.1002/int.22032
MacLaurin, C. IV. (1730). A second letter from Mr. Colin McLaurin, Professor of Mathematicks in the University of Edinburgh and F. R. S. to Martin Folkes, Esq; concerning the roots of equations, with the demonstration of other rules in algebra; being the continuation of the letter published in the Philosophical Transactions, N°394. Philosophical Transactions of the Royal Society of London, 36(408), 59–96. https://doi.org/10.1098/rstl.1729.0011
Muirhead, R. F. (1902). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21, 144–162. https://doi.org/10.1017/S001309150003460X
Peng, X., & Dai, J. (2019). Research on the assessment of classroom teaching quality with q‐rung orthopair fuzzy information based on multiparametric similarity measure and combinative distancebased assessment. International Journal of Intelligent Systems, 34(7), 1588–1630. https://doi.org/10.1002/int.22109
Peng, X., & Liu, L. (2019). Information measures for q-rung orthopair fuzzy sets. International Journal of Intelligent Systems, 34(8), 1795–1834. https://doi.org/10.1002/int.22115
Peng, X., & Selvachandran, G. (2019). Pythagorean fuzzy set: state of the art and future directions. Artificial Intelligence Review, 52(3), 1873–1927. https://doi.org/10.1007/s10462-017-9596-9
Peng, X., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 30(11), 1133–1160. https://doi.org/10.1002/int.21738
Peng, X., Dai, J., & Garg, H. (2018). Exponential operation and aggregation operator for q‐rung orthopair fuzzy set and their decision-making method with a new score function. International Journal of Intelligent Systems, 33(11), 2255–2282. https://doi.org/10.1002/int.22028
Peng, X., Krishankumar, R., & Ravichandran, K. S. (2019). Generalized orthopair fuzzy weighted distance‐ based approximation (WDBA) algorithm in emergency decision‐making. International Journal of Intelligent Systems, 34(10), 2364–2402. https://doi.org/10.1002/int.22140
Shu, X., Ai, Z., Xu, Z., & Ye, J. (2019). Integrations of q-Rung orthopair fuzzy continuous information. IEEE Transactions on Fuzzy Systems, 24(10), 1974–1985. https://doi.org/10.1109/TFUZZ.2019.2893205
Wang, J., Zhang, R., Li, L., Shang, X., Li, W., & Xu, Y. (2018, November). Some q-rung orthopair fuzzy dual Maclaurin symmetric mean operators with their application to multiple criteria decision making. In International Symposium on Knowledge and Systems Sciences. Springer, Singapore https://doi.org/10.1007/978-981-13-3149-7_19
Wang, J., Zhang, R., Zhu, X., Zhou, Z., Shang, X., & Li, W. (2019). Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. Journal of Intelligent & Fuzzy Systems, 36(2), 1599–1614. https://doi.org/10.3233/JIFS-18607
Wang, R., & Li, Y. (2018). A novel approach for green supplier selection under a q-rung orthopair fuzzy environment. Symmetry, 10(12), 687. https://doi.org/10.3390/sym10120687
Wei, G., Gao, H., & Wei, Y. (2018). Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(7), 1426–1458. https://doi.org/10.1002/int.21985
Wei, G., Wei, C., Wang, J., Gao, H., & Wei, Y. (2019). Some q‐rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. International Journal of Intelligent Systems, 34(1), 50–81. https://doi.org/10.1002/int.22042
Xing, Y., Zhang, R., Zhou, Z., & Wang, J. (2019). Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making. Soft Computing, 23(22), 11627–11649. https://doi.org/10.1007/s00500-018-03712-7
Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222– 1230. https://doi.org/10.1109/TFUZZ.2016.2604005
Yang, W., & Pang, Y. (2019). New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making. International Journal of Intelligent Systems, 34(3), 439–476. https://doi.org/10.1002/int.22060
Yazdani, M., Zarate, P., Zavadskas, E. K., & Turskis, Z. (2018). A Combined Compromise Solution (CoCoSo) method for multi-criteria decision-making problems. Management Decision, 57(9), 25012519. https://doi.org/10.1108/MD-05-2017-0458
Ye, J., Ai, Z., & Xu, Z. (2019). Single variable differential calculus under q-rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application. International Journal of Intelligent Systems, 34(7), 1387–1415. https://doi.org/10.1002/int.22100
Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. https://doi.org/10.1002/int.21676