In the current era of big data and artificial intelligence, multi-criteria decision-making is facing numerous uncertain issues such as incomplete information and ambiguous evaluation. Nevertheless, the traditional precise mathematical models have significant limitations when it comes to expressing these uncertainties. In order to better address these kinds of uncertainty issues, the CC-integral on the interval-valued Sugeno probability measure has been proposed in this paper. By introducing the Choquet integral based on the Copula, a reasonable measure and integral are established to solve the complexity of the decision environment. Among them, due to different Copula functions, the application of the Choquet integral based on Copula is more extensive. So as to verify the effectiveness of the proposed method, it was applied to the end-of-life (EOL) strategy problem. Comparing with the decision results of the Choquet integral based on triangular norms, it is found that the method proposed in this paper is more accurate, simpler to calculate, and has a smaller computational cost.
References
[1]
Choquet, G. (1954) Theory of Capacities. Annales de l’Institut Fourier, 5, 131-295. https://doi.org/10.5802/aif.53
[2]
Sugeno, M. and Murofushi, T. (1987) Pseudo-Additive Measures and Integrals. Journal of Mathematical Analysis and Applications, 122, 197-222. https://doi.org/10.1016/0022-247x(87)90354-4
[3]
Barrenechea, E., Bustince, H., Fernandez, J., Paternain, D. and Sanz, J. (2013) Using the Choquet Integral in the Fuzzy Reasoning Method of Fuzzy Rule-Based Classification Systems. Axioms, 2, 208-223. https://doi.org/10.3390/axioms2020208
[4]
Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Mesiar, R., Kolesarova, A., et al. (2016) Preaggregation Functions: Construction and an Application. IEEE Transactions on Fuzzy Systems, 24, 260-272. https://doi.org/10.1109/tfuzz.2015.2453020
[5]
Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Asiain, M.J., Elkano, M., et al. (2017) CC-Integrals: Choquet-Like Copula-Based Aggregation Functions and Its Application in Fuzzy Rule-Based Classification Systems. Knowledge-Based Systems, 119, 32-43. https://doi.org/10.1016/j.knosys.2016.12.004
[6]
Lucca, G., Antonio Sanz, J., Dimuro, G.P., Bedregal, B., Bustince, H. and Mesiar, R. (2018) CF-Integrals: A New Family of Pre-Aggregation Functions with Application to Fuzzy Rule-Based Classification Systems. Information Sciences, 435, 94-110. https://doi.org/10.1016/j.ins.2017.12.029
[7]
Dimuro, G.P., Fernández, J., Bedregal, B., Mesiar, R., Sanz, J.A., Lucca, G., et al. (2020) The State-of-Art of the Generalizations of the Choquet Integral: From Aggregation and Pre-Aggregation to Ordered Directionally Monotone Functions. Information Fusion, 57, 27-43. https://doi.org/10.1016/j.inffus.2019.10.005
[8]
Schmeidler, D. (1986) Integral Representation without Additivity. Proceedings of the American Mathematical Society, 97, 255-261. https://doi.org/10.1090/s0002-9939-1986-0835875-8
[9]
Tanaka, K. and Sugeno, M. (1991) A Study on Subjective Evaluations of Printed Color Images. International Journal of Approximate Reasoning, 5, 213-222. https://doi.org/10.1016/0888-613x(91)90009-b
[10]
Chen, S. and Hwang, C.L. (1992) Fuzzy Multiple Attribute Decision-Making: Methods and Application. Springer.
[11]
Garg, H., Krishankumar, R. and Ravichandran, K.S. (2022) Decision Framework with Integrated Methods for Group Decision-Making under Probabilistic Hesitant Fuzzy Context and Unknown Weights. Expert Systems with Applications, 200, Article 117082. https://doi.org/10.1016/j.eswa.2022.117082
[12]
Garg, H. (2018) Some Methods for Strategic Decision-Making Problems with Immediate Probabilities in Pythagorean Fuzzy Environment. International Journal of Intelligent Systems, 33, 687-712. https://doi.org/10.1002/int.21949
[13]
Rani, P., Govindan, K., Mishra, A.R., Mardani, A., Alrasheedi, M. and Hooda, D.S. (2020) Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection. Symmetry, 12, Article 90. https://doi.org/10.3390/sym12010090
[14]
Wieczynski, J.C., Lucca, G. and Borges, E. (2021) CC-Separation Measure Applied in Business Group Decision Making. Proceedings of the 23rd International Conference on Enterprise Information Systems, Online, 26-28 April 2021, 26-28.
[15]
Wieczynski, J.C., Fumanal-Idocin, J. and Lucca, G. (2022) d-XC Integrals: On the Generalization of the Expanded Form of the Choquet Integral by Restricted Dissimilarity Functions and Their Applications. IEEETransactionsonFuzzySystems, 30, 5376-5389. https://doi.org/10.1109/tfuzz.2022.3176916
[16]
Di Marco, P., Eubanks, C.F. and Ishii, K. (1994) Compatibility Analysis of Product Design for Recyclability and Reuse. ASME 1994 International Computers in Engineering Conference and Exhibition, Minneapolis, 11-14 September 1994, 11-14. https://doi.org/10.1115/cie1994-0392
[17]
Ma, J., Kremer, G.E.O. and Ray, C.D. (2018) A Comprehensive End-of-Life Strategy Decision Making Approach to Handle Uncertainty in the Product Design Stage. Research in Engineering Design, 29, 469-487. https://doi.org/10.1007/s00163-017-0277-0
[18]
Chen, L., Duan, G., Wang, S. and Ma, J. (2020) A Choquet Integral Based Fuzzy Logic Approach to Solve Uncertain Multi-Criteria Decision Making Problem. Expert Systems with Applications, 149, Article 113303. https://doi.org/10.1016/j.eswa.2020.113303
[19]
Yang, H., Shang, L.Y. and Gong, Z.T. (2022) CC-Integral on Interval-Valued Sugeno Probability Measure and Its Application in Multi-Criteria Decision-Making Problems. Axioms, 11, Article 317.
[20]
Sugeno, M. (1974) Theory of Fuzzy Integral and Its Application. Doctorial Dissertation, Tokyo Institute of Technology.
[21]
Mayor, G. and Trillas, E. (1986) On the Representation of Some Aggregation Functions. Proceedings of IEEE International Symposium on Multiple-Valued Logic, Los Alamitos, 27-29 May 1986, 110-114.
[22]
Alsina, C., Frank, M.J. and Schweizer, B. (2006). Associative Functions: Triangular Norms and Copulas. World Scientific Publishing. https://doi.org/10.1142/9789812774200
[23]
Bustince, H., Fernandez, J., Mesiar, R., Montero, J. and Orduna, R. (2010) Overlap Functions. Nonlinear Analysis: Theory, Methods & Applications, 72, 1488-1499. https://doi.org/10.1016/j.na.2009.08.033
[24]
Nelsen, R.B. (1999) An Introduction to Copulas. Springer.
[25]
Dimuro, G.P. and Bedregal, B. (2014) Archimedean Overlap Functions: The Ordinal Sum and the Cancellation, Idempotency and Limiting Properties. FuzzySetsandSystems, 252, 39-54. https://doi.org/10.1016/j.fss.2014.04.008
[26]
Klement, E.P., Mesiar, R. and Pap, E. (2000) Triangular Norms. Kluwer Academic Publisher.
[27]
Wang, Z. and Zklir, G.J. (1992) Fuzzy Measure Theory. Plenum Press.
[28]
Beliakov, G., Pradera, A. and Calvo, T. (2007) Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing, Springer. https://doi.org/10.1007/978-3-540-73721-6
[29]
Guo, Y.W. (2021) Interval-Valued Choquet Integrals and Their Properties. Journal of Shanxi Normal University (Natural Science Edition), 35, 16-21.
[30]
Chung, W., Okudan, G.E. and Wysk, R.A. (2011) A Modular Design Approach to Improve the Life Cycle Performance Derived from Optimized Closed-Loop Suply Chain. Proceedings of the ASME 2011 International Design Engineering Technical Conference Computers and Information in Engineering Conference, Washington, 28-31 August 2011, 28-31.
