A possibilistic programming approach for biomass supply chain network design under hesitant fuzzy membership function estimation

Document Type : Article

Authors

Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran

Abstract

The recognition of membership function by knowledge acquisition from experts is an important factor for many fuzzy mathematical programming models. Thus, the hesitant fuzzy membership function (HFMF) estimation could help users of the mathematical programming approaches to provide a powerful solution in continuous space problems. Therefore, this study proposes a possibilistic programming approach based on Bezier curve mechanism for estimating the HFMF. In the process of possibilistic programming approach, an optimization model is presented to tune the primary parameters of Bezier curve by the goal of minimizing the sum of the squared errors (SSE) between the empirical data and fitted HFMF. After that, the efficiency and applicability of the proposed approach is checked by proposing a novel mathematical model for biomass supply chain network design problem. In this case, the bio-products demand is declared as an imprecise parameter that follows from the estimated HFMF to increase the accuracy of the obtained results by addressing the uncertainty and unreliability of the information. Finally, a computational experiment and validation procedure about the biomass supply chain network design is provided to peruse the verification and validation of the proposed approaches.

Keywords

References

References:
1. Medasani, S., Kim, J., and Krishnapuram, R. "An overview of membership function generation techniques for pattern recognition", International Journal of Approximate Reasoning, 19(3-4), pp. 391-417 (1998). https://doi.org/10.1016/S0888- 613X(98)10017-8.
2. Bilgic, T. and Turksen, I.B. "Measurement of membership functions: theoretical and empirical work, in fundamentals of fuzzy sets", Springer, pp. 195- 227 (2000). https://doi.org/10.1061/(ASCE)CO.1943- 7862.0002015.
3. Uddin, M.S., Miah, M., Khan, M.A.-A., et al. "Goal programming tactic for uncertain multi-objective transportation problem using fuzzy linear membership function", Alexandria Engineering Journal, 60(2), pp. 2525-2533 (2021). https://doi.org/10.1016/j.aej.2020.12.039.
4. Ashtari, P., Karami, R., and Farahmand-Tabar, S. "Optimum geometrical pattern and design of real-size diagrid structures using accelerated fuzzygenetic algorithm with bilinear membership function", Applied Soft Computing, 110, p. 107646 (2021). https://doi.org/10.1016/j.asoc.2021.107646.
5. Xu, P., Liu, B., Hu, X., et al. "State-of-charge estimation for lithium-ion batteries based on fuzzy information granulation and asymmetric gaussian membership function", IEEE Transactions on Industrial Electronics, 69(7), pp. 6635-6644 (2021). https://doi.org/10.1109/TIE.2021.3097613.
6. Gao, J., Yao, J., and Chen, L. "The statistical methods of membership function in structural serviceability failure criterion", KSCE Journal of Civil Engineering, 25, pp. 1-8 (2021). https://doi.org/10.1007/s12205- 021-2089-z.
7. Ubukata, S., Notsu, A., and Honda, K. "Objective function-based rough membership C-means clustering", Information Sciences, 548, pp. 479-496 (2021).https://doi.org/10.1016/j.ins.2020.10.037.
8. Lin, F.-J., Chen, C.-I., Xiao, G.-D., et al. "Voltage stabilization control for microgrid with asymmetric membership function based wavelet petri fuzzy neural network", IEEE Transactions on Smart Grid, 548 (2021). https://doi.org/10.1109/TSG.2021.3071357.
9. Pelalak, R., Nakhjiri, A.T., Marjani, A., et al. "Influence of machine learning membership functions and degree of membership function on each input parameter for simulation of reactors", Scientific Reports, 11(1), pp. 1-11 (2021). https://doi.org/10.1038/s41598-021- 81514-y.
10. Meng, F., Tan, C., and Chen, X. "Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study", Omega, 68, pp. 17-38 (2017). https://doi.org/10.1016/j.omega.2016.05.006.
11. Yang, L., Zhou, X., and Gao, Z. "Credibility-based rescheduling model in a double-track railway network: a fuzzy reliable optimization approach", Omega, 48, pp. 75-93 (2014). https://doi.org/10.1016/j.omega.2013.11.004.
12. Anighoro, A. and Bajorath, J. "Compound ranking based on fuzzy three-dimensional similarity improves the performance of docking into homology models of G-protein-coupled receptors", ACS Omega, 2(6), pp. 2583-2592 (2017). https://doi.org/10.1021/acsomega.7b00330.
13. Krampe, V., Edme, P., and Maurer, H. "A suitable objective function for optimizing the experimental design for seismic full waveform inversion", In 82nd EAGE Annual Conference and Exhibition, European Association of Geoscientists and Engineers (2020). https://doi.org/10.3997/2214-4609.202010737.
14. Turksen, I. "Measurement of membership functions and their acquisition", Fuzzy Sets and Systems, 40(1), pp. 5-38 (1991). https://doi.org/10.1016/0165- 0114(91)90045-R.
15. Klir, G. and Yuan, B., Fuzzy Sets and Fuzzy Logic, 4. Prentice hall New Jersey (1995). https://doi.org/10.1007/978-3-642-34895-2 1.
16. Medaglia, A.L., Fang, S.-C., Nuttle, H.L. et al. "An efficient and  flexible mechanism for constructing membership functions", European Journal of Operational Research, 139(1), pp. 84-95 (2002). https://doi.org/10.1016/S0377-2217(01)00157-6.
17. Zimmermann, H.-J. and Zysno, P. "Quantifying vagueness in decision models", European Journal of Operational Research, 22(2), pp. 148-158 (1985). https://doi.org/10.1016/0377-2217(85)90223-1.
18. Chen, J.E. and Otto, K.N. "Constructing membership functions using interpolation and measurement theory", Fuzzy Sets and Systems, 73(3), pp. 313-327 (1995). https://doi.org/10.1016/0165-0114(94)00322-X..
19. Marchant, T. "A measurement-theoretic axiomatization of trapezoidal membership functions", IEEE Transactions on Fuzzy Systems, 15(2), pp. 238-242 (2007). https://doi.org/10.1109/TFUZZ.2006.880000.
20. Huynh, V.-N., Nakamori, Y., Ho, T.B., et al. "A context model for constructing membership functions of fuzzy concepts based on modal logic", In International Symposium on Foundations of Information and Knowledge Systems, Springer (2002). https://doi.org/10.1007/3-540-45758-5 7.
21. Chen, S. and Tsai F. "A new method to construct membership functions and generate fuzzy rules from training instances", International Journal of Information and Management Sciences, 16(2), p. 47 (2005). https://doi.org/10.1109/FUZZY.2004.1375510.
22. Sanchez, A., Alvarez, R., Moctezuma, J., et al. "Clustering and artificial neural networks as a tool to generate membership functions", In Electronics, Communications and Computers, CONIELECOMP, 16th International Conference on IEEE (2006). https://doi.org/10.1109/CONIELECOMP.2006.22.
23. Sami, M. and Badie. K. "Generating fuzzy membership functions through a meta-function: An experience mining approach", In Automation Congress, 2006. WAC'06. World. IEEE (2006). https://doi.org/10.1109/WAC.2006.376030.
24. Jain, S. and Khare, M. "Construction of fuzzy membership functions for urban vehicular exhaust emissions modeling", Environmental Monitoring and Assessment, 167(1-4), pp. 691-699 (2010). https://doi.org/10.1007/s10661-009-1085-4.
25. Bouhentala, M., Ghanai, M., and Chafaa, K. "Intervalvalued membership function estimation for fuzzy modeling", Fuzzy Sets and Systems, 361, pp. 101-113 (2019). https://doi.org/10.1016/j.fss.2018.06.008.
26. Mousavi, M., Gitinavard, H., and Mousavi, S. "A soft computing based-modified ELECTRE model for renewable energy policy selection with unknown information", Renewable and Sustainable Energy Reviews, 68, pp. 774-787 (2017). https://doi.org/10.1016/j.rser.2016.09.125.
27. Wu, P., Li, H., Merigo, J.M., et al. "Integer programming modeling on group decision making with incomplete hesitant fuzzy linguistic preference relations", IEEE Access, 7, pp. 136867-136881 (2019). https://doi.org/10.1109/ACCESS.2019.2942412.
28. Wan, S.-P., Qin, Y.-L., and Dong, J.-Y. "A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees", Knowledge-Based Systems, 138, pp. 232-248 (2017).https://doi.org/10.1016/j.knosys.2017.10.002.
29. Song, Y. and Li, G. "A mathematical programming approach to manage group decision making with incomplete hesitant fuzzy linguistic preference relations", Computers and Industrial Engineering, 135, pp. 467- 475 (2019). https://doi.org/10.1016/j.cie.2019.06.036.
30. Li, J. and Wang, Z.-x. "A programming model for consistency and consensus in group decision making with probabilistic hesitant fuzzy preference relations", International Journal of Fuzzy Systems, 20(8), pp. 2399-2414 (2018). https://doi.org/10.1007/s40815- 018-0501-8.
31. Zhang, Y., Tang, J., and Meng, F. "Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations", Applied Intelligence, 49(3), pp. 837-857 (2019). https://doi.org/10.1007/s10489-018- 1292-1.
32. Rashid, T. and Sindhu, M.S. "Application of linear programming model in multiple criteria decision making under the framework of interval-valued hesitant fuzzy sets", In International Conference on Intelligent and Fuzzy Systems, Springer (2020). https://doi.org/10.1007/978-3-030-51156-2 34.
33. Wei, G., Alsaadi, F.E., Hayat, T., et al. "A linear assignment method for multiple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure", International Journal of Fuzzy Systems, 19(3), pp. 607-614 (2017). https://doi.org/10.1007/s40815-016- 0177-x.
34. Azadeh, A., Babazadeh, R., and Asadzadeh, S. "Optimum estimation and forecasting of renewable energy consumption by artificial neural networks", Renewable and Sustainable Energy Reviews, 27, pp. 605-612 (2013). https://doi.org/10.1016/j.rser.2013.07.007.
35. Ghaderi, H., Moini, A. and Pishvaee, M.S. "A multiobjective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design", Journal of Cleaner Production, 179, pp. 368-406 (2018). https://doi.org/10.1016/j.jclepro.2017.12.218.
36. Ghaderi, H., Pishvaee, M.S., and Moini, A. "Biomass supply chain network design: an optimization-oriented review and analysis", Industrial Crops and Products, 94, pp. 972-1000 (2016). https://doi.org/10.1016/j.indcrop.2016.09.027.
37. Babazadeh, R., Razmi, J., Rabbani, M., et al. "An integrated data envelopment analysis-mathematical programming approach to strategic biodiesel supply chain network design problem", Journal of Cleaner Production, 147, pp. 694-707 (2017). https://doi.org/10.1016/j.jclepro.2015.09.038.
38. Bai, Y., Hwang, T., Kang, S., et al. "Biofuel  refinery location and supply chain planning under traffic congestion", Transportation Research Part B: Methodological, 45(1), pp. 162-175 (2011). https://doi.org/10.1016/j.trb.2010.04.006.
39. Bai, Y., Ouyang, Y., and Pang, J.-S. "Biofuel supply chain design under competitive agricultural land use and feedstock market equilibrium", Energy Economics, 34(5), pp. 1623-1633 (2012). https://doi.org/10.1016/j.eneco.2012.01.003.
40. Tong, K., You, F., and Rong G. "Robust design and operations of hydrocarbon biofuel supply chain integrating with existing petroleum refineries considering unit cost objective", Computers and Chemical Engineering, 68, pp. 128-139 (2014). https://doi.org/10.1016/j.compchemeng.2014.05.003.
41. Li, Q. and Hu G. "Supply chain design under uncertainty for advanced biofuel production based on bio-oil gasification", Energy, 74, pp. 576-584 (2014). https://doi.org/10.1016/j.energy.2014.07.023.
42. Mohseni, S. and Pishvaee M.S. "A robust programming approach towards design and optimization of microalgae-based biofuel supply chain", Computers and Industrial Engineering, 100, pp. 58-71 (2016). https://doi.org/10.1016/j.cie.2016.08.003.
43. Kesharwani, R., Sun, Z., and Dagli C. "Biofuel supply chain optimal design considering economic, environmental, and societal aspects towards sustainability", International Journal of Energy Research, 42(6), pp. 2169-2198 (2018). https://doi.org/10.1002/er.4006.
44. Fattahi, M. and Govindan K. "A multi-stage stochastic program for the sustainable design of biofuel supply chain networks under biomass supply uncertainty and disruption risk: A real-life case study", Transportation Research Part E: Logistics and Transportation Review, 118, pp. 534-567 (2018). https://doi.org/10.1016/j.tre.2018.08.008.
45. Farin, G., Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, Elsevier (2014).https://doi.org/10.1137/1033072.
46. Torra, V. and Narukawa. Y. "On hesitant fuzzy sets and decision. in Fuzzy Systems", FUZZ-IEEE 2009. IEEE International Conference on. 2009. IEEE 2009. https://doi.org/10.1109/FUZZY.2009.5276884.
47. Torra, V. "Hesitant fuzzy sets", International Journal of Intelligent Systems, 25(6), pp. 529-539 (2010). https://doi.org/10.1002/int.20418.
48. Xia, M. and Xu, Z. "Hesitant fuzzy information aggregation in decision making", International Journal of Approximate Reasoning, 52(3), pp. 395-407 (2011). https://doi.org/10.1016/j.ijar.2010.09.002.
49. Xu, Z. and Zhang, X. "Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information", Knowledge-Based Systems, 52, pp. 53-64 (2013). https://doi.org/10.1016/j.knosys.2013.05.011.
50. Pishvaee, M.S. and Torabi, S.A. "A possibilistic  programming approach for closed-loop supply chain network design under uncertainty", Fuzzy Sets and Systems, 161(20), pp. 2668-2683 (2010). https://doi.org/10.1016/j.fss.2010.04.010.
51. Parra, M.A., Terol, A.B. Gladish, B.P., et al. "Solving a multiobjective possibilistic problem through compromise programming", European Journal of Operational Research, 164(3), pp. 748-759 (2005). https://doi.org/10.1016/j.ejor.2003.11.028.
52. Jimenez, M., Arenas, M., Bilbao, A., et al. "Linear programming with fuzzy parameters: an interactive method resolution", European Journal of Operational Research, 177(3), pp. 1599-1609 (2007). https://doi.org/10.1016/j.ejor.2005.10.002.
53. Jimenez, M. "Ranking fuzzy numbers through the comparison of its expected intervals", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4(04), pp. 379-388 (1996). https://doi.org/10.1142/S0218488596000226.
Scientia Iranica
Volume 31, Issue 18
Transactions on Industrial Engineering (E)
November and December 2024
Pages 1606-1624

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