Designing a sustainable closed-loop supply chain using robust possibilistic-stochastic programming in pentagonal fuzzy numbers
Abstract
The lack of information and hybrid uncertainties in Supply Chain (SC) parameters affect managerial decisions. It is inevitable to consider random uncertainty based on fuzzy scenarios and cognitive uncertainty to model a Sustainable Closed-Loop SC (SCLSC) problem. Using Pentagonal Fuzzy Numbers (PFNs) has higher comprehensiveness and accuracy than triangular and trapezoidal fuzzy numbers due to taking into account higher uncertainty, less lack of information, and taking into account maximum subjectivity Decision-Makers (DMs). There is a gap in the literature regarding the use of PFNs in SCLSC problems. This research presents a new model using PFNs to solve deficiencies in stochastic-possibilistic programming. Developing a Robust Stochastic-Possibilistic (RSP) based on PFNs under fuzzy scenarios, presenting measures of necessity, possibility, and credibility for making decisions founded on different levels of DMs’ risk, and proposing global solutions through providing linear programming models are the main innovations and contributions of the present research. An actual case study evaluates the presented approach to reduce the cost and carbon pollution in the stone paper SC. In the suggested method, trade-offs could be formed between the mean of objective functions and risk by modifying the robustness coefficients. According to the proposed approach, an optimal value of confidence is specified. Additionally, robustness deviations are controlled in the model, which results in more accurate and reliable results. Numerical simulations confirmed the efficacy of the robust approach proposed.
First published online 7 February 2025
Keyword : closed-loop supply chain, possibilistic programming, fuzzy scenarios, robust approach, sustainable design, stochastic programming
How to Cite
Hosseini Dehshiri, S. J., Amiri, M., Hajiaghaei-Keshteli, M., Keshavarz-Ghorabaee, M., Zavadskas, E. K., & Antuchevičienė, J. (2024). Designing a sustainable closed-loop supply chain using robust possibilistic-stochastic programming in pentagonal fuzzy numbers. Transport, 39(4), 323–349. https://doi.org/10.3846/transport.2024.23099
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Abdolazimi, O.; Salehi Esfandarani, M.; Salehi, M.; Shishebori, D. 2020. Robust design of a multi-objective closed-loop supply chain by integrating on-time delivery, cost, and environmental aspects, case study of a tire factory, Journal of Cleaner Production 264: 121566. https://doi.org/10.1016/j.jclepro.2020.121566
Ala, A.; Simic, V.; Bacanin, N.; Babaee Tirkolaee, E. B. 2024. Blood supply chain network design with lateral freight: a robust possibilistic optimization model, Engineering Applications of Artificial Intelligence 133: 108053. https://doi.org/10.1016/j.engappai.2024.108053
Alharbi, M. G.; El-Wahed Khalifa, H. A. 2021. On a flow-shop scheduling problem with fuzzy pentagonal processing time, Journal of Mathematics 2021: 6695174. https://doi.org/10.1155/2021/6695174
Amoozad Mahdiraji, H.; Beheshti, M.; Razavi Hajiagha, S. H.; Zavadskas, E. K. 2018. A fuzzy binary bi objective transportation model: Iranian steel supply network, Transport 33(3): 810–820. https://doi.org/10.3846/transport.2018.5800
Anitha, P.; Parvathi, P. 2017. An inventory model with stock dependent demand, two parameter Weibull distribution deterioration in a fuzzy environment, in 2016 Online International Conference on Green Engineering and Technologies (IC-GET), 19 November 2016, Coimbatore, India, 1–8. https://doi.org/10.1109/GET.2016.7916660
Atabaki, M. S.; Mohammadi, M.; Naderi, B. 2020. New robust optimization models for closed-loop supply chain of durable products: towards a circular economy, Computers & Industrial Engineering 146: 106520. https://doi.org/10.1016/j.cie.2020.106520
Avakh Darestani, S.; Hemmati, M. 2019. Robust optimization of a bi-objective closed-loop supply chain network for perishable goods considering queue system, Computers & Industrial Engineering 136: 277–292. https://doi.org/10.1016/j.cie.2019.07.018
Babaee Tirkolaee, E. B.; Golpîra, H.; Javanmardan, A.; Maihami, R. 2023. A socio-economic optimization model for blood supply chain network design during the COVID-19 pandemic: an interactive possibilistic programming approach for a real case study, Socio-Economic Planning Sciences 85: 101439. https://doi.org/10.1016/j.seps.2022.101439
Baghizadeh, K.; Cheikhrouhou, N.; Govindan, K.; Ziyarati, M. 2022. Sustainable agriculture supply chain network design considering water-energy-food nexus using queuing system: a hybrid robust possibilistic programming, Natural Resource Modeling 35(1): e12337. https://doi.org/10.1111/nrm.12337
Báez-Sánchez, A.; Flores-Franulic, A.; Moretti, A. C.; Chalco-Cano, Y.; Rojas-Medar, M. A. 2022. Weighted polygonal approximation of fuzzy numbers preserving their main characteristics, Fuzzy Sets and Systems 443: 34–51. https://doi.org/10.1016/j.fss.2021.11.002
Chakraborty, A.; Pal, S.; Mondal, S. P.; Alam, S. 2022. Nonlinear pentagonal intuitionistic fuzzy number and its application in EPQ model under learning and forgetting, Complex & Intelligent Systems 8(2): 1307–1322. https://doi.org/10.1007/s40747-021-00574-9
Chen, Z.-S.; Zhu, Z.; Wang, Z.-J.; Tsang, Y. 2023. Fairness-aware large-scale collective opinion generation paradigm: A case study of evaluating blockchain adoption barriers in medical supply chain, Information Sciences 635: 257–278. https://doi.org/10.1016/j.ins.2023.03.135
Dehghan, E.; Shafiei Nikabadi, M. S.; Amiri, M.; Jabbarzadeh, A. 2018. Hybrid robust, stochastic and possibilistic programming for closed-loop supply chain network design, Computers & Industrial Engineering 123: 220–231. https://doi.org/10.1016/j.cie.2018.06.030
Dhanamandand, K.; Parimaldevi, M. 2016. Cost analysis on a probabilistic multi objective-multi item inventory model using pentagonal fuzzy number, Global Journal of Applied Mathematics and Mathematics Sciences 9: 151–163.
Farrokh, M.; Azar, A.; Jandaghi, G.; Ahmadi, E. 2018. A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty, Fuzzy Sets and Systems 341: 69–91. https://doi.org/10.1016/j.fss.2017.03.019
Foroozesh, N.; Karimi, B.; Mousavi, S. M. 2022. Green-resilient supply chain network design for perishable products considering route risk and horizontal collaboration under robust interval-valued type-2 fuzzy uncertainty: a case study in food industry, Journal of Environmental Management 307: 114470. https://doi.org/10.1016/j.jenvman.2022.114470
Gao, Y.; Lu, S.; Cheng, H.; Liu, X. 2024. Data-driven robust optimization of dual-channel closed-loop supply chain network design considering uncertain demand and carbon cap-and-trade policy, Computers & Industrial Engineering 187: 109811. https://doi.org/10.1016/j.cie.2023.109811
Garai, A.; Chowdhury, S.; Sarkar, B.; Roy, T. K. 2021. Cost-effective subsidy policy for growers and biofuels-plants in closed-loop supply chain of herbs and herbal medicines: an interactive bi-objective optimization in T-environment, Applied Soft Computing 100: 106949. https://doi.org/10.1016/j.asoc.2020.106949
Ghahremani-Nahr, J.; Kian, R.; Sabet, E. 2019. A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm, Expert Systems with Applications 116: 454–471. https://doi.org/10.1016/j.eswa.2018.09.027
Ghahremani-Nahr, J.; Kian, R.; Sabet, E.; Akbari, V. 2022. A bi-objective blood supply chain model under uncertain donation, demand, capacity and cost: a robust possibilistic-necessity approach, Operational Research 22: 4685–4723. https://doi.org/10.1007/s12351-022-00710-4
Ghasemi, P.; Goodarzian, F.; Abraham, A.; Khanchehzarrin, S. 2022. A possibilistic-robust-fuzzy programming model for designing a game theory based blood supply chain network, Applied Mathematical Modelling 112: 282–303. https://doi.org/10.1016/j.apm.2022.08.003
Ghosh, S.; Roy, S. K. 2023. Closed-loop multi-objective waste management through vehicle routing problem in neutrosophic hesitant fuzzy environment, Applied Soft Computing 148: 110854. https://doi.org/10.1016/j.asoc.2023.110854
Gilani, H.; Sahebi, H. 2021. Optimal design and operation of the green pistachio supply network: a robust possibilistic programming model, Journal of Cleaner Production 282: 125212. https://doi.org/10.1016/j.jclepro.2020.125212
Guo, Y.; Shi, Q.; Wang, Y.; Song, M.; Wu, W. 2024. A scenario-based robust possibilistic-flexible programming model for responsive supply chain network design with a performance-oriented solution methodology, Expert Systems with Applications 238: 121895. https://doi.org/10.1016/j.eswa.2023.121895
Günay, E. E.; Okudan Kremer, G. E.; Zarindast, A. 2021. A multi-objective robust possibilistic programming approach to sustainable public transportation network design, Fuzzy Sets and Systems 412: 106–129. https://doi.org/10.1016/j.fss.2020.09.007
Habib, M. S.; Asghar, O.; Hussain, A.; Imran, M.; Mughal, M. P.; Sarkar, B. 2021. A robust possibilistic programming approach toward animal fat-based biodiesel supply chain network design under uncertain environment, Journal of Cleaner Production 278: 122403. https://doi.org/10.1016/j.jclepro.2020.122403
Habib, M. S.; Maqsood, M. H.; Ahmed, N.; Tayyab, M.; Omair, M. 2022. A multi-objective robust possibilistic programming approach for sustainable disaster waste management under disruptions and uncertainties, International Journal of Disaster Risk Reduction 75: 102967. https://doi.org/10.1016/j.ijdrr.2022.102967
Hassanpour, A.; Bagherinejad, J.; Bashiri, M. 2019. A robust leader-follower approach for closed loop supply chain network design considering returns quality levels, Computers & Industrial Engineering 136: 293–304. https://doi.org/10.1016/j.cie.2019.07.031
Hemalatha, S.; Annadurai, K. 2023. A fuzzy EOQ inventory model with advance payment and various fuzzy numbers, Indian Journal of Science and Technology 16(27): 2076–2089. https://doi.org/10.17485/IJST/v16i27.451
Hosseini Dehshiri, S. J.; Amiri, M. 2024. Considering the circular economy for designing closed-loop supply chain under hybrid uncertainty: a robust scenario-based possibilistic-stochastic programming, Expert Systems with Applications 238: 121745. https://doi.org/10.1016/j.eswa.2023.121745
Hosseini Dehshiri, S. J.; Amiri, M.; Mostafaeipour, A.; Le, T. 2024. Evaluation of renewable energy projects based on sustainability goals using a hybrid Pythagorean fuzzy-based decision approach, Energy 297: 131272. https://doi.org/10.1016/j.energy.2024.131272
Hosseini Dehshiri, S. J.; Amiri, M.; Olfat, L.; Pishvaee, M. S. 2023. A robust fuzzy stochastic multi-objective model for stone paper closed-loop supply chain design considering the flexibility of soft constraints based on Me measure, Applied Soft Computing 134: 109944. https://doi.org/10.1016/j.asoc.2022.109944
Hosseini Dehshiri, S. J.; Amiri, M.; Olfat, L.; Pishvaee, M. S. 2022. Multi-objective closed-loop supply chain network design: a novel robust stochastic, possibilistic, and flexible approach, Expert Systems with Applications 206: 117807. https://doi.org/10.1016/j.eswa.2022.117807
Izadikhah, M.; Azadi, M.; Toloo, M.; Hussain, F. K. 2021. Sustainably resilient supply chains evaluation in public transport: a fuzzy chance-constrained two-stage DEA approach, Applied Soft Computing 113: 107879. https://doi.org/10.1016/j.asoc.2021.107879
Kazda, A.; Novák Sedláčková, A.; Bračić, M. 2023. Airport planning: approaches to determining the planning horizon, Transport 38(3): 139–151. https://doi.org/10.3846/transport.2023.19797
Kuppulakshmi, V.; Sugapriya, C.; Nagarajan, D. 2021. Economic fish production inventory model for perishable fish items with the detoriation rate and the added value under pentagonal fuzzy number, Complex & Intelligent Systems 7: 417–428. https://doi.org/10.1007/s40747-020-00222-8
Lahri, V.; Shaw, K.; Ishizaka, A. 2021. Sustainable supply chain network design problem: using the integrated BWM, TOPSIS, possibilistic programming, and ε-constrained methods, Expert Systems with Applications 168: 114373. https://doi.org/10.1016/j.eswa.2020.114373
Liu, Yi.; Ma, L.; Liu, Ya. 2021. A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity, Applied Mathematical Modelling 92: 99–135. https://doi.org/10.1016/j.apm.2020.10.042
Ma, R.; Yao, L.; Jin, M.; Ren, P.; Lv, Z. 2016. Robust environmental closed-loop supply chain design under uncertainty, Chaos, Solitons & Fractals 89: 195–202. https://doi.org/10.1016/j.chaos.2015.10.028
Mary, A. A.; Sangeetha, S. 2016. Application of fuzzy linguistic SAW and TOPSIS multiple criteria group decision making method using pentagonal fuzzy number for supplier selection problem, International Journal of Mathematics And its Applications 55: 7.
Mondal, S. P.; Mandal, M. 2017. Pentagonal fuzzy number, its properties and application in fuzzy equation, Future Computing and Informatics Journal 2(2): 110–117. https://doi.org/10.1016/j.fcij.2017.09.001
Nayeri, S.; Paydar, M. M.; Asadi-Gangraj, E.; Emami, S. 2020. Multi-objective fuzzy robust optimization approach to sustainable closed-loop supply chain network design, Computers & Industrial Engineering 148: 106716. https://doi.org/10.1016/j.cie.2020.106716
Panda, A.; Pal, M. 2015. A study on pentagonal fuzzy number and its corresponding matrices, Pacific Science Review B: Humanities and Social Sciences 1(3): 131–139. https://doi.org/10.1016/j.psrb.2016.08.001
Pei, H.; Li, H.; Liu, Y. 2022. Optimizing a robust capital-constrained dual-channel supply chain under demand distribution uncertainty, Expert Systems with Applications 204: 117546. https://doi.org/10.1016/j.eswa.2022.117546
Pishvaee, M. S.; Rabbani, M.; Torabi, S. A. 2011. A robust optimization approach to closed-loop supply chain network design under uncertainty, Applied Mathematical Modelling 35(2): 637–649. https://doi.org/10.1016/j.apm.2010.07.013
Pishvaee, M. S.; Razmi, J.; Torabi, S. A. 2012. Robust possibilistic programming for socially responsible supply chain network design: a new approach, Fuzzy Sets and Systems 206: 1–20. https://doi.org/10.1016/j.fss.2012.04.010
Qahtan, S; Alsattar, H. A.; Zaidan, A. A.; Deveci, M.; Pamucar, D.; Martinez, L. 2023. A comparative study of evaluating and benchmarking sign language recognition system-based wearable sensory devices using a single fuzzy set, Knowledge-Based Systems 269: 110519. https://doi.org/10.1016/j.knosys.2023.110519
Qiao, J.; Chen, Y. 2023. Stochastic configuration networks with chaotic maps and hierarchical learning strategy, Information Sciences 629: 96–108. https://doi.org/10.1016/j.ins.2023.01.128
Rouhani, S.; Amin, S. H. 2022. A robust convex optimization approach to design a hierarchical organ transplant network: a case study, Expert Systems with Applications 197: 116716. https://doi.org/10.1016/j.eswa.2022.116716
Sengupta, D.; Datta, A.; Das, A.; Bera, U. K. 2018. The expected value defuzzification method for pentagonal fuzzy number to solve a carbon cost integrated solid transportation problem, in 2018 3rd International Conference for Convergence in Technology (I2CT), 6–8 April 2018, Pune, India, 1–6. https://doi.org/10.1109/I2CT.2018.8529538
Serrano-Guerrero, J.; Romero, F. P.; Olivas, J. A. 2021. Fuzzy logic applied to opinion mining: a review, Knowledge-Based Systems 222: 107018. https://doi.org/10.1016/j.knosys.2021.107018
Seydanlou, P.; Sheikhalishahi, M.; Tavakkoli-Moghaddam, R.; Fathollahi-Fard, A. M. 2023. A customized multi-neighborhood search algorithm using the tabu list for a sustainable closed-loop supply chain network under uncertainty, Applied Soft Computing 144: 110495. https://doi.org/10.1016/j.asoc.2023.110495
Srinivasan, R.; Nakkeeran, T.; Renganathan, K.; Vijayan, V. 2021. The performance of pentagonal fuzzy numbers in finite source queue models using Pascal’s triangular graded mean, Materials Today: Proceedings 37: 947–949. https://doi.org/10.1016/j.matpr.2020.06.171
Torabi, S. A.; Hassini, E. 2008. An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems 159(2): 193–214. https://doi.org/10.1016/j.fss.2007.08.010
Torabi, S. A.; Namdar, J.; Hatefi, S. M.; Jolai, F. 2016. An enhanced possibilistic programming approach for reliable closed-loop supply chain network design, International Journal of Production Research 54(5): 1358–1387. https://doi.org/10.1080/00207543.2015.1070215
Veryard, L.; Hagras, H.; Conway, A.; Owusu, G. 2023. A heated stack based type-2 fuzzy multi-objective optimisation system for telecommunications capacity planning, Knowledge-Based Systems 260: 110134. https://doi.org/10.1016/j.knosys.2022.110134
Visalakshi, V.; Suvitha, V. 2018. Performance measure of fuzzy queue using pentagonal fuzzy numbers, Journal of Physics: Conference Series 1000: 012015. https://doi.org/10.1088/1742-6596/1000/1/012015
Yousefi Nejad Attari, M.; Ebadi Torkayesh, A.; Malmir, B.; Neyshabouri Jami, E. 2021. Robust possibilistic programming for joint order batching and picker routing problem in warehouse management, International Journal of Production Research 59(14): 4434–4452. https://doi.org/10.1080/00207543.2020.1766712
Yu, C.-S.; Li, H.-L. 2000. A robust optimization model for stochastic logistic problems, International Journal of Production Economics 64(1–3): 385–397. https://doi.org/10.1016/S0925-5273(99)00074-2
Yu, H.; Solvang, W. D. 2020. A fuzzy-stochastic multi-objective model for sustainable planning of a closed-loop supply chain considering mixed uncertainty and network flexibility, Journal of Cleaner Production 266: 121702. https://doi.org/10.1016/j.jclepro.2020.121702
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, H.; Wang, Z.; Hong, X.; Gong, Y.; Zhong, Q. 2022. Fuzzy closed-loop supply chain models with quality and marketing effort-dependent demand, Expert Systems with Applications 207: 118081. https://doi.org/10.1016/j.eswa.2022.118081
Zhang, J.; Hou, Y.; Han, H. 2023. Hybrid evolutionary robust optimization-based optimal control for time-delay nonlinear systems, Information Sciences 647: 119395. https://doi.org/10.1016/j.ins.2023.119395
Zhou, J.; Liang, D.; Liu, Y.; Huang, T. 2023a. Robust possibilistic programming-based three-way decision approach to product inspection strategy, Information Sciences 646: 119373. https://doi.org/10.1016/j.ins.2023.119373
Zhou, X.; Wu, L.; Zhang, Y.; Chen, Z.-S.; Jiang, S. 2023b. A robust deep reinforcement learning approach to driverless taxi dispatching under uncertain demand, Information Sciences 646: 119401. https://doi.org/10.1016/j.ins.2023.119401
Zohrehvandi, S.; Khalilzadeh, M.; Amiri, M.; Shadrokh, S. 2020. A heuristic buffer sizing algorithm for implementing a renewable energy project, Automation in Construction 117: 103267. https://doi.org/10.1016/j.autcon.2020.103267
Ala, A.; Simic, V.; Bacanin, N.; Babaee Tirkolaee, E. B. 2024. Blood supply chain network design with lateral freight: a robust possibilistic optimization model, Engineering Applications of Artificial Intelligence 133: 108053. https://doi.org/10.1016/j.engappai.2024.108053
Alharbi, M. G.; El-Wahed Khalifa, H. A. 2021. On a flow-shop scheduling problem with fuzzy pentagonal processing time, Journal of Mathematics 2021: 6695174. https://doi.org/10.1155/2021/6695174
Amoozad Mahdiraji, H.; Beheshti, M.; Razavi Hajiagha, S. H.; Zavadskas, E. K. 2018. A fuzzy binary bi objective transportation model: Iranian steel supply network, Transport 33(3): 810–820. https://doi.org/10.3846/transport.2018.5800
Anitha, P.; Parvathi, P. 2017. An inventory model with stock dependent demand, two parameter Weibull distribution deterioration in a fuzzy environment, in 2016 Online International Conference on Green Engineering and Technologies (IC-GET), 19 November 2016, Coimbatore, India, 1–8. https://doi.org/10.1109/GET.2016.7916660
Atabaki, M. S.; Mohammadi, M.; Naderi, B. 2020. New robust optimization models for closed-loop supply chain of durable products: towards a circular economy, Computers & Industrial Engineering 146: 106520. https://doi.org/10.1016/j.cie.2020.106520
Avakh Darestani, S.; Hemmati, M. 2019. Robust optimization of a bi-objective closed-loop supply chain network for perishable goods considering queue system, Computers & Industrial Engineering 136: 277–292. https://doi.org/10.1016/j.cie.2019.07.018
Babaee Tirkolaee, E. B.; Golpîra, H.; Javanmardan, A.; Maihami, R. 2023. A socio-economic optimization model for blood supply chain network design during the COVID-19 pandemic: an interactive possibilistic programming approach for a real case study, Socio-Economic Planning Sciences 85: 101439. https://doi.org/10.1016/j.seps.2022.101439
Baghizadeh, K.; Cheikhrouhou, N.; Govindan, K.; Ziyarati, M. 2022. Sustainable agriculture supply chain network design considering water-energy-food nexus using queuing system: a hybrid robust possibilistic programming, Natural Resource Modeling 35(1): e12337. https://doi.org/10.1111/nrm.12337
Báez-Sánchez, A.; Flores-Franulic, A.; Moretti, A. C.; Chalco-Cano, Y.; Rojas-Medar, M. A. 2022. Weighted polygonal approximation of fuzzy numbers preserving their main characteristics, Fuzzy Sets and Systems 443: 34–51. https://doi.org/10.1016/j.fss.2021.11.002
Chakraborty, A.; Pal, S.; Mondal, S. P.; Alam, S. 2022. Nonlinear pentagonal intuitionistic fuzzy number and its application in EPQ model under learning and forgetting, Complex & Intelligent Systems 8(2): 1307–1322. https://doi.org/10.1007/s40747-021-00574-9
Chen, Z.-S.; Zhu, Z.; Wang, Z.-J.; Tsang, Y. 2023. Fairness-aware large-scale collective opinion generation paradigm: A case study of evaluating blockchain adoption barriers in medical supply chain, Information Sciences 635: 257–278. https://doi.org/10.1016/j.ins.2023.03.135
Dehghan, E.; Shafiei Nikabadi, M. S.; Amiri, M.; Jabbarzadeh, A. 2018. Hybrid robust, stochastic and possibilistic programming for closed-loop supply chain network design, Computers & Industrial Engineering 123: 220–231. https://doi.org/10.1016/j.cie.2018.06.030
Dhanamandand, K.; Parimaldevi, M. 2016. Cost analysis on a probabilistic multi objective-multi item inventory model using pentagonal fuzzy number, Global Journal of Applied Mathematics and Mathematics Sciences 9: 151–163.
Farrokh, M.; Azar, A.; Jandaghi, G.; Ahmadi, E. 2018. A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty, Fuzzy Sets and Systems 341: 69–91. https://doi.org/10.1016/j.fss.2017.03.019
Foroozesh, N.; Karimi, B.; Mousavi, S. M. 2022. Green-resilient supply chain network design for perishable products considering route risk and horizontal collaboration under robust interval-valued type-2 fuzzy uncertainty: a case study in food industry, Journal of Environmental Management 307: 114470. https://doi.org/10.1016/j.jenvman.2022.114470
Gao, Y.; Lu, S.; Cheng, H.; Liu, X. 2024. Data-driven robust optimization of dual-channel closed-loop supply chain network design considering uncertain demand and carbon cap-and-trade policy, Computers & Industrial Engineering 187: 109811. https://doi.org/10.1016/j.cie.2023.109811
Garai, A.; Chowdhury, S.; Sarkar, B.; Roy, T. K. 2021. Cost-effective subsidy policy for growers and biofuels-plants in closed-loop supply chain of herbs and herbal medicines: an interactive bi-objective optimization in T-environment, Applied Soft Computing 100: 106949. https://doi.org/10.1016/j.asoc.2020.106949
Ghahremani-Nahr, J.; Kian, R.; Sabet, E. 2019. A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm, Expert Systems with Applications 116: 454–471. https://doi.org/10.1016/j.eswa.2018.09.027
Ghahremani-Nahr, J.; Kian, R.; Sabet, E.; Akbari, V. 2022. A bi-objective blood supply chain model under uncertain donation, demand, capacity and cost: a robust possibilistic-necessity approach, Operational Research 22: 4685–4723. https://doi.org/10.1007/s12351-022-00710-4
Ghasemi, P.; Goodarzian, F.; Abraham, A.; Khanchehzarrin, S. 2022. A possibilistic-robust-fuzzy programming model for designing a game theory based blood supply chain network, Applied Mathematical Modelling 112: 282–303. https://doi.org/10.1016/j.apm.2022.08.003
Ghosh, S.; Roy, S. K. 2023. Closed-loop multi-objective waste management through vehicle routing problem in neutrosophic hesitant fuzzy environment, Applied Soft Computing 148: 110854. https://doi.org/10.1016/j.asoc.2023.110854
Gilani, H.; Sahebi, H. 2021. Optimal design and operation of the green pistachio supply network: a robust possibilistic programming model, Journal of Cleaner Production 282: 125212. https://doi.org/10.1016/j.jclepro.2020.125212
Guo, Y.; Shi, Q.; Wang, Y.; Song, M.; Wu, W. 2024. A scenario-based robust possibilistic-flexible programming model for responsive supply chain network design with a performance-oriented solution methodology, Expert Systems with Applications 238: 121895. https://doi.org/10.1016/j.eswa.2023.121895
Günay, E. E.; Okudan Kremer, G. E.; Zarindast, A. 2021. A multi-objective robust possibilistic programming approach to sustainable public transportation network design, Fuzzy Sets and Systems 412: 106–129. https://doi.org/10.1016/j.fss.2020.09.007
Habib, M. S.; Asghar, O.; Hussain, A.; Imran, M.; Mughal, M. P.; Sarkar, B. 2021. A robust possibilistic programming approach toward animal fat-based biodiesel supply chain network design under uncertain environment, Journal of Cleaner Production 278: 122403. https://doi.org/10.1016/j.jclepro.2020.122403
Habib, M. S.; Maqsood, M. H.; Ahmed, N.; Tayyab, M.; Omair, M. 2022. A multi-objective robust possibilistic programming approach for sustainable disaster waste management under disruptions and uncertainties, International Journal of Disaster Risk Reduction 75: 102967. https://doi.org/10.1016/j.ijdrr.2022.102967
Hassanpour, A.; Bagherinejad, J.; Bashiri, M. 2019. A robust leader-follower approach for closed loop supply chain network design considering returns quality levels, Computers & Industrial Engineering 136: 293–304. https://doi.org/10.1016/j.cie.2019.07.031
Hemalatha, S.; Annadurai, K. 2023. A fuzzy EOQ inventory model with advance payment and various fuzzy numbers, Indian Journal of Science and Technology 16(27): 2076–2089. https://doi.org/10.17485/IJST/v16i27.451
Hosseini Dehshiri, S. J.; Amiri, M. 2024. Considering the circular economy for designing closed-loop supply chain under hybrid uncertainty: a robust scenario-based possibilistic-stochastic programming, Expert Systems with Applications 238: 121745. https://doi.org/10.1016/j.eswa.2023.121745
Hosseini Dehshiri, S. J.; Amiri, M.; Mostafaeipour, A.; Le, T. 2024. Evaluation of renewable energy projects based on sustainability goals using a hybrid Pythagorean fuzzy-based decision approach, Energy 297: 131272. https://doi.org/10.1016/j.energy.2024.131272
Hosseini Dehshiri, S. J.; Amiri, M.; Olfat, L.; Pishvaee, M. S. 2023. A robust fuzzy stochastic multi-objective model for stone paper closed-loop supply chain design considering the flexibility of soft constraints based on Me measure, Applied Soft Computing 134: 109944. https://doi.org/10.1016/j.asoc.2022.109944
Hosseini Dehshiri, S. J.; Amiri, M.; Olfat, L.; Pishvaee, M. S. 2022. Multi-objective closed-loop supply chain network design: a novel robust stochastic, possibilistic, and flexible approach, Expert Systems with Applications 206: 117807. https://doi.org/10.1016/j.eswa.2022.117807
Izadikhah, M.; Azadi, M.; Toloo, M.; Hussain, F. K. 2021. Sustainably resilient supply chains evaluation in public transport: a fuzzy chance-constrained two-stage DEA approach, Applied Soft Computing 113: 107879. https://doi.org/10.1016/j.asoc.2021.107879
Kazda, A.; Novák Sedláčková, A.; Bračić, M. 2023. Airport planning: approaches to determining the planning horizon, Transport 38(3): 139–151. https://doi.org/10.3846/transport.2023.19797
Kuppulakshmi, V.; Sugapriya, C.; Nagarajan, D. 2021. Economic fish production inventory model for perishable fish items with the detoriation rate and the added value under pentagonal fuzzy number, Complex & Intelligent Systems 7: 417–428. https://doi.org/10.1007/s40747-020-00222-8
Lahri, V.; Shaw, K.; Ishizaka, A. 2021. Sustainable supply chain network design problem: using the integrated BWM, TOPSIS, possibilistic programming, and ε-constrained methods, Expert Systems with Applications 168: 114373. https://doi.org/10.1016/j.eswa.2020.114373
Liu, Yi.; Ma, L.; Liu, Ya. 2021. A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity, Applied Mathematical Modelling 92: 99–135. https://doi.org/10.1016/j.apm.2020.10.042
Ma, R.; Yao, L.; Jin, M.; Ren, P.; Lv, Z. 2016. Robust environmental closed-loop supply chain design under uncertainty, Chaos, Solitons & Fractals 89: 195–202. https://doi.org/10.1016/j.chaos.2015.10.028
Mary, A. A.; Sangeetha, S. 2016. Application of fuzzy linguistic SAW and TOPSIS multiple criteria group decision making method using pentagonal fuzzy number for supplier selection problem, International Journal of Mathematics And its Applications 55: 7.
Mondal, S. P.; Mandal, M. 2017. Pentagonal fuzzy number, its properties and application in fuzzy equation, Future Computing and Informatics Journal 2(2): 110–117. https://doi.org/10.1016/j.fcij.2017.09.001
Nayeri, S.; Paydar, M. M.; Asadi-Gangraj, E.; Emami, S. 2020. Multi-objective fuzzy robust optimization approach to sustainable closed-loop supply chain network design, Computers & Industrial Engineering 148: 106716. https://doi.org/10.1016/j.cie.2020.106716
Panda, A.; Pal, M. 2015. A study on pentagonal fuzzy number and its corresponding matrices, Pacific Science Review B: Humanities and Social Sciences 1(3): 131–139. https://doi.org/10.1016/j.psrb.2016.08.001
Pei, H.; Li, H.; Liu, Y. 2022. Optimizing a robust capital-constrained dual-channel supply chain under demand distribution uncertainty, Expert Systems with Applications 204: 117546. https://doi.org/10.1016/j.eswa.2022.117546
Pishvaee, M. S.; Rabbani, M.; Torabi, S. A. 2011. A robust optimization approach to closed-loop supply chain network design under uncertainty, Applied Mathematical Modelling 35(2): 637–649. https://doi.org/10.1016/j.apm.2010.07.013
Pishvaee, M. S.; Razmi, J.; Torabi, S. A. 2012. Robust possibilistic programming for socially responsible supply chain network design: a new approach, Fuzzy Sets and Systems 206: 1–20. https://doi.org/10.1016/j.fss.2012.04.010
Qahtan, S; Alsattar, H. A.; Zaidan, A. A.; Deveci, M.; Pamucar, D.; Martinez, L. 2023. A comparative study of evaluating and benchmarking sign language recognition system-based wearable sensory devices using a single fuzzy set, Knowledge-Based Systems 269: 110519. https://doi.org/10.1016/j.knosys.2023.110519
Qiao, J.; Chen, Y. 2023. Stochastic configuration networks with chaotic maps and hierarchical learning strategy, Information Sciences 629: 96–108. https://doi.org/10.1016/j.ins.2023.01.128
Rouhani, S.; Amin, S. H. 2022. A robust convex optimization approach to design a hierarchical organ transplant network: a case study, Expert Systems with Applications 197: 116716. https://doi.org/10.1016/j.eswa.2022.116716
Sengupta, D.; Datta, A.; Das, A.; Bera, U. K. 2018. The expected value defuzzification method for pentagonal fuzzy number to solve a carbon cost integrated solid transportation problem, in 2018 3rd International Conference for Convergence in Technology (I2CT), 6–8 April 2018, Pune, India, 1–6. https://doi.org/10.1109/I2CT.2018.8529538
Serrano-Guerrero, J.; Romero, F. P.; Olivas, J. A. 2021. Fuzzy logic applied to opinion mining: a review, Knowledge-Based Systems 222: 107018. https://doi.org/10.1016/j.knosys.2021.107018
Seydanlou, P.; Sheikhalishahi, M.; Tavakkoli-Moghaddam, R.; Fathollahi-Fard, A. M. 2023. A customized multi-neighborhood search algorithm using the tabu list for a sustainable closed-loop supply chain network under uncertainty, Applied Soft Computing 144: 110495. https://doi.org/10.1016/j.asoc.2023.110495
Srinivasan, R.; Nakkeeran, T.; Renganathan, K.; Vijayan, V. 2021. The performance of pentagonal fuzzy numbers in finite source queue models using Pascal’s triangular graded mean, Materials Today: Proceedings 37: 947–949. https://doi.org/10.1016/j.matpr.2020.06.171
Torabi, S. A.; Hassini, E. 2008. An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems 159(2): 193–214. https://doi.org/10.1016/j.fss.2007.08.010
Torabi, S. A.; Namdar, J.; Hatefi, S. M.; Jolai, F. 2016. An enhanced possibilistic programming approach for reliable closed-loop supply chain network design, International Journal of Production Research 54(5): 1358–1387. https://doi.org/10.1080/00207543.2015.1070215
Veryard, L.; Hagras, H.; Conway, A.; Owusu, G. 2023. A heated stack based type-2 fuzzy multi-objective optimisation system for telecommunications capacity planning, Knowledge-Based Systems 260: 110134. https://doi.org/10.1016/j.knosys.2022.110134
Visalakshi, V.; Suvitha, V. 2018. Performance measure of fuzzy queue using pentagonal fuzzy numbers, Journal of Physics: Conference Series 1000: 012015. https://doi.org/10.1088/1742-6596/1000/1/012015
Yousefi Nejad Attari, M.; Ebadi Torkayesh, A.; Malmir, B.; Neyshabouri Jami, E. 2021. Robust possibilistic programming for joint order batching and picker routing problem in warehouse management, International Journal of Production Research 59(14): 4434–4452. https://doi.org/10.1080/00207543.2020.1766712
Yu, C.-S.; Li, H.-L. 2000. A robust optimization model for stochastic logistic problems, International Journal of Production Economics 64(1–3): 385–397. https://doi.org/10.1016/S0925-5273(99)00074-2
Yu, H.; Solvang, W. D. 2020. A fuzzy-stochastic multi-objective model for sustainable planning of a closed-loop supply chain considering mixed uncertainty and network flexibility, Journal of Cleaner Production 266: 121702. https://doi.org/10.1016/j.jclepro.2020.121702
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, H.; Wang, Z.; Hong, X.; Gong, Y.; Zhong, Q. 2022. Fuzzy closed-loop supply chain models with quality and marketing effort-dependent demand, Expert Systems with Applications 207: 118081. https://doi.org/10.1016/j.eswa.2022.118081
Zhang, J.; Hou, Y.; Han, H. 2023. Hybrid evolutionary robust optimization-based optimal control for time-delay nonlinear systems, Information Sciences 647: 119395. https://doi.org/10.1016/j.ins.2023.119395
Zhou, J.; Liang, D.; Liu, Y.; Huang, T. 2023a. Robust possibilistic programming-based three-way decision approach to product inspection strategy, Information Sciences 646: 119373. https://doi.org/10.1016/j.ins.2023.119373
Zhou, X.; Wu, L.; Zhang, Y.; Chen, Z.-S.; Jiang, S. 2023b. A robust deep reinforcement learning approach to driverless taxi dispatching under uncertain demand, Information Sciences 646: 119401. https://doi.org/10.1016/j.ins.2023.119401
Zohrehvandi, S.; Khalilzadeh, M.; Amiri, M.; Shadrokh, S. 2020. A heuristic buffer sizing algorithm for implementing a renewable energy project, Automation in Construction 117: 103267. https://doi.org/10.1016/j.autcon.2020.103267