Spherical Fuzzy BW-AHP Strategy and its Applications in Renewable Energy
Résumé
The current work proposes a new hybrid decision-making method called the Spherical Fuzzy Best Worst Analytic Hierarchy Process (SF-BWAHP). The fuzzy AHP technique calculates the weights of elements using advanced relationships among selections, transactions, and feedback of criteria and alternatives. However, the potency and utility of this methodology have been reduced due to the large number of pairwise comparisons and difficulties in understanding the comparison method for experts. SF-BWAHP exploits the Fuzzy Best-Worst technique to overcome the demerits mentioned above. A special feature of the proposed method is that it requires less information for comparisons. Numerous reliable results are obtained from various consistent comparisons, making it easier for experts to make decisions. Lastly, the Bhakra Nangal hydroelectric power plant is used as a case study to illustrate the stability and support of this technology.
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Références
References
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2. Majumder, P., Majumder, M., & Saha, A. K. (2020). Real-time monitoring of power production in modular hydropower plant: most significant parameter approach. Environment, Development and Sustainability, 22, 4025-4042.
3. Majumder, P., & Saha, A. K. (2018). Efficiency assignment of hydropower plants by DEMATEL-MAPPAC approach. Water Conservation Science and Engineering, 3(2), 91-97.
4. Majumder, P., & Saha, A. (2021). Optimal Trade-Off Between the Energy—Economy of a Hydropower Plant for Better Management of the Renewable Energy Resources. Water and Energy Management in India: Artificial Neural Networks and Multi-Criteria Decision Making Approaches, 181-198.
5. Majumder, P., Balas, V. E., Paul, A., & Baidya, D. (2021). Application of improved fuzzy best worst analytic hierarchy process on renewable energy. PeerJ Computer Science, 7, e453.
6. Shahzad, K., Lu, B., & Abdul, D. (2022). Entrepreneur barrier analysis on renewable energy promotion in the context of Pakistan using Pythagorean fuzzy AHP method. Environmental Science and Pollution Research, 29(36), 54756-54768.
7. Shahzad, K., Abdul, D., Umar, M., Safi, A., Maqsood, S., Baseer, A., & Lu, B. (2023). Analysis of obstacles to adoption of solar energy in emerging economies using spherical fuzzy AHP decision support system: A case of Pakistan. Energy Reports, 10, 381-395.
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9. Saaty T. (2008). Decision making with the analytic hierarchy process. International journal of services sciences. 1(1), 83-98 https://doi.org/10.1504/IJSSCI.2008.017590
10. Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making methods. In Fuzzy multiple attribute decision making: Methods and applications (pp. 289-486). Berlin, Heidelberg: Springer Berlin Heidelberg.
11. Opricovic, S. (1998). Visekriterijumska optimizacija u građevinarstvu-Multi-criteria optimization of civil engineering systems (PhD thesis). Faculty of Civil Engineering, Belgrade.
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13. Guo, S, & Zhao, H. (2017). Fuzzy best-worst multi-criteria decision-making method and its applications. Knowledge-Based Systems 121, 23-31.
14. Amoozad Mahdiraji, H., Arzaghi, S., Stauskis, G., & Zavadskas, E. K. (2018). A hybrid fuzzy BWM-COPRAS method for analyzing key factors of sustainable architecture. Sustainability, 10, 1626. https://doi.org/10.3390/su10051626
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26. Majumder, P., Saha, A. K. (2019). Identification of most significant parameter of impact of climate change and urbanization on operational efficiency of hydropower plant. International Journal of Energy Optimization and Engineering ,8(3), 43-68. doi: 10.4018/ijeoe.2019070103
27. Majumder, P., Majumder, M., & Saha, A. K. (2018). Climate change and urbanization impact on hydropower plant by neural network-based decision-making methods: identification of the most significant parameter. Water Conservation Science and Engineering, 3, 169-79.
28. Spalding-Fecher R, Chapman A, Yamba F, et al. The vulnerability of hydropower production in the Zambezi River Basin to the impacts of climate change and irrigation development. Mitigation and Adaptation Strategies for Global Change. 2016 Jun;21:721-42.
29. Carvajal PE, Anandarajah G, Mulugetta Y, et al. Assessing uncertainty of climate change impacts on long-term hydropower generation using the CMIP5 ensemble—the case of Ecuador. Climatic Change 2017;144:611-24.
30. Moslem S, Gul M, Farooq D, et al. An integrated approach of best-worst method (BWM) and triangular fuzzy sets for evaluating driver behavior factors related to road safety. Mathematics 2020;8(3):414.
31. Dong, J., Wan, S., & Chen, S. M. (2021) Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Information Sciences. 2021;547:1080-104.
32. Amiri M, Hashemi-Tabatabaei M, Ghahremanloo M, et al. A new fuzzy BWM approach for evaluating and selecting a sustainable supplier in supply chain management. International Journal of Sustainable Development & World Ecology 2021;28(2):125-42.
33. Majumder, P,& Saha, A. K. (2019). Identification of most significant parameter of impact of climate change and urbanization on operational efficiency of hydropower plant. International Journal of Energy Optimization and Engineering, 8(3), 43-68.
34. Wan, S., Dong, J., Chen, S. M. (2021). Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making. Information Sciences, 573, 493-518.
35. Yucesan, M., & Gul. M. (2021). Failure prioritization and control using the neutrosophic best and worst method. Granular Computing. 6, 435-49.
36. Li, J., Wang, J. Q, & Hu, J. H. (2019). Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information. International Journal of Machine Learning and Cybernetics, 10, 1671-85.
37. Liao H, Mi X, Yu Q, et al. Hospital performance evaluation by a hesitant fuzzy linguistic best worst method with inconsistency repairing. Journal of Cleaner Production. 2019;232:657-71.
38. Amoozad Mahdiraji H, Kazimieras Zavadskas E, Skare M, et al. Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of BWM and interval valued intuitionistic fuzzy TODIM. Economic research-Ekonomska istraživanja. 2020;33(1):1600-20.
39. Yang, Q., Zhang, Z., You, X., & Chen, T. Evaluation and classification of overseas talents in China based on the BWM for intuitionistic relations. Symmetry 8(11): 137. doi: 10.3390/sym8110137
40. Kieu, P.T., Nguyen, V.T., Nguyen, V. T., & Ho, T. P. (2021). A Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Combined Compromise Solution (CoCoSo) Algorithm in Distribution Center Location Selection: A Case Study in Agricultural Supply Chain. Axioms, 10, 53. https://doi.org/10.3390/axioms10020053
41. Unal, Y., & Temur, G. T. (2021). Using Spherical Fuzzy AHP Based Approach for Prioritization of Criteria Affecting Sustainable Supplier Selection. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds) Intelligent and fuzzy techniques: smart and innovative solutions. INFUS 2020. Advances in Intelligent Systems and Computing, vol 1197 (pp. pp. 160–168). Springer, Cham. https://doi.org/10.1007/978-3-030-51156-2_20
42. Global Energy Observatory. http://globalenergyobservatory.org/geoid/2330 (accessed on 15 November 2023
43. Hamby, D. M. (1994). A review of techniques for parameter sensitivity analysis of environmental models. Environmental Monitoring and Assessment, 32, 135-54.
44. Kausar, R., Riaz, M., Yasin, Y., Deveci, M., & Pamucar, D. (2023). Measuring efficiency of retrieval algorithms with Schweizer-Sklar information aggregation. Information Sciences, 119438.
45. Habib, A., Khan, Z. A., Riaz, M., & Marinkovic, D. (2023). performance evaluation of healthcare supply chain in industry 4.0 with linear diophantine fuzzy sine-trigonometric aggregation operations. Mathematics, 11(12), 2611.
1. Majumder, P., Kar, S., & Majumder, M. (2021). Real-time vulnerability analysis of hydropower projects under changed climatic scenarios. International Journal of Global Warming, 24(3-4), 383-399.
2. Majumder, P., Majumder, M., & Saha, A. K. (2020). Real-time monitoring of power production in modular hydropower plant: most significant parameter approach. Environment, Development and Sustainability, 22, 4025-4042.
3. Majumder, P., & Saha, A. K. (2018). Efficiency assignment of hydropower plants by DEMATEL-MAPPAC approach. Water Conservation Science and Engineering, 3(2), 91-97.
4. Majumder, P., & Saha, A. (2021). Optimal Trade-Off Between the Energy—Economy of a Hydropower Plant for Better Management of the Renewable Energy Resources. Water and Energy Management in India: Artificial Neural Networks and Multi-Criteria Decision Making Approaches, 181-198.
5. Majumder, P., Balas, V. E., Paul, A., & Baidya, D. (2021). Application of improved fuzzy best worst analytic hierarchy process on renewable energy. PeerJ Computer Science, 7, e453.
6. Shahzad, K., Lu, B., & Abdul, D. (2022). Entrepreneur barrier analysis on renewable energy promotion in the context of Pakistan using Pythagorean fuzzy AHP method. Environmental Science and Pollution Research, 29(36), 54756-54768.
7. Shahzad, K., Abdul, D., Umar, M., Safi, A., Maqsood, S., Baseer, A., & Lu, B. (2023). Analysis of obstacles to adoption of solar energy in emerging economies using spherical fuzzy AHP decision support system: A case of Pakistan. Energy Reports, 10, 381-395.
8. Rehan, M., Raza, M. A., Aman, M. M., Abro, A. G., Ismail, I. M. I., Munir, S., ... & Ali, N. (2023). Untapping the potential of bioenergy for achieving sustainable energy future in Pakistan. Energy, 275, 127472.
9. Saaty T. (2008). Decision making with the analytic hierarchy process. International journal of services sciences. 1(1), 83-98 https://doi.org/10.1504/IJSSCI.2008.017590
10. Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making methods. In Fuzzy multiple attribute decision making: Methods and applications (pp. 289-486). Berlin, Heidelberg: Springer Berlin Heidelberg.
11. Opricovic, S. (1998). Visekriterijumska optimizacija u građevinarstvu-Multi-criteria optimization of civil engineering systems (PhD thesis). Faculty of Civil Engineering, Belgrade.
12. Rezaei, J.(2015). Best-worst multi-criteria decision-making method. Omega, 53, 49-57.
13. Guo, S, & Zhao, H. (2017). Fuzzy best-worst multi-criteria decision-making method and its applications. Knowledge-Based Systems 121, 23-31.
14. Amoozad Mahdiraji, H., Arzaghi, S., Stauskis, G., & Zavadskas, E. K. (2018). A hybrid fuzzy BWM-COPRAS method for analyzing key factors of sustainable architecture. Sustainability, 10, 1626. https://doi.org/10.3390/su10051626
15. Majumder P, Das A, Hezam I. ,M, Alshamrani, A, & Aqlan, F. (2023). Integrating trapezoidal fuzzy best–worst method and single-valued neutrosophic fuzzy MARCOS for efficiency analysis of surface water treatment plants. Soft Computing 31, 1-24. doi: 10.1007/s00500-023-08532-y
16. Altay, B. C., Celik, E., Okumus, A., Balin, A., & Gul, M. (2023). An integrated interval type-2 fuzzy BWM-MARCOS model for location selection of e-scooter sharing stations: The case of a university campus. Engineering Applications of Artificial Intelligence, 122: 106095. https://doi.org/10.1016/j.engappai.2023.106095
17. Majumder, P., Paul, A., Saha, P., Majumder, M., Baidya, D., &Saha, D. (2023). Trapezoidal fuzzy BWM-TOPSIS approach and application on water resources. Environment, Development and Sustainability, 25(3), 2648-69. https://doi.org/10.1007/s10668-022-02126-8
18. Liu, P., & Wang, P. (2017). Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Information Technology & Decision Making, 16(3), 817-850. doi: 10.1142/s0219622017500110
19. Zadeh, L. (1965). Fuzzy sets. Inform Control, 8(3), 338-353.
20. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences 9(1), 43-80.
21. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20(1), 87-96.
22. Torra, V. (2010).. Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529-39. ; 25(6): 529–539. doi: 10.1002/int.20418
23. Yager, R. R. (2013). Pythagorean fuzzy subsets, Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).
24. Smarandache, F. (2010). Neutrosophic set–a generalization of the intuitionistic fuzzy set. Journal of Defense Resources Management, 1(1), 107-16.
25. Kutlu Gündoğdu, F., & Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent & Fuzzy Systems, 36(1), 337-52.
26. Majumder, P., Saha, A. K. (2019). Identification of most significant parameter of impact of climate change and urbanization on operational efficiency of hydropower plant. International Journal of Energy Optimization and Engineering ,8(3), 43-68. doi: 10.4018/ijeoe.2019070103
27. Majumder, P., Majumder, M., & Saha, A. K. (2018). Climate change and urbanization impact on hydropower plant by neural network-based decision-making methods: identification of the most significant parameter. Water Conservation Science and Engineering, 3, 169-79.
28. Spalding-Fecher R, Chapman A, Yamba F, et al. The vulnerability of hydropower production in the Zambezi River Basin to the impacts of climate change and irrigation development. Mitigation and Adaptation Strategies for Global Change. 2016 Jun;21:721-42.
29. Carvajal PE, Anandarajah G, Mulugetta Y, et al. Assessing uncertainty of climate change impacts on long-term hydropower generation using the CMIP5 ensemble—the case of Ecuador. Climatic Change 2017;144:611-24.
30. Moslem S, Gul M, Farooq D, et al. An integrated approach of best-worst method (BWM) and triangular fuzzy sets for evaluating driver behavior factors related to road safety. Mathematics 2020;8(3):414.
31. Dong, J., Wan, S., & Chen, S. M. (2021) Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Information Sciences. 2021;547:1080-104.
32. Amiri M, Hashemi-Tabatabaei M, Ghahremanloo M, et al. A new fuzzy BWM approach for evaluating and selecting a sustainable supplier in supply chain management. International Journal of Sustainable Development & World Ecology 2021;28(2):125-42.
33. Majumder, P,& Saha, A. K. (2019). Identification of most significant parameter of impact of climate change and urbanization on operational efficiency of hydropower plant. International Journal of Energy Optimization and Engineering, 8(3), 43-68.
34. Wan, S., Dong, J., Chen, S. M. (2021). Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making. Information Sciences, 573, 493-518.
35. Yucesan, M., & Gul. M. (2021). Failure prioritization and control using the neutrosophic best and worst method. Granular Computing. 6, 435-49.
36. Li, J., Wang, J. Q, & Hu, J. H. (2019). Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information. International Journal of Machine Learning and Cybernetics, 10, 1671-85.
37. Liao H, Mi X, Yu Q, et al. Hospital performance evaluation by a hesitant fuzzy linguistic best worst method with inconsistency repairing. Journal of Cleaner Production. 2019;232:657-71.
38. Amoozad Mahdiraji H, Kazimieras Zavadskas E, Skare M, et al. Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of BWM and interval valued intuitionistic fuzzy TODIM. Economic research-Ekonomska istraživanja. 2020;33(1):1600-20.
39. Yang, Q., Zhang, Z., You, X., & Chen, T. Evaluation and classification of overseas talents in China based on the BWM for intuitionistic relations. Symmetry 8(11): 137. doi: 10.3390/sym8110137
40. Kieu, P.T., Nguyen, V.T., Nguyen, V. T., & Ho, T. P. (2021). A Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Combined Compromise Solution (CoCoSo) Algorithm in Distribution Center Location Selection: A Case Study in Agricultural Supply Chain. Axioms, 10, 53. https://doi.org/10.3390/axioms10020053
41. Unal, Y., & Temur, G. T. (2021). Using Spherical Fuzzy AHP Based Approach for Prioritization of Criteria Affecting Sustainable Supplier Selection. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds) Intelligent and fuzzy techniques: smart and innovative solutions. INFUS 2020. Advances in Intelligent Systems and Computing, vol 1197 (pp. pp. 160–168). Springer, Cham. https://doi.org/10.1007/978-3-030-51156-2_20
42. Global Energy Observatory. http://globalenergyobservatory.org/geoid/2330 (accessed on 15 November 2023
43. Hamby, D. M. (1994). A review of techniques for parameter sensitivity analysis of environmental models. Environmental Monitoring and Assessment, 32, 135-54.
44. Kausar, R., Riaz, M., Yasin, Y., Deveci, M., & Pamucar, D. (2023). Measuring efficiency of retrieval algorithms with Schweizer-Sklar information aggregation. Information Sciences, 119438.
45. Habib, A., Khan, Z. A., Riaz, M., & Marinkovic, D. (2023). performance evaluation of healthcare supply chain in industry 4.0 with linear diophantine fuzzy sine-trigonometric aggregation operations. Mathematics, 11(12), 2611.
Publiée
2026-04-17
Rubrique
Special Issue: Global Assembly for Mathematical Modeling and Analysis
Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática
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