A Novel Pythagorean Fuzzy Distance Measure for Multicriteria Decision Making in Renewable Energy Resource Selection
Abstract
Selecting the most suitable renewable energy resource is vital for ensuring long-term sustainability, reducing environmental impact, and decreasing dependence on conventional fossil fuels. However, this selection process involves managing complex, uncertain, and imprecise information arising from diverse evaluation criteria. Pythagorean fuzzy sets (PFSs), combined with distance measures, offer a more expressive and flexible framework than traditional fuzzy or intuitionistic fuzzy sets for modeling such uncertainty, particularly in multicriteria decision-making (MCDM) problems. However, existing distance measures for PFSs often suffer from limitations such as zero-divisor problems, counterintuitive outcomes, and violations of axiomatic conditions. To address these issues, this study introduces a novel distance measure for PFSs, whose mathematical properties are thoroughly analyzed to ensure consistency, boundedness, and interpretability. A hybrid Pythagorean fuzzy- stepwise weight assessment ratio analysis–technique for order preference by similarity to ideal solution (PF-SWARA–TOPSIS) framework is proposed, where the SWARA method determines the importance weights of the criteria, and the TOPSIS method ranks the alternatives using the proposed distance measure. The approach is applied to evaluate five renewable energy resources based on multiple criteria. The results indicate that solar energy (alternative D1) is the most preferred option, followed by the ranking order: D1 > D3 > D4 > D2 > D5. Comparative analysis with existing methods validates the robustness and effectiveness of the proposed model, offering a reliable tool for sustainable energy planning under uncertainty. Finally, the study highlights the future potential of the proposed distance measure and methodology, providing insights for further advancements in renewable energy resource selection.
References
G. Büyüközkan and S. Güleryüz, “An integrated dematel-anp approach for renewable energy resources selection in Turkey,” International journal of production economics, vol. 182, pp. 435–448, 2016.
R. M. Elavarasan, G. Shafiullah, S. Padmanaban, N. M. Kumar, A. Annam, A. M. Vetrichelvan, L. Mihet-Popa, and J. B. Holm-Nielsen, “A comprehensive review on renewable energy development, challenges, and policies of leading indian states with an international perspective,” Ieee Access, vol. 8, pp. 74432–74457, 2020.
L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
K. T. Atanassov and S. Stoeva, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, vol. 20, no. 1, pp. 87–96, 1986.
R. R. Yager, “Pythagorean fuzzy subsets,” in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS). IEEE, 2013, pp. 57–61.
X. Zhang and Z. Xu, “Extension of topsis to multiple criteria decision making with pythagorean fuzzy sets,” International journal of intelligent systems, vol. 29, no. 12, pp. 10611078, 2014.
X. Peng, H. Yuan, and Y. Yang, “Pythagorean fuzzy information measures and their applications,” International Journal of Intelligent Systems, vol. 32, no. 10, pp. 991–1029, 2017.
D. Li and W. Zeng, “Distance measure of pythagorean fuzzy sets,” International journal of intelligent systems, vol. 33, no. 2, pp. 348–361, 2018.
W. Zeng, D. Li, and Q. Yin, “Distance and similarity measures of pythagorean fuzzy sets and their applications to multiple criteria group decision making,” International Journal of Intelligent Systems, vol. 33, no. 11, pp. 2236–2254, 2018.
X. Peng, “New similarity measure and distance measure for pythagorean fuzzy set,” Complex &Intelligent Systems, vol. 5, no. 2, pp. 101–111, 2019.
Z. Hussian and M.-S. Yang, “Distance and similarity measures of pythagorean fuzzy sets based on the hausdorff metric with application to fuzzy topsis,” International Journal of Intelligent Systems, vol. 34, no. 10, pp. 2633–2654, 2019.
P. Ejegwa and J. Awolola, “Novel distance measures for pythagorean fuzzy sets with applications to pattern recognition problems,” Granular computing, vol. 6, no. 1, pp. 181–189, 2021.
P. A. Ejegwa, “Distance and similarity measures for pythagorean fuzzy sets,” Granular Computing, vol. 5, no. 2, pp. 225–238, 2020.
Y. He, “A new distance measure of pythagorean fuzzy sets based on matrix and and its application in medical diagnosis,” arXiv preprint arXiv:2102.01538, 2021.
J. Mahanta and S. Panda, “Distance measure for pythagorean fuzzy sets with varied applications,” Neural Computing and Applications, vol. 33, no. 24, pp. 17161–17171, 2021.
P. Rani, A. R. Mishra, A. Mardani, F. Cavallaro, M. Alrasheedi, and A. Alrashidi, “A novel approach to extended fuzzy topsis based on new divergence measures for renewable energy sources selection,” Journal of Cleaner Production, vol. 257, p. 120352, 2020.
S. Sen, S. Ganguly, A. Das, J. Sen, and S. Dey, “Renewable energy scenario in india: Opportunities and challenges,” Journal of African Earth Sciences, vol. 122, pp. 25–31, 2016.
P. P. Dwivedi and D. K. Sharma, “Assessment of appropriate renewable energy resources for india using entropy and waspas techniques,” Renewable Energy Research and Applications, vol. 5, no. 1, pp. 51–61, 2024.
M. Mukherjee and A. K. Sharma, “Survey-based assessment for strategic deployment of renewable energy resources for selected places in india: enabling advances in framework responsibility,” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, vol. 46, no. 1, pp. 1873–1889, 2024.
Q. Li, J. Cherian, M. S. Shabbir, M. S. Sial, J. Li, I. Mester, and A. Badulescu, “Exploring the relationship between renewable energy sources and economic growth. the case of saarc countries,” Energies, vol. 14, no. 3, p. 520, 2021.
B. Shah, H. Lakhani, K. Abhishek, and S. Kumari, “Application of fuzzy linguistic modeling aggregated with vikor for optimal selection of solar power plant site: an empirical study,” in Renewable Energy and Climate Change: Proceedings of REC 2019. Springer, 2020, pp. 119–127.
K. Suvitha, S. Narayanamoorthy, M. Sandra, D. Pamucar, V. Simic, and D. Kang, “Effective hydropower renewable energy source selection using fuzzy neutrosophic boundary approximate area,” Renewable Energy Focus, vol. 48, p. 100537, 2024.
T. Manirathinam, S. Narayanamoorthy, S. Geetha, M. F. I. Othman, B. S. Alotaibi, A. Ahmadian, and D. Kang, “Sustainable renewable energy system selection for self-sufficient households using integrated fermatean neutrosophic fuzzy stratified ahp-marcos approach,” Renewable Energy, vol. 218, p. 119292, 2023.
S. Geetha, S. Narayanamoorthy, J. V. Kureethara, D. Baleanu, and D. Kang, “The hesitant pythagorean fuzzy electre iii: an adaptable recycling method for plastic materials,” Journal of Cleaner Production, vol. 291, p. 125281, 2021.
S. Geetha, S. Narayanamoorthy, D. Kang, and D. Baleanu, “Retracted: An adoptive renewable energy resource selection using hesitant pythagorean fuzzy dematel and vikor methods,” Journal of Intelligent & Fuzzy Systems, vol. 43, no. 4, pp. 4285–4302, 2022.
K. Suvitha, S. Narayanamoorthy, D. Pamucar, and D. Kang, “An ideal plastic waste management system based on an enhanced mcdm technique,” Artificial Intelligence Review, vol. 57, no. 4, p. 96, 2024.
M.Sandra, S. Narayanamoorthy, K. Suvitha, D. Pamucar, V. Simic, and D. Kang, “An insightful multicriteria model for the selection of drilling technique for heat extraction from geothermal reservoirs using a fuzzy-rough approach,” Information Sciences, vol. 686, p. 121353, 2025.
K. Suvitha, S. Narayanamoorthy, M. Sandra, D. Pamucar, V. Simic, and D. Kang, “Evaluation of extracting biomass energy using a strategic decision support system,” Applied Soft Computing, vol. 161, p. 111766, 2024.
D. Kang, T. Manirathinam, S. Geetha, S. Narayanamoorthy, M. Ferrara, and A. Ahmadian, “An advanced stratified decision-making strategy to explore viable plastic waste-to-energy method: A step towards sustainable dumped wastes management,” Applied Soft Computing, vol. 143, p. 110452, 2023.
V. Keršuliene, E. K. Zavadskas, and Z. Turskis, “Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (swara),” Journal of business economics and management, vol. 11, no. 2, pp. 243–258, 2010.
T.-Y. Chen, “Multiple criteria decision analysis under complex uncertainty: A pearson-like correlation-based pythagorean fuzzy compromise approach,” International Journal of Intelligent Systems, vol. 34, no. 1, pp. 114–151, 2019.
Ž. Stević, D. K. Das, R. Tešić, M. Vidas, and D. Vojinović, “Objective criticism and negative conclusions on using the fuzzy swara method in multi-criteria decision making,” Mathematics, vol. 10, no. 4, p. 635, 2022.
P. Rani, A. R. Mishra, R. Krishankumar, K. Ravichandran, and A. H. Gandomi, “A new pythagorean fuzzy based decision framework for assessing healthcare waste treatment,” IEEE Transactions on Engineering Management, vol. 69, no. 6, pp. 2915–2929, 2020.
M. Alipour, R. Hafezi, P. Rani, M. Hafezi, and A. Mardani, “A new pythagorean fuzzy-based decision-making method through entropy measure for fuel cell and hydrogen components supplier selection,” Energy, vol. 234, p. 121208, 2021.
M. K. Saraji, A. Mardani, M. Köppen, A. R. Mishra, and P. Rani, “An extended hesitant fuzzy set using swara-multimoora approach to adapt online education for the control of the pandemic spread of covid-19 in higher education institutions,” Artificial Intelligence Review, vol. 55, no. 1, pp. 181–206, 2022.
X. Peng, X. Zhang, and Z. Luo, “Pythagorean fuzzy mcdm method based on cocoso and critic with score function for 5g industry evaluation,” Artificial Intelligence Review, vol. 53, no. 5, pp. 3813–3847, 2020.
I. M. Hezam, A. R. Mishra, P. Rani, F. Cavallaro, A. Saha, J. Ali, W. Strielkowski, and D. ˇ Streimikien˙e, “A hybrid intuitionistic fuzzy-merec-rs-dnma method for assessing the alternative fuel vehicles with sustainability perspectives,” Sustainability, vol. 14, no. 9, p. 5463, 2022.
P.Rani, A.R.Mishra, andP.Liu, “Newsimilarityanddivergence measures-based pythagorean fuzzy multimoora approach for decision-making problems,” Computational and Applied Mathematics, vol. 42, no. 1, p. 29, 2023.
C.-L. Hwang, Y.-J. Lai, and T.-Y. Liu, “A new approach for multiple objective decision making,” Computers & operations research, vol. 20, no. 8, pp. 889–899, 1993.
D.LiangandZ.Xu,“Thenewextensionoftopsismethodformultiplecriteria decision making with hesitant pythagorean fuzzy sets,” Applied Soft Computing, vol. 60, pp. 167–179, 2017.
H. Arora and A. Naithani, “Significance of topsis approach to madm in computing exponential divergence measures for pythagorean fuzzy sets,” Decision Making: Applications in Management and Engineering, vol. 5, no. 1, pp. 246–263, 2022.
N. Kumar, A. Patel, and J. Mahanta, “K–l divergence-based distance measure for pythagorean fuzzy sets with various applications,” Journal of Experimental & Theoretical Artificial Intelligence, pp. 1–21, 2023.
K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. doi: 10.1016/S0165-0114(86)80034-3
Y. Qin, Y. Liu, and Z. Hong, “Multicriteria decision making method based on generalized pythagorean fuzzy ordered weighted distance measures,” Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3665–3675, 2017.
T.-Y. Chen, “Remoteness index-based pythagorean fuzzy vikor methods with a generalized distance measure for multiple criteria decision analysis,” Information Fusion, vol. 41, pp. 129–150, 2018.
B. Sarkar and A. Biswas, “Pythagorean fuzzy ahp-topsis integrated approach for transportation management through a new distance measure,” Soft Computing, vol. 25, no. 5, pp. 40734089, 2021.
A. Ohlan, “Multiple attribute decision-making based on distance measure under pythagorean fuzzy environment,” International Journal of Information Technology, pp. 1–13, 2021.
M. J. Khan, M. I. Ali, P. Kumam, W. Kumam, M. Aslam, and J. C. R. Alcantud, “Improved generalized dissimilarity measure-based vikor method for pythagorean fuzzy sets,” International Journal of Intelligent Systems, vol. 37, no. 3, pp. 1807–1845, 2022.
P. Dutta, G. Borah, B. Gohain, and R. Chutia, “Nonlinear distance measures under the framework of pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and covid-19 medicine selection,” Beni-Suef University Journal of Basic and Applied Sciences, vol. 12, no. 1, p. 42, 2023.
F. E. Boran, S. Genc¸, M. Kurt, and D. Akay, “A multi-criteria intuitionistic fuzzy group decision making for supplier selection with topsis method,” Expert systems with applications, vol. 36, no. 8, pp. 11363–11368, 2009.
E. K. Zavadskas and V. Podvezko, “Integrated determination of objective criteria weights in mcdm,” International Journal of Information Technology & Decision Making, vol. 15, no. 02, pp. 267–283, 2016.
R. Chaurasiya and D. Jain, “Pythagorean fuzzy mcdm method in renewable energy resources assessment,” Research Square, 2023. [Online]. Available: https://www.researchsquare.com/article/rs-2569784/v1
V. Arya and S. Kumar, “A picture fuzzy multiple criteria decision-making approach based on the combined todim-vikor and entropy weighted method,” Cognitive Computation, vol. 13, no. 5, pp. 1172–1184, 2021.
R. M. Elavarasan, G. Shafiullah, S. Padmanaban, N. M. Kumar, A. Annam, A. M. Vetrichelvan, L. Mihet-Popa, and J. B. Holm-Nielsen, “A comprehensive review on renewable energy development, challenges, and policies of leading indian states with an international perspective,” Ieee Access, vol. 8, pp. 74432–74457, 2020.
L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
K. T. Atanassov and S. Stoeva, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, vol. 20, no. 1, pp. 87–96, 1986.
R. R. Yager, “Pythagorean fuzzy subsets,” in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS). IEEE, 2013, pp. 57–61.
X. Zhang and Z. Xu, “Extension of topsis to multiple criteria decision making with pythagorean fuzzy sets,” International journal of intelligent systems, vol. 29, no. 12, pp. 10611078, 2014.
X. Peng, H. Yuan, and Y. Yang, “Pythagorean fuzzy information measures and their applications,” International Journal of Intelligent Systems, vol. 32, no. 10, pp. 991–1029, 2017.
D. Li and W. Zeng, “Distance measure of pythagorean fuzzy sets,” International journal of intelligent systems, vol. 33, no. 2, pp. 348–361, 2018.
W. Zeng, D. Li, and Q. Yin, “Distance and similarity measures of pythagorean fuzzy sets and their applications to multiple criteria group decision making,” International Journal of Intelligent Systems, vol. 33, no. 11, pp. 2236–2254, 2018.
X. Peng, “New similarity measure and distance measure for pythagorean fuzzy set,” Complex &Intelligent Systems, vol. 5, no. 2, pp. 101–111, 2019.
Z. Hussian and M.-S. Yang, “Distance and similarity measures of pythagorean fuzzy sets based on the hausdorff metric with application to fuzzy topsis,” International Journal of Intelligent Systems, vol. 34, no. 10, pp. 2633–2654, 2019.
P. Ejegwa and J. Awolola, “Novel distance measures for pythagorean fuzzy sets with applications to pattern recognition problems,” Granular computing, vol. 6, no. 1, pp. 181–189, 2021.
P. A. Ejegwa, “Distance and similarity measures for pythagorean fuzzy sets,” Granular Computing, vol. 5, no. 2, pp. 225–238, 2020.
Y. He, “A new distance measure of pythagorean fuzzy sets based on matrix and and its application in medical diagnosis,” arXiv preprint arXiv:2102.01538, 2021.
J. Mahanta and S. Panda, “Distance measure for pythagorean fuzzy sets with varied applications,” Neural Computing and Applications, vol. 33, no. 24, pp. 17161–17171, 2021.
P. Rani, A. R. Mishra, A. Mardani, F. Cavallaro, M. Alrasheedi, and A. Alrashidi, “A novel approach to extended fuzzy topsis based on new divergence measures for renewable energy sources selection,” Journal of Cleaner Production, vol. 257, p. 120352, 2020.
S. Sen, S. Ganguly, A. Das, J. Sen, and S. Dey, “Renewable energy scenario in india: Opportunities and challenges,” Journal of African Earth Sciences, vol. 122, pp. 25–31, 2016.
P. P. Dwivedi and D. K. Sharma, “Assessment of appropriate renewable energy resources for india using entropy and waspas techniques,” Renewable Energy Research and Applications, vol. 5, no. 1, pp. 51–61, 2024.
M. Mukherjee and A. K. Sharma, “Survey-based assessment for strategic deployment of renewable energy resources for selected places in india: enabling advances in framework responsibility,” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, vol. 46, no. 1, pp. 1873–1889, 2024.
Q. Li, J. Cherian, M. S. Shabbir, M. S. Sial, J. Li, I. Mester, and A. Badulescu, “Exploring the relationship between renewable energy sources and economic growth. the case of saarc countries,” Energies, vol. 14, no. 3, p. 520, 2021.
B. Shah, H. Lakhani, K. Abhishek, and S. Kumari, “Application of fuzzy linguistic modeling aggregated with vikor for optimal selection of solar power plant site: an empirical study,” in Renewable Energy and Climate Change: Proceedings of REC 2019. Springer, 2020, pp. 119–127.
K. Suvitha, S. Narayanamoorthy, M. Sandra, D. Pamucar, V. Simic, and D. Kang, “Effective hydropower renewable energy source selection using fuzzy neutrosophic boundary approximate area,” Renewable Energy Focus, vol. 48, p. 100537, 2024.
T. Manirathinam, S. Narayanamoorthy, S. Geetha, M. F. I. Othman, B. S. Alotaibi, A. Ahmadian, and D. Kang, “Sustainable renewable energy system selection for self-sufficient households using integrated fermatean neutrosophic fuzzy stratified ahp-marcos approach,” Renewable Energy, vol. 218, p. 119292, 2023.
S. Geetha, S. Narayanamoorthy, J. V. Kureethara, D. Baleanu, and D. Kang, “The hesitant pythagorean fuzzy electre iii: an adaptable recycling method for plastic materials,” Journal of Cleaner Production, vol. 291, p. 125281, 2021.
S. Geetha, S. Narayanamoorthy, D. Kang, and D. Baleanu, “Retracted: An adoptive renewable energy resource selection using hesitant pythagorean fuzzy dematel and vikor methods,” Journal of Intelligent & Fuzzy Systems, vol. 43, no. 4, pp. 4285–4302, 2022.
K. Suvitha, S. Narayanamoorthy, D. Pamucar, and D. Kang, “An ideal plastic waste management system based on an enhanced mcdm technique,” Artificial Intelligence Review, vol. 57, no. 4, p. 96, 2024.
M.Sandra, S. Narayanamoorthy, K. Suvitha, D. Pamucar, V. Simic, and D. Kang, “An insightful multicriteria model for the selection of drilling technique for heat extraction from geothermal reservoirs using a fuzzy-rough approach,” Information Sciences, vol. 686, p. 121353, 2025.
K. Suvitha, S. Narayanamoorthy, M. Sandra, D. Pamucar, V. Simic, and D. Kang, “Evaluation of extracting biomass energy using a strategic decision support system,” Applied Soft Computing, vol. 161, p. 111766, 2024.
D. Kang, T. Manirathinam, S. Geetha, S. Narayanamoorthy, M. Ferrara, and A. Ahmadian, “An advanced stratified decision-making strategy to explore viable plastic waste-to-energy method: A step towards sustainable dumped wastes management,” Applied Soft Computing, vol. 143, p. 110452, 2023.
V. Keršuliene, E. K. Zavadskas, and Z. Turskis, “Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (swara),” Journal of business economics and management, vol. 11, no. 2, pp. 243–258, 2010.
T.-Y. Chen, “Multiple criteria decision analysis under complex uncertainty: A pearson-like correlation-based pythagorean fuzzy compromise approach,” International Journal of Intelligent Systems, vol. 34, no. 1, pp. 114–151, 2019.
Ž. Stević, D. K. Das, R. Tešić, M. Vidas, and D. Vojinović, “Objective criticism and negative conclusions on using the fuzzy swara method in multi-criteria decision making,” Mathematics, vol. 10, no. 4, p. 635, 2022.
P. Rani, A. R. Mishra, R. Krishankumar, K. Ravichandran, and A. H. Gandomi, “A new pythagorean fuzzy based decision framework for assessing healthcare waste treatment,” IEEE Transactions on Engineering Management, vol. 69, no. 6, pp. 2915–2929, 2020.
M. Alipour, R. Hafezi, P. Rani, M. Hafezi, and A. Mardani, “A new pythagorean fuzzy-based decision-making method through entropy measure for fuel cell and hydrogen components supplier selection,” Energy, vol. 234, p. 121208, 2021.
M. K. Saraji, A. Mardani, M. Köppen, A. R. Mishra, and P. Rani, “An extended hesitant fuzzy set using swara-multimoora approach to adapt online education for the control of the pandemic spread of covid-19 in higher education institutions,” Artificial Intelligence Review, vol. 55, no. 1, pp. 181–206, 2022.
X. Peng, X. Zhang, and Z. Luo, “Pythagorean fuzzy mcdm method based on cocoso and critic with score function for 5g industry evaluation,” Artificial Intelligence Review, vol. 53, no. 5, pp. 3813–3847, 2020.
I. M. Hezam, A. R. Mishra, P. Rani, F. Cavallaro, A. Saha, J. Ali, W. Strielkowski, and D. ˇ Streimikien˙e, “A hybrid intuitionistic fuzzy-merec-rs-dnma method for assessing the alternative fuel vehicles with sustainability perspectives,” Sustainability, vol. 14, no. 9, p. 5463, 2022.
P.Rani, A.R.Mishra, andP.Liu, “Newsimilarityanddivergence measures-based pythagorean fuzzy multimoora approach for decision-making problems,” Computational and Applied Mathematics, vol. 42, no. 1, p. 29, 2023.
C.-L. Hwang, Y.-J. Lai, and T.-Y. Liu, “A new approach for multiple objective decision making,” Computers & operations research, vol. 20, no. 8, pp. 889–899, 1993.
D.LiangandZ.Xu,“Thenewextensionoftopsismethodformultiplecriteria decision making with hesitant pythagorean fuzzy sets,” Applied Soft Computing, vol. 60, pp. 167–179, 2017.
H. Arora and A. Naithani, “Significance of topsis approach to madm in computing exponential divergence measures for pythagorean fuzzy sets,” Decision Making: Applications in Management and Engineering, vol. 5, no. 1, pp. 246–263, 2022.
N. Kumar, A. Patel, and J. Mahanta, “K–l divergence-based distance measure for pythagorean fuzzy sets with various applications,” Journal of Experimental & Theoretical Artificial Intelligence, pp. 1–21, 2023.
K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. doi: 10.1016/S0165-0114(86)80034-3
Y. Qin, Y. Liu, and Z. Hong, “Multicriteria decision making method based on generalized pythagorean fuzzy ordered weighted distance measures,” Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3665–3675, 2017.
T.-Y. Chen, “Remoteness index-based pythagorean fuzzy vikor methods with a generalized distance measure for multiple criteria decision analysis,” Information Fusion, vol. 41, pp. 129–150, 2018.
B. Sarkar and A. Biswas, “Pythagorean fuzzy ahp-topsis integrated approach for transportation management through a new distance measure,” Soft Computing, vol. 25, no. 5, pp. 40734089, 2021.
A. Ohlan, “Multiple attribute decision-making based on distance measure under pythagorean fuzzy environment,” International Journal of Information Technology, pp. 1–13, 2021.
M. J. Khan, M. I. Ali, P. Kumam, W. Kumam, M. Aslam, and J. C. R. Alcantud, “Improved generalized dissimilarity measure-based vikor method for pythagorean fuzzy sets,” International Journal of Intelligent Systems, vol. 37, no. 3, pp. 1807–1845, 2022.
P. Dutta, G. Borah, B. Gohain, and R. Chutia, “Nonlinear distance measures under the framework of pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and covid-19 medicine selection,” Beni-Suef University Journal of Basic and Applied Sciences, vol. 12, no. 1, p. 42, 2023.
F. E. Boran, S. Genc¸, M. Kurt, and D. Akay, “A multi-criteria intuitionistic fuzzy group decision making for supplier selection with topsis method,” Expert systems with applications, vol. 36, no. 8, pp. 11363–11368, 2009.
E. K. Zavadskas and V. Podvezko, “Integrated determination of objective criteria weights in mcdm,” International Journal of Information Technology & Decision Making, vol. 15, no. 02, pp. 267–283, 2016.
R. Chaurasiya and D. Jain, “Pythagorean fuzzy mcdm method in renewable energy resources assessment,” Research Square, 2023. [Online]. Available: https://www.researchsquare.com/article/rs-2569784/v1
V. Arya and S. Kumar, “A picture fuzzy multiple criteria decision-making approach based on the combined todim-vikor and entropy weighted method,” Cognitive Computation, vol. 13, no. 5, pp. 1172–1184, 2021.
Published
2025-11-10
How to Cite
KUMAR, Naveen; MAHANTA, Juthika.
A Novel Pythagorean Fuzzy Distance Measure for Multicriteria Decision Making in Renewable Energy Resource Selection.
Yugoslav Journal of Operations Research, [S.l.], nov. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1371>. Date accessed: 20 dec. 2025.
doi: https://doi.org/10.2298/YJOR240715036K.
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Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
