A Novel Generalization of Hesitant Fuzzy Model with Application in Sustainable Supply Chain Optimization

Wajid Ali ¹ ( Department of Mathematics, Air University Islamabad, Islamabad, Pakistan. )
Tanzeela Shaheen ² ( Department of Mathematics, Air University Islamabad, Islamabad, Pakistan. )
Iftikhar  Ul Haq ³ ( Department of Mathematics, Air University Islamabad, Islamabad, Pakistan. )
Mohammad Mehedi  Hassan ⁴ ( Information Systems Department, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia. )

Submited date : 2024-07-26 Accepted date : 2024-09-25

Keywords: Hesitant fuzzy sets, c, d‐rung orthopair fuzzy sets, Decision making, MADM, Sustainable supply chain.,

Abstract :

The n,m‐rung orthopair fuzzy set theory is a robust model for managing uncertainty, particularly in multi‐attribute  decision‐making. Meanwhile, the hesitant fuzzy model is a well‐established tool in decision‐making processes. Recognizing the  similarities between these models, we propose a new framework called "c,d‐rung orthopair hesitant fuzzy sets," which integrates  both approaches. We examine key operations such as union, intersection, complement, subset, and equality, and introduce  aggregation operators like the c,d‐RHFPA, c,d‐RHFWA, c,d‐RHFPG, and c,d‐RHFWPG operators. Additionally, an algorithm for  multi‐attribute decision‐making is developed, which is applied to determine optimal business strategies for sustainable supply chain management. A comparative analysis with existing methods demonstrates the model's effectiveness, offering insights into  its strengths and limitations. This paper introduces a novel approach to decision‐making, outlining its real‐world application and  future research directions

References:

[1] Eskandarpour M, Dejax P, Miemczyk J, Péton O. Sustainable supply chain network design: An optimization‐ oriented review. Omega. 2015; 54: 11‐32.
DOI: hƩps://doi.org/10.1016/j.omega.2015.01.006
[2] Jayarathna CP, Agdas D, Dawes L, Yigitcanlar T. Multi‐objective optimization for sustainable supply chain and logistics: A re‐view. Sustainability. 2021; 13(24): 13617. DOI: hƩps://doi.org/10.3390/su132413617
[3] Linton, Jonathan D., Robert Klassen, and Vaidyanathan Jayaraman. "Sustainable supply chains: An introducƟon." Journal of operaƟons management 25.6 (2007): 1075‐1082. DOI: https://onlinelibrary.wiley.com/doi/10.1016/j.jom.2007.01.012
[4] Fahimnia B, Sarkis J, Gunasekaran A, Farahani R. Decision models for sustainable supply chain design and management. Annals of Operations Research. 2017; 250: 277‐278. DOI: hƩps://doi.org/10.1007/s10479‐017‐2428‐0
[5] Resat HG, Unsal B. A novel multi‐objective optimization approach for sustainable supply chain: A case study in packaging industry. Sustainable production and consumption. 2019; 20: 29‐39. DOI: hƩps://doi.org/10.1016/j.spc.2019.04.008
[6] Zhou Z, Cheng S, Hua B. Supply chain optimization of continuous process industries with sustainability considerations. Computers & Chemical Engineering. 2000; 24(2‐7): 1151‐1158. DOI: hƩps://doi.org/10.1016/S0098‐1354(00)00496‐8
[7] Eskandari‐Khanghahi M, Tavakkoli‐Moghaddam R, Taleizadeh AA, Amin SH. Designing and optimizing a sustainable supply chain network for a blood platelet bank under uncertainty. Engineering Applications of Artificial Intelligence. 2018; 71: 236‐250. DOI: https://doi.org/10.1016/j.engappai.2018.03.004
[8] Zhang, Shuzhu, Carman Ka Man Lee, Kan Wu, and King Lun Choy. "Multi‐objective optimization for sustainable supply chain network design considering multiple distribution channels." Expert Systems with Applications 65 (2016): 87‐99. DOI: https://doi.org/10.1016/j.eswa.2016.081037
[9] Yu Z, Khan SAR. Green supply chain network optimization under random and fuzzy environment. International Journal of Fuzzy Systems. 2022; 24: 1170‐1181. DOI: https://doi.org/10.1007/s40815‐020‐00979‐7
[10] Kazancoglu I, Ozbiltekin‐Pala M, Mangla SK, Kumar A, Kazancoglu Y. Using emerging technologies to improve the sustainability and resilience of supply chains in a fuzzy environment in the context of COVID‐ 19. Annals of Operations Research. 2023; 322(1): 217‐240. DOI: https://doi.org/10.1007/s10479‐022‐04775‐4
[11] Goodarzian F, Wamba SF, Mathiyazhagan K, Taghipour A. A new bi‐objective green medicine supply chain network design under fuzzy environment: Hybrid metaheuristic algorithms. Computers & industrial engineering. 2021; 160: 107535. DOI: hƩps://doi.org/10.1016/j.cie.2021.107535
[12] Liu S‐C, Jian Q‐Y, Wen H‐Y, Chung C‐H. A crop harvest time prediction model for better sustainability, integrating feature selection and artificial intelligence methods. Sustainability. 2022; 14(21): 14101. DOI: hƩps://doi.org/10.3390/su142114101
[13] Yadav D, Kumari R, Kumar N. Sustainable supply chain model for multi‐stage manufacturing with partial backlogging under the fuzzy environment with the effect of learning in screening process. International Journal of Applied and Computational Mathematics. 2021; 7(2): 40.
DOI: https://doi.org/10.1007/s40819‐021‐00951‐5
[14] Pourjavad E, Shahin A. A hybrid model for analyzing the risks of green supply chain in a fuzzy environment. Journal of Industrial and Production Engineering. 2020; 37(8): 422‐433. DOI: https://doi.org/10.1080/21681015.2020.1833995
[15] Alsaedi BSO, Alamri OA, Jayaswal MK, Mittal M. A sustainable green supply chain model with carbon emissions for defective items under learning in a fuzzy environment. Mathematics. 2023; 11(2): 301. DOI: hƩps://doi.org/10.3390/math11020301
[16] Su J, Xu B, Li L, Wang D, Zhang F. A green supply chain member selection method considering green innovation capability in a hesitant fuzzy environment. Axioms. 2023; 12(2): 188. DOI: hƩps://doi.org/10.3390/axioms12020188
[17] Wang S, Hu Z‐H. Green logistics service supply chain games considering risk preference in fuzzy environments. Sustainability. 2021; 13(14): 8024. DOI: hƩps://doi.org/10.3390/su13148024
[18] Mistarihi MZ, Magableh GM. Unveiling supply chain nervousness: A strategic framework for disruption management under fuzzy environment. Sustainability. 2023; 15(14): 11179. DOI: hƩps://doi.org/10.3390/su151411179
[19] Liu L, Cao W, Shi B, Tang M. Large‐scale green supplier selection approach under a q‐rung interval‐valued orthopair fuzzy environment. Processes. 2019; 7(9): 573. DOI: hƩps://doi.org/10.3390/pr7090573
[20] Chang J‐F, Lai CJ, Wang CN, Hsueh MH, Nguyen VT. Fuzzy optimization model for decision‐making in supply chain management. Mathematics. 2021; 9(4): 312. DOI: hƩps://doi.org/10.3390/math9040312
[21] Rehman O, Ali Y. Enhancing healthcare supply chain resilience: Decision‐making in a fuzzy environment. The International Journal of Logistics Management. 2022; 33(2): 520‐546. DOI: https://doi.org/10.1108/IJLM‐01‐2021‐0004
[22] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338‐353. DOI: hƩps://doi.org/10.1016/S0019‐9958(65)90241‐X
[23] Dubois D, Prade H. Fundamentals of Fuzzy Sets. Springer Science & Business Media; 2012.
[24] Atanassov KT, Intuitionistic Fuzzy Sets. Physica‐Verlag HD, 1999. DOI: hƩps://doi.org/10.1007/978‐3‐7908‐1870‐3_1
[25] Senapati T, Yager RR. Fermatean fuzzy sets. Journal of Ambient Intelligence and Humanized Computing. 2020; 11: 663‐674. DOI: hƩps://doi.org/10.1007/s12652‐019‐01377‐0
[26] Cuong BC. Picture fuzzy sets. Journal of Computer Science and Cybernetics . 2014; 30(4): 409‐420. DOI:
https://doi.org/10.15625/1813‐9663/30/4/5032
[27] Yager RR. Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems. 2016; 25(5): 1222‐1230. DOI: https://doi.org/10.1109/TFUZZ.2016.2604005
[28] Torra V. Hesitant fuzzy sets. International journal of intelligent systems. 2010; 25(6): 529‐539. DOI: hƩps://doi.org/10.1002/int.20418
[29] Ali W, Shaheen T, Haq IU, Toor HG, Akram F, Jafari S, et al. Multiple‐attribute decision making based on intuitionistic hesitant fuzzy connection set environment. Symmetry. 2023; 15(3): 77. DOI: hƩps://doi.org/10.3390/sym15030778
[30] Radenovic S, Ali W, Shaheen T, Haq IU, Akram F, Toor H. Multiple attribute decision‐making based on bonferroni mean operators under square root fuzzy set environment. Journal of Computational and Cognitive Engineering. 2023; 2(3): 236‐248. DOI: hƩps://doi.org/10.47852/bonviewJCCE2202366
[31] Ali W, Shaheen T, Haq IU, Alballa T, Alburaikan A, Khalifa HAEl‐W. A novel generalization of Q‐Rung Orthopair Fuzzy Aczel Alsina Aggregation Operators and their application in wireless sensor networks. Sensors. 2023; 23(19): 8105. DOI: hƩps://doi.org/10.3390/s23198105
[32] Rodriguez, Rosa M., Luis Martinez, and Francisco Herrera. "Hesitant fuzzy linguistic term sets for decision making." IEEE TransacƟons on fuzzy systems 20.1 (2011): 109‐119. DOI: 10.1109/TFUZZ.2011.2170076
[33] Kutlu Gündoğdu, Fatma, and Cengiz Kahraman. "Spherical fuzzy sets and decision‐making applications." Intelli‐gent and Fuzzy Techniques in Big Data Analytics and Decision Making: Proceedings of the INFUS 2019 Conference, Istanbul, Turkey, July 23‐25, 2019. Springer InternaƟonal Publishing, 2020. DOI: hƩps://doi.org/10.1007/9
[34] Garg H. A new possibility degree measure for interval‐valued q‐rung orthopair fuzzy sets in decision‐ making. International Journal of Intelligent Systems. 2021; 36(1): 526‐557. DOI: https://doi.org/10.1002/int.22308
[35] Al‐shami TM, Mhemdi A. Generalized frame for orthopair fuzzy sets: (m,n)‐fuzzy sets and their applications to multi‐criteria decision‐making methods. Information. 2023; 14(1): 56. DOI: hƩps://doi.org/10.3390/info14010056
[36] Shahzadi G, Luqman A, Shahzadi S, Deveci M. A new (p,q)‐rung orthopair fuzzy SIR method with a multi‐ criteria decision‐making approach. Granular Computing. 2024; 9(2): 30. DOI: https://doi.org/10.21203/rs.3.rs‐3251960/v1
[37] Ibrahim HZ. Topological approaches for n, m‐rung orthopair fuzzy sets with applications to diagnosis of learning disability. Journal of Intelligent & Fuzzy Systems. 2023; 44(1): 855‐869. DOI: https://doi.org/10.3233/JIFS‐221528
[38] Ibrahim, Hariwan Z. "Multi‐attribute group decision‐making based on bipolar n, m‐rung orthopair fuzzy sets." Granular CompuƟng (2023): 1‐18. DOI: https://doi.org/10.1007/s41066-023-00405-x
[39] Ibrahim, Hariwan Z. "Innovative method for group decision‐making using n, m‐rung orthopair fuzzy soft expert set knowledge." SoŌ CompuƟng (2023): 1‐20. DOI: hƩps://doi.org/10.1007/s00500‐023‐08980‐6
[40] Mahmood T, Ali W, Ali Z, Chinram R. Power aggregation operators and similarity measures based on improved intuitionistic hesitant fuzzy sets and their applications to multiple attribute decision making. Computer Modeling in Engineering & Sciences. 2021; 126(3): 1165‐1187.
DOI: hƩps://doi.org/10.32604/cmes.2021.014393
[41] Qahtan S, Alsattar HA, Zaidan AA, Deveci M, Pamucar D, Ding W. A novel fuel supply system modelling approach for electric vehicles under Pythagorean probabilistic hesitant fuzzy sets. Information Sciences. 2023; 622: 1014‐1032. DOI: https://doi.org/10.1016/j.ins.2022.11.166
[42] Ali W, Shaheen T, Toor HG, Akram F, Uddin MZ, Hassan MM. Selection of investment policy using a novel three‐way group decision model under intuitionistic hesitant fuzzy sets. Applied Sciences. 2023; 13(7): 4416. DOI: hƩps://doi.org/10.3390/app13074416
[43] Kirişci M. Fermatean hesitant fuzzy sets with medical decision‐making application. Research Square. 2022; DOI:
https://doi.org/10.21203/rs.3.rs‐1151389/v1
[44] Liu D, Peng D, Liu Z. The distance measures between q‐rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making. International Journal of Intelligent Systems. 2019; 34(9): 2104‐2121. DOI: https://doi.org/10.1002/int.22133
[45] Sarwar M, Ali G, Chaudhry NR. Decision‐making model for failure modes and effect analysis based on
rough fuzzy integrated clouds. Applied Soft Computing. 2023; 136: 110148. DOI: hƩps://doi.org/10.1016/j.asoc.2023.110148
[46] Punnam Chander, G., and Sujit Das. "A Linear Diophantine Fuzzy Soft Set‐Based Decision‐Making Approach Using Revised Max‐Min Average Composition Method." Fuzzy, Rough and Intuitionistic Fuzzy Set Approaches for Data Handling: Theory and Applications. Singapore: Springer Nature Singapore, 2023. 165‐ 181. DOI: hƩps://doi.org/10.1007/9
[47]Garg H. A novel exponential‐logarithm‐q‐rung orthopair fuzzy set and their applications to multiple attribute group decision‐making process. Granular Computing. 2023; 8(6): 1991‐2004. DOI: https://doi.org/10.1007/s41066‐023‐00418‐6
[48] Wan B, Hu Z, Garg H, Cheng Y, Han M. An integrated group decision‐making method for the evaluation of hypertension follow‐up systems using interval‐valued q‐rung orthopair fuzzy sets. Complex & Intelligent Systems. 2023; 9(4): 4521‐4554. DOI: https://doi.org/10.1007/s40747‐022‐00953‐w
[49] Wang C‐N, Chung YC, Wibowo FD, Dang TT, Nguyen NAT. Sustainable last‐mile delivery solution evaluation in the context of a developing country: A novel OPA–Fuzzy MARCOS approach. Sustainability. 2023; 15(17): 12866. DOI: hƩps://doi.org/10.3390/su151712866
[50] Yager RR. The power average operator. IEEE Transactions on Systems, Man, and Cybernetics‐Part A: Systems and Humans. 2001; 31(6): 724‐731. DOI: https://doi.org/10.1109/3468.983429
[51] Xu Z, Yager RR. Power‐geometric operators and their use in group decision making. IEEE Transac‐tions on Fuzzy Systems. 2009; 18(1): 94‐105. DOI: https://doi.org/10.1109/TFUZZ.2009.2036907
[52] Yager RR. Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making. 2004; 3: 93‐ 107. DOI: https://doi.org/10.1023/B: FODM.0000013074.68765.97
[53] Dhankhar C, Kumar K. Multi‐attribute decision making based on the q‐rung orthopair fuzzy Yager power weighted geometric aggregation operator of q‐rung orthopair fuzzy values. Granular Computing. 2023; 8(3): 467‐478. DOI: hƩps://doi.org/10.1007/s41066‐022‐00343‐0
[54] Ali W, Shaheen T, Toor HG, Akram F, Uddin MZ, Hassan MM. An innovative decision model utilizing intuitionistic hesitant fuzzy Aczel‐Alsina aggregation operators and its application. Mathematics. 2023; 11(12): 2768. DOI: hƩps://doi.org/10.3390/math11122768
[55] Haq IU, Shaheen T, Ali W, Toor H, Senapati T, Pilla F, Moslem S. Novel fermatean fuzzy Aczel–Alsina model for investment strategy selection. Mathematics. 2023; 11(14): 3211. DOI: hƩps://doi.org/10.3390/math11143211
[56] Ali W, Shaheen T, Toor HG, Alballa T, Alburaikan A, Khalifa HAEW. An improved intuitionistic fuzzy decision‐theoretic rough set model and its application. Axioms. 2023; 12(11): 1003. DOI: hƩps://doi.org/10.3390/axioms12111003
[57] Ali, Wajid, et al. "A Novel Interval‐Valued Decision Theoretic Rough Set Model with Intuitionistic Fuzzy Numbers Based on Power Aggregation Operators and Their Application in Medical Diagnosis." Mathematics 11.19 (2023): 4153. DOI: hƩps://doi.org/10.3390/math11194153
[58] Qayyum A, Mushtaq N, Shaheen T, Ali W, Smarandache F. Some similarity measures on generalized interval‐valued intuitionistic fuzzy soft expert sets and their applications in medical diagnosis. Neutrosophic Systems with Applications. 2024; 23: 47‐67. DOI: hƩps://doi.org/10.61356/j.nswa.2024.23398