Document Type : Article

**Authors**

Department of Mathematics, University of the Punjab, Lahore, Pakistan

**Abstract**

Road freight transport, in particular, is associated with a number of negative external factors, including environmental and health care concerns, as well as the excessive use of nonrenewable natural resources. In the metropolitan climate, urban freight transport has a particularly noticeable ecological footprint. This is the most pressing issue confronting all stake holders involved in urban freight transportation. In multi-criteria group decision-making (MCGDM) strategies, the lack of contact between membership degree (MSD) and non-membership degree (NMSD) would be the basic factor for poor results in many MCGDM. To address these drawbacks, we define new aggregation operators (AOs) methods based on generalized membership grades of q-rung orthopair fuzzy (q-ROF) information, in this way, the input evaluation is interpreted in terms of q-rung orthopair fuzzy numbers (q-ROFNs). While interactive operators are well-known for interrelationship between generalized membership grades, prioritized operators are well-suited to exploit prioritized relationships among various criterion. Based on the characteristics of such flexible operators, two novel hybrid aggregation operators are proposed named as "q-rung orthopair fuzzy prioritized interactive weighted averaging operator and the q-rung orthopair fuzzy prioritized interactive weighted geometric operator".

**Keywords**

References:

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[2] Jaller, M., Pineda, L., Ambrose, H. "Evaluating the use of zero-emission vehicles in last mile deliveries", ITS Reports, (2017). http://dx.doi.org/10.7922/G2JM27TW Retrieved from https://escholarship.org/uc/item/7kr753nm.

[3] Davis, B. A., Figliozzi, M. A. "A methodology to evaluate the competitiveness of electric delivery trucks", Transportation Research Part E: Logistics and Transportation Review, 49(1), pp 8–23 (2013).

[4] Rasouli, S., Timmermans, H. "Uncertainty in travel demand forecasting models: Literature review and research agenda", Transportation Letters, 4(1), pp 55-73 (2012).

[5] Klemick, H., Kopits, E., Wolverton, A. et al. "Heavy-duty trucking and the energy efficiency paradox: evidence from focus groups and interviews", Transportation Research Part A: Policy and Practice, 77, pp 154–166 (2015).

[6] Brownstone, D., Bunch, D. S., Golob, T. F. et al. "Atransactions choice model for forecasting demand for alternative-fuel vehicles", Research in Transportation Economics, 4, pp 87–129 (1996).

[7] Miller, M., Wang, Q., Fulton, L. "Truck Choice Modeling: Understanding California’s Transition to Zero-Emission Vehicle Trucks Taking into Account Truck Technologies, Costs, and Fleet Decision Behavior", (2017), UC Davis: National Center for Sustainable Transportation. Retrieved from https://escholarship.org/uc/item/1xt3k10x.

[8] Zhang, Y., Jiang, Y., Rui, W. et al. "Analyzing truck fleets’ acceptance of alternative fuel freight vehicles in China", Renewable Energy, 134, pp 1148–1155 (2019).

[9] Bunch, D. S., Brandley, M., Golob, T. F. et al. "Demand for clean alternative-fuel vehicles in California: A discrete-choice stated preference pilot project", Transportation Research Part A: Policy and Practice, 27(3), pp 237–253 (1993).

[10] Kurani, K. S., Turrentine, T. Sperling, D. "Demand for electric vehicles in hybrid household: An exploratory analysis", Transport Policy, 1(4), pp 224–256 (1994).

[11] Jeremy, H., Richard, N. "Life cycle model of alternative fuel vehicles: Emissions, energy, and cost trade-offs", Transportation Research Part, 35, pp 243–266 (2001).

[12] Aydin, S., Kahraman, C. "Vehicle selection for public transportation using an integrated multi criteria decision making approach: a case of Ankara", Journal of Intelligent & Fuzzy Systems, 26(5), pp 2467-2481.

[13] Yavuz, M., Oztaysi, B., Onar, S. C. et al. "Multi-criteria evaluation of alternativefuel vehicles via a hierarchical hesitant fuzzy linguistic model", Expert System and Application, 42(5), pp 2835–2848 (2015).

[14] Wtróbski, J., Maecki, K., Kijewska, K. et al. "Multi-criteria analysis of electric vans for city logistics", Sustainability 9(8), pp 1453 (2017).

[15] Jaller, M., Otay, I., "Evaluating sustainable vehicle technologies for freight transportation using spherical fuzzy AHP and TOPSIS", Advances in Intelligent Systems and Computing, 1197, pp 118–126 (2020).

[16] Alkharabsheh, A., Moslem, S., Oubahman, L. et al. "An integrated approach of multi-criteria decision-making and grey theory for evaluating urban public transportation systems", Sustainability, 13, Article no. 2740 (2021).

[17] Ma, J., Wang, N., Kong, D. "Market forecasting modeling study for new energy vehicle based on AHP and logit regression", Journal of Tongji University, 37(8), pp 1079–1084 (2009).

[18] Erdem, C., Enturk, I. S., Simsek, T. "Identifying the factors affecting the willingness to pay for fuel-efficient vehicles in Turkey: A case of hybrids", Energy Policy, 38(6), pp 3038–3043 (2010).

[19] Maria, Y. R., Susana, M., Manfred, F. et al. "Public attitudes towards and demand for hydrogen and fuel cell vehicles: A review of the evidence and methodological implications", Energy Policy, 38, pp 5301–5310 (2010).

[20] Mabit, S. L., Fosgerau, M. "Demand for alternativefuel vehicles when registration taxes are high", Transportation Research Part D: Transport and Environment, 16(3), pp 225–231 (2011).

[21] Behnam, V., Zandieh, M., Moghaddam, R. T. "Two novel FMCDM methods for alternative-fuel buses selection", Applied Mathematical Modeling, 35, pp 1396–1412 (2011).

[22] Zhang, Y., Yu, Y., Zou, B. "Analyzing public awareness and acceptance of alternative fuel vehicles in China: The case of EV", Energy Policy, 39, pp 7015–7024 (2011).

[23] Koohathongsumrit, N., Meethom, W. "An integrated approach of fuzzy risk assessment model and data envelopment analysis for route selection in multimodal transportation networks", Expert Systems with Applications, 171, Articel no. 114342 (2021).

[24] Poudenx, P. "The effect of transportation policies on energy consumption and greenhouse gas emission from urban passenger transportation", Transportation Research Part A: Policy and Practice, 42(6), pp 901-909 (2008).

[25] Daryanto, Y., Wee, H. M., Astanti, R. D., "Three-echelon supply chain model considering carbon emission and item deterioration", Transportation Research Part E: Logistics and Transportation Review, 122, pp 368-383 (2019).

[26] Zadeh, L.A. "Fuzzy sets", Information and Control, 8, pp 338-353 (1965).

[27] Atanassov, K.T. "Intuitionistic fuzzy sets", Fuzzy Sets ans Systems, 20(1), pp 87-96 (1986).

[28] Yager, R.R., Abbasov, A.M. "Pythagorean membership grades, complex numbers, and decision making", International Journal of Intelligent Systems, 28, pp 436-452 (2013).

[29] Yager, R.R. "Pythagorean fuzzy subsets", IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint,

Edmonton, Canada, IEEE, pp 57-61 (2013).

[30] Yager, R.R. "Pythagorean membership grades in multi criteria decision-making", IEEE Transactions on Fuzzy Systems, 22, pp 958-965 (2014).

[31] Yager, R.R. "Generalized orthopair fuzzy sets", IEEE Transactions on Fuzzy Systems, 25, pp 1222-1230 (2017).

[32] Liu, P., Wang, P. "Some q-rung orthopair fuzzy aggregation operator and their application to multi-attribute decision making", International Journal of Intelligent Systems, 33(2), pp 259-280 (2018).

[33] Garg, H. "CN-ROFS: connection number-based q-rung orthopair fuzzy set and their application to decision-making process", International Journal of Intelligent Systems, 36(7), pp 3106–3143 (2021).

[34] Peng, X., Dai, J., Garg, H. "Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decisionmaking method with a new score function", International Journal of Intelligent Systems, 33(11), pp 2255–2282 (2018).

[35] Jana, C., Muhiuddin, G., Pal, M. "Some Dombi aggregation of q-rung orthopair fuzzy numbers in multiple-attribute decision making", International Journal of Intelligent Systems, 34(12), pp 3220–3240 (2019).

[36] Wei, G., Gao, H., Wei, Y. "Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making", International Journal of Intelligent Systems, 33(7), pp 1426–1458 (2018).

[37] Lin, M., Li, X., Chen, L. "Linguistic q-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators", International Journal of Intelligent Systems, 35(2), pp 217–249 (2020).

[38] Riaz, M., Salabun, W., Farid, H. M. A. et al. "A robust q-rung orthopair fuzzy information aggregation using Einstein operations with application to sustainable energy planning decision management", Energies, 13(9), Article no. 2125 (2020).

[39] Riaz, M., Pamucar, D., Farid, H. M. A. et al. "q-Rung orthopair fuzzy prioritized aggregation operators and their application towards green supplier chain management", Symmetry, 12(6), Article no. 976 (2020).

[40] Riaz, M., Farid, H. M. A., Kalsoom, H. et al. "A Robust q-rung orthopair fuzzy Einstein prioritized aggregation operators with application towards MCGDM", Symmetry, 12(6), Article no. 1058 (2020).

[41] Farid, H. M. A., Riaz, M., "Some generalized q-rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws", International Journal of Intelligent Systems, 36, pp 7239-7273 (2021).

[42] Liu, P., Liu, J. "Some q-Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi-Attribute Group

Decision Making", International Journal of Intelligent Systems, 33(2), pp 315-347 (2018).

[43] Joshi, B. P., Gegov, A. " Confidence levels q-rung orthopair fuzzy aggregation operators and its applications to MCDM problems", International Journal of Intelligent Systems, 35(1), pp 125-149 (2020).

[44] Riaz, M., Razzaq, A., Kalsoom, H., et al. "q-rung orthopair fuzzy geometric aggregation operators based on generalized and group-generalized parameters with application to water loss management", Symmetry, 12(8), Article no. 1236 (2020).

[45] Riaz, M., Garg, H., Farid, H. M. A., Aslam, M. "Novel q-rung orthopair fuzzy interaction aggregation operators and their

application to low-carbon green supply chain management", Journal of Intelligent & Fuzzy Systems, 41(2), pp 4109-4126 (2021).

[46] Akram, M., Khan, A., Alcantud, J.C. R. et al. "A hybrid decision-making framework under complex spherical fuzzy prioritized weighted aggregation operators", Expert Systems, 4, Article no. 12712 (2021).

[47] Jana, C., Pal, M., Liu, P. "Multiple attribute dynamic decision making method based on some complex aggregation functions in CQROF setting", Comp. Appl. Math, 41, Article no. 103, (2022).

[48] Feng, F., Zheng, Y., Alcantud, J. C. R. et al. "Minkowski weighted score functions of intuitionistic fuzzy values", Mathematics, 8(7), pp 1-30 (2020).

[49] Ashraf, S., Abdullah, S., Zeng, S. et al. "Fuzzy decision support modeling for hydrogen power plant selection based on single valued neutrosophic Sine trigonometric aggregation operators", Symmetry, 12(2), Article no 298 (2020).

[50] Liu, P., Chen, S. M., Wang, P. "Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators", IEEE Transactions on Systems, Man, and Cybernetics, 99, pp 1–16 (2019).

[51] Xing, Y., Zhang, R., Zhou, Z. "Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making", Soft Computing, 23(11), pp 627–649 (2019).

[52] Liu, P., Wang, P. "Multiple-attribute decision-making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers", IEEE Transactions on Fuzzy Systems, 27(5), pp 834–848 (2019).

[53] Liu, Z., Liu, P. Liang, X. "Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment", International Journal of Intelligent Systems, 33, pp 1900–1928 (2018).

[54] Mahmood, T., Ali, Z. "A novel approach of complex q-rung orthopair fuzzy hamacher aggregation operators and their application for cleaner production assessment in gold mines", Journal of Ambient Intelligence and Humanized Computing, 12, pp 8933–8959 (2021).

[55] Saha, A., Majumder, P., Dutta, D. et al. "Multi-attribute decision making using q-rung orthopair fuzzy weighted fairly aggregation operators ", Journal of Ambient Intelligence and Humanized Computing, 12, pp 8149–8171 (2021).

[56] Hussain, A., Ali, M. I., Mahmood, T. "Hesitant q-rung orthopair fuzzy aggregation operators with their applications in multicriteria decision making ", Iranian Journal of Fuzzy Systems, 17(3), pp 117-134 (2020).

[57] Jana, C., Pal, M., Wang, J. "A robust aggregation operator for multi-criteria decision-making method with bipolar fuzzy soft environment", Iranian Journal of Fuzzy Systems, 16(6), pp 1-16 (2019).

[58] Wang, L., Garg, H., Li, N. "Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight", Soft Computing, 25, pp 973–993 (2021).

[59] Wang, L., Garg, H. "Algorithm for multiple attribute decision-making with interactive archimedean norm operations under pythagorean fuzzy uncertainty", International Journal of Computational Intelligence Systems, 14(1), pp 503-527 (2021).

[60] Wang, L., Li, N. "Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making", International Journal of Intelligent Systems, 35(1), pp 150-183 (2020).

[61] Wei, G. "Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making", Journal of Intelligent & Fuzzy Systems, 33(4), pp 2119-2132 (2017).

[62] Gao, H., Lu, M., Wei, G. et al. "Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making", Fundamenta Informaticae, 159(4), pp 385-428 (2018).

[63] Garg, H. "Some series of intuitionistic fuzzy interactive averaging aggregation operators", Springer Plus, 5, Artilce no. 999 (2016).

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Articles in Press, Accepted Manuscript

Available Online from 11 July 2022