Interval-Valued Spherical Fuzzy Analytic Hierarchy Process Method to Evaluate Public Transportation Development
Volume 32, Issue 4 (2021), pp. 661–686
Pub. online: 29 April 2021
Type: Research Article
Open Access
Open Access
Received
1 October 2020
1 October 2020
Accepted
1 April 2021
1 April 2021
Published
29 April 2021
29 April 2021
Abstract
Consensus creation is a complex challenge in decision making for conflicting or quasi-conflicting evaluator groups. The problem is even more difficult to solve, if one or more respondents are non-expert and provide uncertain or hesitant responses in a survey. This paper presents a methodological approach, the Interval-valued Spherical Fuzzy Analytic Hierarchy Process, with the objective to handle both types of problems simultaneously; considering hesitant scoring and synthesizing different stakeholder group opinions by a mathematical procedure. Interval-valued spherical fuzzy sets are superior to the other extensions with a more flexible characterization of membership function. Interval-valued spherical fuzzy sets are employed for incorporating decision makers’ judgements about the membership functions of a fuzzy set into the model with an interval instead of a single point. In the paper, Interval-valued spherical fuzzy AHP method has been applied to public transportation problem. Public transport development is an appropriate case study to introduce the new model and analyse the results due to the involvement of three classically conflicting stakeholder groups: passengers, non-passenger citizens and the representatives of the local municipality. Data from a real-world survey conducted recently in the Turkish big city, Mersin, help in understanding the new concept. As comparison, all likenesses and differences of the outputs have been pointed out in the reflection with the picture fuzzy AHP computation of the same data. The results are demonstrated and analysed in detail and the step-by-step description of the procedure might foment other applications of the model.
References
Abastante, F., Corrente, S., Greco, S., Ishizaka, A., Lami, I.M. (2019). A new parsimonious AHP methodology: assigning priorities to many objects by comparing pairwise few reference objects. Expert Systems with Applications, 127, 109–120. https://doi.org/10.1016/j.eswa.2019.02.036.
Abdel-Basset, M., Mohamed, M., Zhou, Y., Hezam, I. (2017). Multi-criteria group decision making based on neutrosophic analytic hierarchy process. Journal of Intelligent and Fuzzy Systems, 33(6), 4055–4066. https://doi.org/10.3233/JIFS-17981.
Abdullah, L., Najib, L. (2014). A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process. Expert Systems with Applications, 41(7), 3297–3305. https://doi.org/10.1016/j.eswa.2013.11.028.
Abdullah, L., Najib, L. (2016). A new preference scale mcdm method based on interval-valued intuitionistic fuzzy sets and the analytic hierarchy process. Soft Computing, 20(2), 511–523. https://doi.org/10.1007/s00500-014-1519-y.
Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3.
Awasthi, A., Chauhan, S.S. (2011). Using AHP and Dempster–Shafer theory for evaluating sustainable transport solutions. Environmental Modelling and Software, 26(6), 787–796. https://doi.org/10.1016/j.envsoft.2010.11.010.
Bolturk, E., Kahraman, C. (2018). A novel interval-valued neutrosophic AHP with cosine similarity measure. Soft Computing, 22(15), 4941–4958. https://doi.org/10.1007/s00500-018-3140-y.
Boltürk, E., Çevik Onar, S., Öztayşi, B., Kahraman, C., Goztepe, K. (2016). Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP. International Journal of the Analytic Hierarchy Process, 8(2), 271–298. https://doi.org/10.13033/ijahp.v8i2.387.
Bozóki, S., Csató, L., Temesi, J. (2016). An application of incomplete pairwise comparison matrices for ranking top tennis players. European Journal of Operational Research, 248(1), 211–218. https://doi.org/10.1016/j.ejor.2015.06.069.
Buckley, J.J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17(3), 233–247. https://doi.org/10.1016/0165-0114(85)90090-9.
Chiclana, F., Herrera, F., Herrera-Viedma, E. (2001). Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets and Systems, 122(2), 277–291. https://doi.org/10.1016/S0165-0114(00)00004-X.
Cho, Y.-G., Cho, K.-T. (2008). A loss function approach to group preference aggregation in the AHP. Computers and Operations Research, 35(3), 884–892. https://doi.org/10.1016/j.cor.2006.04.008.
Chou, Y.-C., Yen, H.-Y., Dang, V.T., Sun, C.-C. (2019). Assessing the human resource in science and technology for Asian countries: application of fuzzy AHP and fuzzy TOPSIS. Symmetry, 11(2), 251. https://doi.org/10.3390/sym11020251.
Cu’ò’ng, B.C. (2015). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30(4), 409–420. https://doi.org/10.15625/1813-9663/30/4/5032.
Duleba, S., Moslem, S. (2019). Examining Pareto optimality in analytic hierarchy process on real data: an application in public transport service development. Expert Systems with Applications, 116, 21–30. https://doi.org/10.1016/j.eswa.2018.08.049.
Duleba, S., Mishina, T., Shimazaki, Y. (2012). A dynamic analysis on public bus transport’s supply quality by using AHP. Transport, 27(3), 268–275. https://doi.org/10.3846/16484142.2012.719838.
Efe, B. (2016). An integrated fuzzy multi criteria group decision making approach for ERP system selection. Applied Soft Computing, 38, 106–117. https://doi.org/10.1016/j.asoc.2015.09.037.
Gargallo, P., Moreno-Jiménez, J.M., Salvador, M. (2007). AHP-group decision making: a Bayesian approach based on mixtures for group pattern identification. Group Decision and Negotiation, 16(6), 485–506. https://doi.org/10.1007/s10726-006-9068-0.
Ghorbanzadeh, O., Moslem, S., Blaschke, T., Duleba, S. (2019). Sustainable urban transport planning considering different stakeholder groups by an interval-AHP decision support model. Sustainability, 11(1), 9. https://doi.org/10.3390/su11010009.
Gündoğdu, F.K., Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent and Fuzzy Systems, 36(1), 337–352. https://doi.org/10.3233/JIFS-181401.
Gündoğdu, F.K., Kahraman, C. (2020). A novel spherical fuzzy analytic hierarchy process and its renewable energy application. Soft Computing, 24(6), 4607–4621. https://doi.org/10.1007/s00500-019-04222-w.
Ishizaka, A. (2019). Analytic hierarchy process and its extensions. In: New Perspectives in Multiple Criteria Decision Making. Springer, pp. 81–93. https://doi.org/10.1007/978-3-030-11482-4_2.
Kahraman, C., Öztayşi, B., Uçal Sari, I., Turanoğlu, E. (2014). Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowledge-Based Systems, 59, 48–57. https://doi.org/10.1016/j.knosys.2014.02.001.
Kar, A.K. (2015). A hybrid group decision support system for supplier selection using analytic hierarchy process, fuzzy set theory and neural network. Journal of Computational Science, 6, 23–33. https://doi.org/10.1016/j.jocs.2014.11.002.
Karapetrovic, S., Rosenbloom, E.S. (1999). A quality control approach to consistency paradoxes in AHP. European Journal of Operational Research, 119(3), 704–718. https://doi.org/10.1016/S0377-2217(98)00334-8.
Kilic, M., Kaya, İ. (2015). Investment project evaluation by a decision making methodology based on type-2 fuzzy sets. Applied Soft Computing, 27, 399–410. https://doi.org/10.1016/j.asoc.2014.11.028.
Lane, E.F., Verdini, W.A. (1989). A consistency test for AHP decision makers. Decision Sciences, 20(3), 575–590. https://doi.org/10.1111/j.1540-5915.1989.tb01568.x.
Lee, J.-H., Li, T.-C. (2011). Supporting user participation design using a fuzzy analytic hierarchy process approach. Engineering Applications of Artificial Intelligence, 24(5), 850–865. https://doi.org/10.1016/j.engappai.2011.01.008.
Liao, H., Xu, Z. (2015). Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process. Applied Soft Computing, 35, 812–826. https://doi.org/10.1016/j.asoc.2015.04.015.
Lin, C., Kou, G., Peng, Y., Alsaadi, F.E. (2020). Aggregation of the nearest consistency matrices with the acceptable consensus in AHP-GDM. Annals of Operations Research, 1(17). https://doi.org/10.1007/s10479-020-03572-1.
Macharis, C., Bernardini, A. (2015). Reviewing the use of multi-criteria decision analysis for the evaluation of transport projects: time for a multi-actor approach. Transport Policy, 37, 177–186. https://doi.org/10.1016/j.tranpol.2014.11.002.
Minatour, Y., Bonakdari, H., Aliakbarkhani, Z.S. (2016). Extension of fuzzy Delphi AHP based on interval-valued fuzzy sets and its application in water resource rating problems. Water Resources Management, 30(9), 3123–3141. https://doi.org/10.1007/s11269-016-1335-5.
Mohd, W.R.W., Abdullah, L. (2017). Pythagorean fuzzy analytic hierarchy process to multi-criteria decision making. AIP Conference Proceedings, 1905. https://doi.org/10.1063/1.5012208.
Moslem, S., Ghorbanzadeh, O., Blaschke, T., Duleba, S. (2019). Analysing stakeholder consensus for a sustainable transport development decision by the fuzzy AHP and interval AHP. Sustainability, 11(12), 3271. https://doi.org/10.3390/su11123271.
Ossadnik, W., Schinke, S., Kaspar, R.H. (2016). Group aggregation techniques for analytic hierarchy process and analytic network process: a comparative analysis. Group Decision and Negotiation, 25(2), 421–457. https://doi.org/10.1007/s10726-015-9448-4.
Öztaysi, B., Onar, S.Ç., Boltürk, E., Kahraman, C. (2015). Hesitant fuzzy analytic hierarchy process. In: 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–7, IEEE. https://doi.org/10.1109/FUZZ-IEEE.2015.7337948.
Pamučar, D., Stević, Ž., Zavadskas, E.K. (2018). Integration of interval rough AHP and interval rough MABAC methods for evaluating university web pages. Applied Soft Computing, 67, 141–163. https://doi.org/10.1016/j.asoc.2018.02.057.
Rallabandi, L.N.P.K., Vandrangi, R., Rachakonda, S.R. (2016). Improved consistency ratio for pairwise comparison matrix in analytic hierarchy processes. Asia-Pacific Journal of Operational Research, 33(03), 1650020. https://doi.org/10.1142/S0217595916500202.
Saaty, T.L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234–281. https://doi.org/10.1016/0022-2496(77)90033-5.
Saaty, T.L. (2008). Decision making with the analytic hierarchy process. International Journal of Services Sciences, 1(1), 83–98. https://doi.org/10.1504/IJSSci.2008.01759.
Sadiq, R., Tesfamariam, S. (2009). Environmental decision-making under uncertainty using intuitionistic fuzzy analytic hierarchy process (IF-AHP). Stochastic Environmental Research and Risk Assessment, 23(1), 75–91. https://doi.org/10.1007/s00477-007-0197-z.
Sahrom, N.A. (2014). A z-number extension of an integrated analytic hierarchy process-fuzzy data envelopment analysis for risk assessment. Masters thesis, Universiti Teknologi MARA. http://ir.uitm.edu.my/id/eprint/16365.
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539. https://doi.org/10.1002/int.20418.
Triantaphyllou, E., Hou, F., Yanase, J. (2020). Analysis of the final ranking decisions made by experts after a consensus has been reached in group decision making. Group Decision and Negotiation, 29, 271–291. https://doi.org/10.1007/s10726-020-09655-5.
Tüysüz, F., Şimşek, B. (2017). A hesitant fuzzy linguistic term sets-based AHP approach for analyzing the performance evaluation factors: an application to cargo sector. Complex and Intelligent Systems, 3(3), 167–175. https://doi.org/10.1007/s40747-017-0044-x.
Van Laarhoven, P.J.M., Pedrycz, W. (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 11(1–3), 229–241. https://doi.org/10.1016/S0165-0114(83)80082-7.
Wang, C.-N., Huang, Y.-F., Cheng, I., Nguyen, V. (2018). A multi-criteria decision-making (MCDM) approach using hybrid SCOR metrics, AHP, and TOPSIS for supplier evaluation and selection in the gas and oil industry. Processes, 6(12), 252. https://doi.org/10.3390/pr6120252.
Wang, B., Song, J., Ren, J., Li, K., Duan, H. (2019). Selecting sustainable energy conversion technologies for agricultural residues: a fuzzy AHP-VIKOR based prioritization from life cycle perspective. Resources, Conservation and Recycling, 142, 78–87. https://doi.org/10.1016/j.resconrec.2018.11.011.
Wu, Z., Jin, B., Fujita, H., Xu, J. (2020). Consensus analysis for AHP multiplicative preference relations based on consistency control: a heuristic approach. Knowledge-Based Systems, 191, 105317. https://doi.org/10.1016/j.knosys.2019.105317.
Yager, R.R. (2013). Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences, 8(3), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5.
Zeshui, X., Cuiping, W. (1999). A consistency improving method in the analytic hierarchy process. European Journal of Operational Research, 116(2), 443–449. https://doi.org/10.1016/S0377-2217(98)00109-X.
Zheng, Y., He, Y., Xu, Z., Pedrycz, W. (2018). Assessment for hierarchical medical policy proposals using hesitant fuzzy linguistic analytic network process. Knowledge-Based Systems, 161, 254–267. https://doi.org/10.1016/j.knosys.2018.07.005.
Zhu, B., Xu, Z. (2014). Analytic hierarchy process-hesitant group decision making. European Journal of Operational Research, 239(3), 794–801. https://doi.org/10.1016/j.ejor.2014.06.019.
Zyoud, S.H., Kaufmann, L.G., Shaheen, H., Samhan, S., Fuchs-Hanusch, D. (2016). A framework for water loss management in developing countries under fuzzy environment: integration of fuzzy AHP with fuzzy TOPSIS. Expert Systems with Applications, 61, 86–105. https://doi.org/10.1016/j.eswa.2016.05.016.
Biographies
Duleba Szabolcs
S. Duleba received the MSc and PhD degrees in management science in 2001 and 2008. He currently holds the position of associate professor at the Budapest University of Technology and Economics, Department of Transport Technology and Economics. His specific research area is multi-criteria decision-making in logistics and transportation management. Apart from being published in top journals, he participated in several national and EU research projects.
Kutlu Gündoğdu Fatma
F. Kutlu Gïndoğdu received the PhD degree in industrial engineering from Istanbul Technical University, in 2019. She currently holds the position of assistant professor at National Defence University, and Department of Industrial Engineering. Her research areas are quality control and management, statistical decision-making, multi-criteria decision-making, spherical fuzzy sets, fuzzy optimization and fuzzy decision-making. She published many journal papers, book chapters and conference papers in the mentioned fields.
Moslem Sarbast
S. Moslem received his BSc in civil engineering from University of Aleppo, in 2012, MSc in civil engineering from Cukurova University, in 2015 and PhD in transportation engineering, in 2020, respectively, with a highest grade from Budapest University of Technology and Economics. He has been a professor of mathematics at the University of Tabriz since 2015. He has more than 30 papers in referred top journals with more than 375 citations. His current research interests include decision-making methods to solve transportation complex problems.
