An integrated CRITIC and MABAC based type-2 neutrosophic model for public transportation pricing system selection rights and content


Public transportation pricing system selection problem is addressed and solved.

Practical and methodological frameworks for public transportation pricing are given.

Integrated CRITIC and MABAC based type-2 neutrosophic model is introduced.

The presented hybrid T2NN-based model is highly robust, reliable, and flexible.

The most advantageous pricing system is the rent-based fare.


The pricing of public transportation services is a complex task that authorities deal with because many criteria should be considered while deciding on the pricing system. Some include decentralization of the cities due to lower rents in outer-city regions and operating costs of longer transportation lines. Hence, four alternative public transportation pricing systems are defined, which are flat fare, distance-based, zonal, and rent-based fare. To prioritize these alternatives, four aspects are determined, namely cost, transportation, social and political, and there are 13 criteria present under these aspects. A two-stage hybrid multi-criteria decision-making model based on type-2 neutrosophic numbers (T2NNs) is introduced to provide a straightforward and flexible decision-making tool for researchers and practitioners. In its first stage, the reputation of the experts is determined under the T2NN environment. Second, the novel T2NN-based CRiteria Importance Through Intercriteria Correlation (CRITIC) method is employed to evaluate the criteria importance, while the new T2NN-based Multi-Attributive Border Approximation area Comparison (MABAC) method is used to rank the public transportation pricing systems. The results show that rent-based fare pricing is the most advantageous alternative. The high reliability and robustness of the integrated CRITIC and MABAC based type-2 neutrosophic model are demonstrated with the comparative and sensitivity analyses.


Public transport
Transportation pricing
Type-2 neutrosophic number
Multi-criteria decision-making

Dr. Vladimir Simic is an Associate Professor of the Transport and Traffic Engineering Department at the University of Belgrade, Serbia. He has been engaged in state-of-the-art research on transportation engineering for almost 15 years. He has conducted intensive research on operations research applications in diverse fields of specialization, with a particular focus on developing advanced hybrid multi-criteria decision-making tools and real-life large-scale stochastic, fuzzy, interval, full- and semi-infinite programming optimization models. He is the second most influential author in the world in the end-of-life vehicle management research area ( He published 35 papers in journals from the JCR list.

Dr. Ilgin Gokasar received a B.S. degree in Civil Engineering from Boğaziçi University, Istanbul, Turkey in 2000 and the M.S. (2003) and Ph.D. (2006) degrees in (Intelligent Transportation Systems) Civil Engineering from Rutgers University, New Jersey, USA. She is an Associate Professor in the Department of Civil Engineering at Bogazici University. She is the founder and director of the BOUN-ITS lab. Her research interests include Intelligent Transportation System, Traffic Safety, Advanced Public Transportation Systems, Real-Time Traffic Control, Smart and Sustainable Transportation Systems, Use of Big Data to Address Challenges in Mobility, Safety, Sustainability, and Resilience in Multimodal Transportation Systems.

Dr. Muhammet Deveci is currently an Associate Professor in the Department of Industrial Engineering in the Turkish Naval Academy at National Defence University, Istanbul, Turkey. He obtained his Ph.D. in Industrial Engineering at Yildiz Technical University, Istanbul, Turkey in 2017. He worked as visiting researcher and postdoctoral researcher in 2014–2015 and 2018–2019, respectively, in the School of Computer Science at the University of Nottingham, UK.

Dr. Deveci has over 60 refereed publications at reputable venues. His research focuses on computational intelligence, handling of uncertainty, fuzzy sets, modeling and optimization, and their hybrids, applied to complex real-world problems.

Ahmet Karakurt is a Ph.D. candidate in the Department of Civil Engineering at Bogazici University. He received his B.S. degree (2014) in Civil Engineering from Istanbul University and M.Sc. degree (2017) in the Transportation Engineering field in the Department of Civil Engineering from Bogazici University. His research interests include travel behavior and public transportation pricing systems.

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