Interval-Valued Spherical Fuzzy Analytic Hierarchy Process Method to Evaluate Public Transportation Development

Consensus creation is a complex challenge in decision making for conflicting or quasiconflicting 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.