Informatica

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.

Three main approaches presently dominate preferences derivation or evaluation process in decision analysis (selecting, ranking or sorting options, alternatives, actions or decisions): value type approach (a value function or an utility measure is derived for each alternative to represent its adequacy with decision goal); outranking methods (a pair comparison of alternatives are carried up under each attribute or criteria to derive a pre-order on the alternatives set); and decision rules approach (a set of decision rules are derived by a learning process from a decision table with possible missing data). All these approaches suppose to have a single decision objective to satisfy and all alternatives characterized by a common set of attributes or criteria. In this paper we adopt an approach that highlights bipolar nature of attributes with regards to objectives that we consider to be inherent to any decision analysis problem. We, therefore, introduce supporting and rejecting notions to describ attributes and objectives relationships leading to an evaluation model in terms of two measures or indices (selectability and rejectability) for each alternative in the framework of satisficing game theory. Supporting or rejecting degree of an attribute with regard to an objective is assessed using known techniques such as analytic hierarchy process (AHP). This model allows alternatives to be characterized by heteregeneous attributes and incomparability between alternatives in terms of Pareto-equilibria.