Development of type-2 Pythagorean fuzzy set with its application to sustainable transport system selection.

In resolving multicriteria decision-making (MCDM) problems, it is observed that the solution process is frequently affected by the available vague information together with intra-personal uncertainties associated with expert's opinion. In most of the time fuzzy set or its existing variants fail to capture such uncertainties for making reasonable balance in decision making processes. To reduce the effects of uncertainties, this paper introduces a new variant of fuzzy set, viz., type-2 Pythagorean fuzzy set (T2PFS). The main advantage of using T2PFS in MCDM is that the membership and non-membership values of each argument are presented by Pythagorean fuzzy numbers rather than using fuzzy number or intuitionistic fuzzy number. In model formulation process, at first, T2PFS is explicitly formulated and some basic operations are defined. Subsequently, four aggregation operators are constructed to aggregate the arguments, and their properties are verified. Afterwards, two information measures and a score function are defined. Moreover, two MCDM algorithms based on the developed aggregation operators and TOPSIS are framed. To show the application potentiality of the proposed method, a case study relating to the selection of sustainable transport system in India is considered and solved. In the case study five different fuel-based vehicles, mostly used in India in recent times, are evaluated by the experts as transport alternatives with the consideration of thirteen sustainability related criteria. From the achieved result it is found that in future electric cars would become the most sustainable vehicle in India. Sensitivity analysis of the developed models and comparative study with existing fuzzy and non-fuzzy MCDM methods establish effectiveness of the developed models. This study may facilitate transport authority to select appropriate transport system in connection with sustainable development of a region. • As a new variant of fuzzy set, type-2 PFS is coined for resolving uncertainties associated with MCDM problems. • Terminologies, ranking of type-2 PFSs with aggregation operators are developed by defining arithmetic operations. • Defining distance and entropy measures, type-2 PF entropy weight model is introduced to determine criteria weights. • Two type-2 PF MCDM algorithms based on aggregation operators and TOPSIS are presented. • A case study is performed for the selection of sustainable transport system in India. [ABSTRACT FROM AUTHOR]