A novel two-stage TOPSIS approach based on interval-valued probabilistic linguistic q-rung orthopair fuzzy sets with its application to MAGDM problems

Fuzzy theories are widely used in multi-attribute group decision-making (MAGDM) problems to describe uncertain and hesitant information. The recently proposed probabilistic linguistic q-rung orthopair fuzzy set (PLq-ROFS) is capable in dealing with quantitative and qualitative information simultaneously. However, in many actual situations, decision-makers (DMs) prefer to utilize interval values to express their minds and evaluations, this paper employs interval values to represent the probabilistic distribution of the membership degrees (MDs) and non-membership degrees (NMDs), and proposes the interval-valued PLq-ROFS (IVPLq-ROFS). Based on which, a novel two-stage approach is introduced. The IVPLq-ROFS weighted extended power average (IVPLq-ROFWEPA) operator is proposed to obtain the comprehensive matrix and weights of each attribute, while a further advanced TOPSIS model is constructed to get the final rank of alternatives. An example of a new-type smart city development evaluation problem is given to illustrate the efficacy of the proposed approach. Results show that our approach is more flexible, more adaptable, more accurate, more freedom, and has much lower calculation complexity in the calculation process of the MAGDM problem. The contributions of the proposed method are mainly manifested in giving the concept of IVPLq-ROFSs, and proposing a novel two-stage TOPSIS model for dealing with MAGDM problems under IVPLq-ROFSs.