WASPAS-based decision making methodology with unknown weight information under uncertain evaluations

Abstract The uncertain probabilistic linguistic term set (UPLTS) one of the modern development in fuzzy set theory, can express not only the decision makers (DMs) linguistic assessment information but also the uncertain probability/weight/importance degree of each linguistic assessment value, so it is an efficient tool for addressing the ignorance problems. The current study mainly focuses on developing a more effective way to cope with multiple criteria group decision making (MCGDM) problems in which the assessment information are in the form of UPLTSs, and the weight information is also entirely unknown. Firstly, some weaknesses of the existing operational laws and score function of UPLTSs are pointed out through some critical examples and then redefined them to overcome existing flaws in order to acquire more accurate results in practical decision making problems. Also, we establish various properties of the revised operational laws along with proofs. To design a novel comparison method, the concept of deviation degree is introduced in order to accommodate the situation in which two different UPLTSs have the same score values. After that, based on the proposed operational laws, several existing aggregation operators are modified, and a novel aggregation operator, namely uncertain probabilistic linguistic simple weighted geometry (UPLSWG) operator is designed. Meanwhile, some interesting properties of these proposed operators are carefully analysed. Furthermore, an entropy technique under uncertain probabilistic linguistic information is structured for computing the completely unknown weights of criteria. Following this, a new extension of weighted aggregated sum product assessment (WASPAS) method called uncertain probabilistic linguistic-WASPAS (UPL-WASPAS) methodology based on the proposed aggregation operators is studied under the UPLTS context for ranking objects in MCGDM problems. To show the applicability and potentiality of the developed method, an example of supplier selection is addressed, and a detailed performance comparison analysis is conducted. Furthermore, sensitivity analysis is also made to determine the impact of the parameter on the ranking of alternatives.