Probabilistic linguistic q-rung orthopair fuzzy Archimedean aggregation operators for group decision-making

To express uncertain and imprecise information systematically, the concept of probabilistic linguistic q-rung ortho-pair fuzzy set (PLqROFS), which is an advanced version of linguistic intuitionistic fuzzy set and linguistic Pythagorean fuzzy set, considering the instantaneous occurrence of stochastic and non-stochastic-uncertainty. There isn't yet any literature on PLqROFSs that addresses the issue of the relative importance of experts and criteria. The evaluation's findings consequently become irrational. Additionally, the aggregation operators that are currently available on PLqROFSs are too rigid. The primary goal is to resolve these problems by creating a new methodology that makes use of a new flexible aggregation operator. In this paper, a novel integrated framework is suggested to address concerns with group decision-making in PLqROFSs settings by combining the strengths of the power average operator (PAO), the Archimedean operator, and the full consistency method (FUCOM). With the extended variance approach on PLqROFSs, the weight of decision experts is methodically determined in this line. Additionally, the FUCOM on PLqROFSs is used to determine the weight of the criterion. Some probabilistic linguistic q-rung ortho-pair fuzzy Archimedean weighted and power weighted aggregation operators are suggested to aggregate decision experts' preferences. To discuss the viability of the suggested technique, the challenge of choosing a CO2 storage location is given. As alternatives, we have taken into account oilfields, gas fields, basalt formations, and coal resources. Basalt is the best choice, according to the outcome. The stability of our method is demonstrated by the sensitivity analysis of the criteria weights. The comparative analysis demonstrates that, in comparison to the ones already in use, our model is more significant and realistic.