Probabilistic linguistic q‐ rung orthopair fuzzy Generalized Dombi and Bonferroni mean operators for group decision‐making with unknown weights of experts

Abstract

In this paper, we develop a multicriteria group decision-making methodology with probabilistic linguistic q-rung orthopair fuzzy sets (PLqROFSs). The benefit of choosing PLqROFSs is that they consider the simultaneous occurrence of stochastic and nonstochastic uncertainty and so are superior to probabilistic hesitant fuzzy sets, linguistic intuitionistic fuzzy sets, and linguistic Pythagorean fuzzy sets. To develop the methodology, we first propose two types of operators, namely, probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi operator which gives the flexibility of choosing the parameter values and probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi Bonferroni mean operator which can consider the interrelationships between criteria. Since both the subjective and objective weights of experts are hardly considered in the current PLqROFSs-based research, so in our proposed methodology, we deploy the thought of consistency and similarity between the experts to calculate the subjective and objective weights, respectively, of the experts and as a result the evaluation results do not get malformed. For measuring the weights of criteria, the gray correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. To exhibit the applicability of the proposed operators, we provide a case study on biomass feedstock selection. Moreover, to make sure that our model is stable, we have investigated a sensitivity analysis of parameters. At the end, we make a comparison of our approach to different existing schemes.