Hybridizations of Archimedean copula and generalized MSM operators and their applications in interactive decision-making with q-rung probabilistic dual hesitant fuzzy environment

The q-rung probabilistic dual hesitant fuzzy sets (qRPDHFSs), which outperform dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets, and probabilistic dual hesitant Pythagorean fuzzy sets, are used in this research to develop an interactive group decision-making approach. We first suggest the Archimedean Copula-based operations on q-rung probabilistic dual hesitant fuzzy (qRPDHF) components and investigate their key features before constructing the approach. We then create some new aggregation operators (AOs) in light of these operations, including the qRPDHF generalized Maclaurin symmetric mean (MSM) operator, qRPDHF geometric generalized MSM operator, qRPDHF weighted generalized MSM operator, and qRPDHF weighted generalized geometric generalized MSM operator. These aggregation operators are better than current operators on qRPDHF because they can take into account the interactions between a large number of criteria and probability distributions. The evaluation findings are distorted since the present methodologies do not take expert involvement into account in order to achieve the required consistency level. We employ the idea of interaction, consistency, resemblance, and consensus-building among the decision-makers in our method to get around this. We create an optimization model based on the cross-entropy of the qRPDHF components to estimate the weights of the criterion. We provide contextual research on the choice of open-source software LMS in order to demonstrate the relevance of the recommended AOs. Likewise, we ran a sensitivity test on the weights of the criterion to make sure that our model is consistent. The comparison investigation has demonstrated that the suggested approach can overcome the challenges of previous works.