Weight Optimization Decision Algorithm in (p,q)-Rung Probabilistic Hesitant Orthopair Fuzzy Environments

Aiming at the fuzzification of a decision environment and the challenge of determining the weights associated with the interaction among decision-makers, this study offers an original method for (p,q)-rung probabilistic hesitant orthopair fuzzy multi-objective group decision-making, which is founded on the weight optimization principle. Firstly, the notion of a probabilistic hesitant fuzzy set is expanded to a (p,q)-rung. Secondly, the determination of subjective and objective weights is accomplished through the utilization of the Analytic Network Process (ANP) and the Entropy Method. According to the degree of deviation and dispersion of each weight, an optimal objective function is constructed, and the neural network is used to iteratively solve for the best scheme of the comprehensive weight. Subsequently, the Elimination Et Choice Translating Reality (ELECTRE) approach was refined and applied to decision-making in the (p,q)-rung probabilistic hesitant orthopair fuzzy environment. Finally, comparative analysis was used to demonstrate the new method’s effectiveness and superiority.