Enhancing sustainable energy strategies through p,q- quasirung orthopair trapezoidal fuzzy numbers in hybrid energy system planning

The problem in hybrid energy system (HES) planning lies in the over-reliance on quantitative optimization data, which may obscure critical qualitative factors like long-term sustainability. Additionally, slight variations in results from different optimization tools, despite identical inputs, further complicated decision-making, highlighting the need for advanced tools like p,q- quasirung orthopair trapezoidal fuzzy numbers (p,q-ROTrFNs) to enhance accuracy and clarity in evaluating alternatives. Therefore, in this study a novel concept of p,q-ROTrFNs is introduced as an extension of traditional trapezoidal fuzzy numbers, designed to address limitations in handling uncertainty and vagueness in HES planning. A more refined representation of membership and non-membership functions is offered by incorporating the p and q parameters, providing enhanced flexibility in managing imprecise data in multi-criteria decision-making processes. Additionally, score and accuracy functions based on expected values are developed to allow the comparison and ranking of p,q-ROTrFNs. Also, New operational rules for p,q-ROTrFNs are formulated to support their application in diverse decision-making scenarios, ensuring mathematical consistency. Moreover, p,q-ROTrFNs Preference Ranking on the Basis of Ideal-average Distance is method is proposed as a comprehensive framework for ranking alternatives in decision-making scenarios characterized by complex uncertainty. To develop the method two types of aggregation operators based on Schweizer-Sklar t-norms and t-conorms and a distance measure are introduced for aggregating p,q-ROTrFNs and quantify the similarity or dissimilarity between p,q-ROTrFNs respectively. After implementing the proposed method, the PV-WT-HKT-DG-BT alternative achieved the highest score among the seven options. A group decision making of seven experts demonstrated consistency in ranking. Additionally, sensitivity analysis confirmed the method's reliability, while a comparative study validated its effectiveness.