Symmetrical and asymmetrical information plays a critical role in resolving many issues. The implications of symmetry and asymmetry in interval-valued picture fuzzy decision-making, lie in their ability to represent and manage complex data. Decision makers approach the problem of information asymmetry through various methods. Integrating symmetric and asymmetric data in the context of a specific physical phenomenon poses significant challenges. To address these challenges, interval-valued picture fuzzy (IVPF) sets have emerged as an effective tool for managing complex data. In decision-making processes, it is essential to consider the complementary and conflicting nature of the analyzed data. This article aims to refine the shortcomings of the existing score function for Multiple Criteria Decision-Making (MCDM) problems in an IVPF environment, and present an improved score function. The IVPF sets are leveraged to propose IVPF weighted arithmetic operators, IVPF ordered weighted arithmetic operators, IVPF weighted geometric operators, and IVPF ordered weighted geometric operators, which are analyzed in terms of their key features. To demonstrate the effectiveness of the proposed score function and newly defined operators, a case study involving the selection of the best food item for manufacturing, is conducted. Additionally, a comparative analysis is established to investigate the significance of the newly defined techniques in solving decision-making problems under IVPF knowledge.

Solar panels hold a significant amount of importance at an industrial level because they contribute to environmental sustainability by reducing carbon emissions, contribute to cost savings through reduced electricity bills, provide energy independence and reliability, and serve as a long-term investment with attractive returns. One of the objectives of this research article is to address the limitations of the current score function utilized in multi-criteria decision-making (MCDM) problems within an interval-valued picture fuzzy (IVPF) environment and to present an enhanced score function. Moreover, IVPF hybrid arithmetic operators and IVPF hybrid geometric operators are introduced in this article. These operators are further thoroughly examined to identify their key characteristics. By conducting a case study, an algorithm is formulated to select the most suitable solar panel to maximize energy availability at the industrial level in the framework of the newly proposed IVPF hybrid operators. In addition, a comprehensive comparative study is conducted to demonstrate the significance and validity of recently proposed novel techniques compared with existing methods.