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.

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The sustainability of the climate is a critical concern in the modern world. A variety of acts are included in sustainability that strive to lessen our carbon footprint and maintain the fragile balance of our world. To preserve a sustainable future for future generations, we must cooperate in adopting renewable energy sources, supporting green transportation, and implementing responsible land use. In this article, we propose the concepts of complex intuitionistic fuzzy Dombi hybrid averaging (CIFDHA) and complex intuitionistic fuzzy Dombi hybrid geometric (CIFDHG) operators within the framework of a complex intuitionistic fuzzy environment. Furthermore, we explore several additional important features of these operators. To overcome the limitations of the existing score function within the CIF knowledge context, we present a new and improved score function. Additionally, we apply the proposed score function and newly defined operators to select an optimal strategy for mitigating the drivers of climate change and saving the planet’s valuable resources for a more livable and resilient planet. In order to demonstrate the validity and practicality of the suggested strategies, we conducted a comparative study of these novel techniques with existing methods.

The conjugate gradient method is a useful method to solve large-scale unconstrained optimisation problems and to be used in some applications in several fields such as engineering, medical science, image restorations, neural network, and many others. The main benefit of the conjugate gradient method is not using the second derivative or its approximation, such as Newton’s method or its approximation. Moreover, the algorithm of the conjugate gradient method is simple and easy to apply. This study proposes a new modified conjugate gradient method that contains four terms depending on popular two- and three-term conjugate gradient methods. The new algorithm satisfies the descent condition. In addition, the new CG algorithm possesses the convergence property. In the numerical results part, we compare the new algorithm with famous methods such as CG-Descent. We conclude from numerical results that the new algorithm is more efficient than other popular CG methods such as CG-Descent 6.8 in terms of number of function evaluations, number of gradient evaluations, number of iterations, and CPU time.

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques.