The primary objective of the water purification process is to remove harmful chemical compounds and microorganisms from water sources in order to produce water suitable for human consumption. Water purification satisfies the demand for drinkable water, which is a requirement for many industries, including the medical, pharmaceutical, and chemical industries, among others. Access to purified water is the single most important factor determining a nation’s strength and prosperity. As a consequence, researchers all over the world are investigating a wide variety of potential strategies for improving and preserving the water supply. In this paper, we present the findings of our research into a possible water strategy for purifying water and improving accessibility to drinkable water in areas prone to drought. This article presents the concepts of the complex intuitionistic fuzzy Dombi weighted averaging (CIFDWA) operator, the complex intuitionistic fuzzy Dombi ordered weighted averaging (CIFDOWA) operator, the complex intuitionistic fuzzy Dombi weighted geometric (CIFDWG) operator, and the complex intuitionistic fuzzy Dombi ordered weighted geometric (CIFDOWG) operator in complex intuitionistic fuzzy (CIF) settings. In addition, we investigate several important key features of these operators. Moreover, we introduce an improved score function to overcome the deficiencies of the existing score function under CIF knowledge. Furthermore, we effectively apply the proposed score function and newly defined operators to select the best technique for purifying water at a commercial scale. Additionally, we establish a comparative analysis to show the validity and feasibility of the proposed techniques compared to existing methods.

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.

Fuzzy set theory is a mathematical method for dealing with uncertainty and imprecision in decision-making. Some of the challenges and complexities involved in medical diagnosis can be addressed with the help of fuzzy set theory. Ovarian cancer is a disease that affects the female reproductive system's ovaries, which also make the hormones progesterone and estrogen. The ovarian cancer stages demonstrate how far the disease has spread from the ovaries to other organs. The TOPSIS technique (Technique for Order Preference by Similarity to Ideal Solution) aids in selecting the best option from a selection of choices by taking into account a number of variables. It provides a ranking or preference order after weighing the benefits and drawbacks of each solution. Intuitionistic fuzzy soft set (IFSS) is the framework to deal with the uncertain information with the help of the parameters. The goal of this article is to develop some basic aggregation operators (AOs) based on the IFSS and then use them to diagnose the stages of the ovarian cancer using the TOPSIS technique. Furthermore, the variation of the parameters used in the developed model AOs is also observed and graphically represented.

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent 5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time.