The selection of an optimal investment sector is of critical importance not only for individual financial success but also to drive economic development. The allocation of capital into sectors with high potential for growth, innovation, and job creation is key. In addressing the complexity of decision-making scenarios associated with investment sector exploration, we introduce a novel data structure known as Picture fuzzy hypersoft set (PF _HSSs ). This specialized approach within computational intelligence and decision-making aims to categorize data into various attributes and sub-attributes, considering the significant role of neutrality. The study stems from the need for a comprehensive framework (PFHSS s ) that can effectively handle intricate decision-making scenarios involving attributes, subattributes, and nuanced factors such as neutrality. Traditional tools such as TOPSIS and its extensions of fuzzy sets, while robust in Multiple Criteria Decision Making (MCDM), may face challenges in modeling and analyzing decision-making information within a PFHSS s environment. The rationale behind this study lies in enhancing the accuracy and efficiency of decision-making processes when dealing with complex, fuzzy, and multi-criteria data. By introducing newly proposed distances and similarity measures tailored to PFHSS s , and constructing a PFHSS s -TOPSIS method, we aim to address the limitations faced by existing models in the PF _HSSs environment. The application of Hamming distance-based similarity measures further distinguishes our method by determining the weights assigned to each decision maker. The proposed PF _HSSs -TOPSIS method is practically applied in designing an optimal investment sector exploration tool for investors. This method has the potential to establish a crucial connection between alternatives and attributes, providing value across various fields and industries. The research emphasizes bridging the gap in decision-making scenarios where alternatives and attributes need to be effectively connected and analyzed, thereby contributing to the advancement of decision-making processes in complex domains.

Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.

The Hamy mean (HM) operator is a powerful parameterized aggregation tool that enables flexible modeling of both conjunctive and disjunctive decision-making behaviors within a unified mathematical framework. Its tunable nature makes it more versatile than traditional fixed aggregation operators such as the arithmetic mean, maximum, or minimum, which are often too rigid to capture the nuanced interactions among decision criteria. Despite its proven potential in other fuzzy environments, the HM operator has not yet been developed in the context of p, q − quasirung orthopair fuzzy (p, q − QOF) sets, a generalized and more expressive extension of orthopair fuzzy models that can handle higher degrees of uncertainty, vagueness, and hesitation. To address this gap, we introduce some novel aggregation operators: the p, q − QOF interaction weighted Hamy mean (p, q − QOFIWHM) and the p, q − QOF interaction weighted dual Hamy mean (p, q − QOFIWDHM) operators. The proposed operators inherit the parametric adaptability of the HM while incorporating the enhanced representational capabilities of p, q − QOF sets. This combination offers significant flexibility in capturing interrelationships among criteria, making the operators well-suited for complex, large-scale, and time-sensitive decision problems. Based on these operators, we develop a multicriteria group decision-making (MCGDM) framework capable of effectively managing heterogeneous expert opinions, uncertain information, and high-dimensional evaluation data. The applicability and effectiveness of the proposed approach are demonstrated through a comprehensive case study on an E-Learning Platform selection. In this study, assessments from three domain experts were considered for 20 candidate platforms evaluated against 20 criteria encompassing technical, pedagogical, usability, and security aspects, such as system performance, course management capabilities, adaptability of learning content, cost-effectiveness, user interface quality, scalability, and data security. A detailed sensitivity analysis of parameters \(p\) and q, as well as of criteria weights, was conducted to examine the robustness of the model. Furthermore, extensive stability and accuracy tests revealed that the proposed approach consistently outperformed existing aggregation operator-based methods, achieving superior accuracy (93.13%), stability (98.83%), and computational efficiency. Comparative analysis confirmed that the p, q − QOFIWHM and p, q − QOFIWDHM-based MCGDM framework not only improves decision reliability but also provides a scalable and adaptable tool for real-world decision-making scenarios.

Opting for the right supplier is critical for a firm’s prosperity due to the impact of decisions made on uncertainty in symmetrical decision factors like pricing, manufacturing, service efficiency, and client satisfaction. Deciding on an appropriate supplier can be problematic due to the fact that there are many considerations to take into account, and they occasionally contradict each other. The supplier selection problem (SuSP) has been discussed in the literature in various situations while taking different considerations into account. Under the symmetry of uncertainty, operational risk analysis is nevertheless inadequate. This study is accomplished in two phases. In the first phase, we delve into the notions, basic properties, and theorems associated with hypersoft mapping (HypSM). These basic features are indispensable, as they endow the theoretical base essential for the subsequent phase. In the second phase, we leverage the aggregations of HypSM to develop a robust decision-assisted organism. This organism, which incorporates the robust algorithm and SuSP analysis, is constructed directly upon the insights and aggregations explored in the first phase, revealing the practical use of HypSM in decision-making. With regard to soft mapping (SOM), HypSM is more adaptable since its approximate function takes into account multiple argument domains in order to help decision-makers handle convoluted structural challenges involving uncertainty. Additionally, the proposed decision system considers various operational risks, like material quality-based risks, service quality-based risks, supplier’s market profile-based risks, and deep-rooted cooperation-based risks, for the approximation and evaluation of appropriate suppliers. This approach is expected to enhance decision-making by providing a comprehensive evaluation of supplier risks.