Healthcare workers, including doctors and medical staff, must consistently make informed decisions that significantly affect patients on individual, community, national, and global scales. Healthcare practitioners must occasionally make judgments with constrained information, resources, and knowledge, yet it is anticipated that these choices are meticulously measured and precise. Familiarizing oneself with precise concepts pertaining to medical decision-making is essential. The complexity of decision-making (DM) arises from the environment’s ambiguous, imprecise, and uncertain characteristics, especially when several attributes are present and further categorized. We have used the hypersoft set concept to address such complex challenges. This article defines interval-valued Fermatean neutrosophic super hyper-soft sets. Its fundamental operations are subsets, equality, null sets, complements, unions, and intersections. Using these algebraic procedures, we establish a numerical example for the prioritization of patients awaiting organ transplantation. This hybrid environment may effectively manage uncertainty and yield distinctive results.

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads.

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.

The evaluation of psychological disorders is a very complicated and sensitive area of study, where emotions, thoughts, and the mental states of different patients are analyzed on the basis of questionnaires and observational techniques. The identification and analysis of people's mental states, emotions, and behaviors are difficult and limited with the aid of conventional approaches since the data gathered from these factors appear to be vague, uncertain, and imprecise. To demonstrate this information systematically, we have proposed a comprehensive mathematical model able to deal with indeterminate and imprecise data, utilizing Intuitionistic Pentagonal Fuzzy Numbers (IPnFNs). To create a coherent mathematical framework, IPnFNs integrate five values of membership and non-membership functions of any constraint, providing an innovative numerical framework that effectively explains the assessment of diagnosis and the patient's condition. The research study analyzes several key psychiatric disorders, such as childhood psychiatric problems, hormonal changes, social stress, cognitive distortions, anxiety, and traumatic life events, as the main factors. The proposed technique provides psychologists with a thorough and clear picture of the issue by depicting the patient's mental health numerically. The research is significantly helpful in cases where the symptoms of psychological illness are not obvious or the patient's information is imprecise or confusing. Furthermore, a comparative analysis of various patients can be developed using the proposed technique, assisting in assessing severity and diagnosis preferences. This mathematical method shows that the use of IPnFNs can be a reliable and scientific method in the evaluation of psychological disorders. This approach is significantly applicable in educational counseling and clinical psychology, where it is a daily routine for individuals to deal with imprecise and inconsistent data in mental health issues while making decisions.

The financial risk evaluation process, which includes the investigation of the risks related to loans, funding, and trading activities in economic decisions, is greatly utilized in advanced financial systems. However, nowadays in an inconsistent, fast, and digitalized world, conventional risk models are inadequate, particularly when there is ambiguity, inconsistency, or incomplete information provided in the data. In such scenarios, the interference of Artificial Intelligence (AI) is playing a crucial role. Not only are the large data sets dealt with by AI, but also the decision-making processes can be enhanced. Conventional mathematical tools cannot analyze the discipline whose limits are complex, ambiguous, and indeterminate. In this research article, to recognize and analyze these mathematical disciplines, Interval-Valued Fermatean Neutrosophic Numbers (I-VFNNs) are used, an argumentation of modern fuzzy logic. I-VFNNs are particularly mapped out for such circumstances where the information in the data contains uncertainty, ambiguity, or inconsistency. We have used Interval-Valued Fermatean Neutrosophic Numbers (I-VFNNs), an extension of modern fuzzy logic, to identify and analyze these mathematical constraints. In this article, firstly, a list of essential aspects is composed that are affected by Artificial Intelligence in financial risk models, like fraud detection and prevention, stress testing and scenario simulation, automation of regulatory compliance, behavioral risk analysis, enhanced predictive accuracy, dynamic risk modeling, and real-time risk monitoring, etc. All these components we visualized as mathematical disciplines, which are non-probabilistic, irregular, and multifaceted in nature. With the help of I-VFNNs, we portrayed these disciplines in the guise of numbers and demonstrated their influence, intensity, and indeterminacy in accordance with the impact of Artificial intelligence. The results demonstrate that I-VFNNs not only composed ambiguity superiorly, but also refined the disparity between various risk factors. In general, not only are modern ways to constructively assess financial risk models based on Artificial Intelligence (AI) developed, but new approaches in the inspection of indeterminate data using I-VFNNs are furnished in this study. By virtue of this model, in financial organizations, better decisions can be made, accelerate the recognition of risks, and put down the right consideration even in uncertain conditions. In the future, this model can also contribute to other innovative research areas such as international financial policies, large investments, and insurance institutions.

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