Waste-to-Energy (WtE) is one of the modern solutions to landfill problems in this century worldwide. The WtE invention is utilized to manage municipal and industrial waste while producing energy. Several key factors are involved in improving the quality, effectiveness and efficiency of those technologies. The purpose of this study is to identify the efficient critical criteria for upgrading WtE technologies. Through the evaluation of the literature review, case studies and comparative analysis, we identified some major criteria for adapting the WtE technologies. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is a widely used Multi-Criteria Decision Making (MCDM) approach for evaluating the importance of criteria. Furthermore, evaluates the degree of significance and relation between these criteria and draws the environmental footprint of WtE technologies. Additionally, the threshold values for the criteria are provided for clarity. Data are obtained from two Decision Makers (DMs) using Dense Neutrosophic Numbers (DNNs) to capture uncertainty and vagueness. Based on the evaluated results, energy efficiency is the most important criterion, followed by environmental impact and is described in more detail in the results section. Finally, sensitivity analysis and comparative analysis are conducted to assess the system’s robustness.

Financial aid plays a crucial role in the sustainability and development of higher educational institutions, particularly those operating without governmental funding. This study proposes a decision-making framework for identifying and prioritizing the key challenges faced by non-governmentally funded higher educational institutions. To address this problem, a hybrid Multi-Criteria Decision-Making (MCDM) approach is employed, where the MEREC method is used to determine the weights of evaluation criteria and the MARCOS method is applied to rank the identified challenges. To effectively handle uncertainty and ambiguity in expert judgments, q-Rung Orthopair Fuzzy Numbers (q-ROFNs) are integrated into the framework. Furthermore, sensitivity analysis is conducted to assess the robustness and reliability of the obtained results under different conditions. The results reveal the most influential challenges affecting the financial sustainability and operational performance of these institutions, providing valuable insights for strategic decision-making. In addition, the proposed framework offers a systematic and flexible tool that can be adapted to similar decision-making problems in the education sector. Overall, the q-ROF-MEREC-MARCOS framework supports policymakers, institutional administrators, and stakeholders in developing effective strategies for enhancing the resilience and sustainable growth of non-governmentally funded higher educational institutions.

Psychological Health is a very important factor in anyone’s life. It may affect both mental and physical health conditions. In this paper, we are interested in finding the weight of the psychological health-related criterion’s and ranking the related alternatives by using the well-known statistical techniques, the Analytic Hierarchy Process (AHP) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods. For the aforementioned problem, we utilise the dataset of Indian women following the COVID-19 pandemic. This study collects data in linguistic terms from decision makers (DMs) who are already experts in the healthcare field. All the data are converted into Generalized Intuitionistic Pentagonal Fuzzy Numbers (GIPFN) to capture the uncertainty of the dataset. Furthermore, a new de-fuzzification method is proposed to de-fuzzify the fuzzy sets. From the given data, analysis the importance of each criterion and assign a weight to it using the AHP methodology. After that, apply the TOPSIS technique to prioritise the health facilities among the different age groups. The numerical illustrations are presented based on different age groups. Lastly, sensitivity analysis and comparative analysis are conducted to demonstrate the applicability of the methodology in psychological health-related applications.

High-speed rail adoption in developing countries faces challenges for several reasons. Our research work identifies the most impactful challenges of it. It is an extremely demanding work. It mainly depends on several factors, including high capital costs and financing issues, the purchase of land and resettlement, political instability that affects policy continuity, maintenance and operating costs, the current market value, technology and technical skills, and the impact on both the environment and human society. In this study, the proposed adoption challenges for high-speed rail networks in developing countries are constructed and processed using the Multi-Criteria Decision Making (MCDM) process in an uncertain environment. Here, we apply the Fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) technique-based MCDM methodology to evaluate the criteria weights. We gather valuable opinions from three decision-makers (DMs) for data collection. Picture Fuzzy Numbers (PFNs) are utilised as uncertainty tools to address ambiguity.

Fuzzy nonlinear equations are used to model real-world problems. Due to the nonlinearity, sometimes obtaining a fuzzy solution is challenging. This paper deals with two methods for solving such equations, the first is the fuzzy Newton–Raphson method (FNRM) and the other is the fuzzy Adomian decomposition method (FADM). Both methods are proposed and demonstrated. We observe that the FADM is better than the FNRM. FADM gives a fuzzy solution also, at the core the fuzzy solution matches with the crisp one. The FNRM initially gives a fuzzy solution, but as iterations increase, the solution does not remain fuzzy, and even the fuzzy solution does not match with the crisp one. Last, one numerical illustration is solved by both methods.

Despite the abundance of reports of mental disorders in medical diagnosis, few studies have employed standard techniques on representative patient groups. Psychiatric disorders are currently the most frequent cause of extended absences due to illness. Fuzzy Multi-Criteria Decision-Making (MCDM) techniques can be helpful in selecting appropriate treatments or interventions for patients with psychiatric disorders. These techniques enable decision-makers to consider multiple criteria that may have varying levels of importance or uncertainty. In this paper, interval-valued Pythagorean trapezoidal fuzzy numbers (IVPTrFN) are used to handle uncertainty or imprecision in a more complex manner. The Fuzzy Analytic Hierarchy Process (FAHP) is used to determine the symptom weight of a patient with a psychiatric disorder. Using this weight, the rank of the alternative disorder of a patient is determined by the Fuzzy Preference Ranking Organization Method for Enrichment Evaluation (FPROMETHEE) technique. Finally, sensitivity and comparative analyses are conducted to assess the reliability and consistency of the results.

Ranking the higher educational institutes is a very challenging task. In ranking higher educational institutions, many criteria and sub-criteria must be considered. These criteria may be beneficial or non-beneficial, which also increases the problem's complexity. Here, our aim is to develop an advanced framework to determine the rankings of higher educational institutions, incorporating uncertainty in the environment and the dataset. Here, we will take the help of Generalized Pentagonal Intuitionistic Fuzzy Numbers (GPIFNs), which are an extension of Pentagonal Fuzzy Numbers (PFNs), to capture the uncertainty of the model. For this purpose, we will include two popular MCDM methodologies: the Entropy weighted method for evaluating the criteria weights and the VIKOR method for ranking alternatives across different higher educational institutions. In this model, the opinions of different decision experts will be taken in linguistic terms as a dataset and will further be converted to GPIFNs. Lastly, sensitivity analysis and comparative analysis will be performed to assess the stability and robustness of the results obtained with this model. This model will be very effective for making policies for the advancement of higher educational institutions, and it will provide a clear view of the strengths and weaknesses of an institution to the administrator so that they can take necessary strategies to improve the quality of education.

Renewable energy is one of the significant energy sources of recent times and a solution to various global problems, including environmental degradation, energy insecurity, and the rising demand for sustainable development. Solar energy is one of the most important renewable sources and helps reduce dependence on fossil fuels. There are several Photovoltaic (PV) technologies, and each has its pros and cons. In this study, we prioritized them based on multiple parameters statistically and mathematically. Two multi-criteria decision-making (MCDM) methodologies are considered for the numerical evaluation in the triangular type-2 fuzzy numbers environment to consider model uncertainty. Further, sensitivity analysis and comparative analysis are conducted to assess the system's stability, robustness, and flexibility. This study provides guidance to select optimal solar technology for government & private companies, policymakers, and individuals to develop sustainable and efficient energy sources.

In multi-criteria group decision-making (MCGDM), aggregation operators (AOs) are mathematical tools that merge evaluations of each individual criterion into a single decision value or overall score. They enable decision-makers to integrate various attributes, each with a specific degree of importance or weight, to arrive at a comprehensive decision. AOs are particularly valuable because they can manage uncertain and unpredictable information, which is often inherent in real-world decision-making scenarios. The paper introduces advanced decision-making methods to handle ambiguity and incomplete information using interval-valued bipolar Pythagorean fuzzy numbers (IVBPyFNs). Specifically, it proposes two novel operators: the Interval-Valued Bipolar Pythagorean Fuzzy weighted Hamy Mean (IVBPyFWHM) and the Interval-Valued Bipolar Pythagorean Fuzzy Weighted Dual Hamy Mean (IVBPyFWDHM). These operators are integrated into multiple attribute group decision-making (MAGDM) framework. The approach is applied to mental health treatment selection for women, where symptom severity is first assessed using fuzzy Stepwise Weighted Assessment Ratio Analysis (SWARA), and therapy options are ranked via the TOmada de Decis & atilde;o Iterativa Multicrit & eacute;rio (TODIM) strategy. Finally, we compare our outcome with a few existing operators to demonstrate the validity of our suggested methodology.

This study represent the exploration of an economic order quantity (EOQ) model where it is perceived that the cost at the starting time of an inventory and the estimated cost of an inventory are not necessarily the same. The reason is defined as a delay in the time interval between cost estimation. and the actual starting time of the inventory. Inflation of money, promotional strategies and debilitation rate of decaying items are included in the model. Instability in political ground or an uncertain situation of a country create more instability in the economic system. Thus, inflation of money is considered. The model represents deterioration rate, inflation of money, and promotional index in fuzzy sense for showing the parametric uncertainty. Therefore, the model is solved by the method of signed distance, triangular fuzzy, and trapezoidal fuzzy for maximization of profit. Carbon emissions due to transportation is calculated for adding the sustainability concept to the model. Optimal order quantity, optimal shortage quantity, optimal selling period and optimal shortage period are found to make the model distinctive. The formulated model is thoroughly explained for both crisp, triangular fuzzy, and trapezoidal fuzzy environment and it is concluded that the trapezoidal fuzzy number is better in its applicability for the decision makers. Because, under the trapezoidal fuzzy environment, the profit value is increased by 10.51% as compared to the crisp environment and 3.89% with respect to the triangular fuzzy environment. One more finding is that, trapezoidal fuzzy number is better with its simple arithmetic operation as well as its easy and intuitive interpretation approach. A practical example from a fertilizer company is considered in the model to add a real touch. Sensitivity analysis is performed and supported by graphical representation. Comparative analysis is derived to show the uniqueness of the model. The model ends with conclusions and direction to possible future studies.

The fractional inventory problem extends classical inventory models by incorporating fractional calculus to better capture memory effects and hereditary properties in real-world systems. This paper reviews the development and applications of fractional-order inventory models, highlighting their advantages over traditional models in addressing non-instantaneous dynamics and demand variability. Key approaches such as fractional-order differential equations, optimization under constraints, fuzzy logic integration, and hybrid demand functions are discussed. Additionally, the paper outlines current trends in research, identifies challenges, and suggests future directions for model improvement and practical deployment in supply chain systems. Recent studies have further expanded the applicability of fractional inventory models by integrating stochastic demand patterns, sustainability considerations, and multi-echelon supply chain structures. Researchers have demonstrated that fractional-order models provide improved flexibility and forecasting accuracy compared to integer-order formulations, particularly in environments characterized by uncertainty and long-term dependency effects. Moreover, advancements in computational techniques and numerical methods have enabled the practical implementation of these models in complex industrial scenarios. The growing intersection between fractional calculus, artificial intelligence, and data-driven optimization is expected to further enhance inventory decision-making and contribute to the development of resilient and adaptive supply chain systems.

Finite hypergraphs generalize ordinary graphs by permitting each hyperedge to join any nonempty set of vertices, and thus provide a natural model for truly multiway interactions. To represent hierarchical and multi-layer structure, SuperHyperGraphs iterate the powerset operation so that set-valued entities created at one level can be treated as vertices at higher levels. Independently, recursive hypergraphs allow edge recursion: an edge may contain not only vertices but also lower-level edges, yielding nested (and possibly self-referential) incidence controlled by a specified recursion depth. In this work we introduce and axiomatize Recursive Neutrosophic SuperHyperGraphs, a unified framework that combines vertex hierarchy with edge recursion and equips incidences with neutrosophic degrees (truth, indeterminacy, and falsity) to capture graded and inconsistent information. The resulting model offers a flexible combinatorial language for complex systems whose higher-order relations are simultaneously nested and uncertain.

In this article, ameliorating items whose quality improves during the early stages of an inventory cycle are considered. The demand rate for ameliorating items is generally unstable. There are times when it rises, periods when it stays the same, and times when it falls. Therefore, a ramp-type demand is allowed to provide a realistic view. Inflation is included in the model. To capture the real-life uncertainties and imprecision of the parameters, an intuitionistic fuzzy number is considered. A numerical example shows that a fuzzy model can achieve the maximum profit at all times, unlike deterministic models. Sensitivity analysis demonstrates the model's real-world applicability to the parameter values. Finally, managerial insights are provided to help the decision-maker make an informed decision.

The fractional differential equation is one of the important tools to realize the importance of the fractional calculus. Also, neutrosophic set provides a more comprehensive framework for handling uncertainty by truth, indeterminacy, and falsity membership function. This study aims to develop fractional differential equation in neutrosophic uncertain environment. A rigorous mathematical theorem has been formulated and proven, which establishes the existence and uniqueness of the solution to the initial-valued neutrosophic fractional differential equation (NFDE). The weak and strong characteristics of the solutions to NFDEs within the context of the Caputo fractional derivative framework is presented. A non-homogeneous linear NFDE is manifested by taking two types of neutrosophic fractional derivative in Caputo’s sense. An economic lot-sizing inventory model of deteriorating items with green level and stock-level dependent demand is presented as an application of the proposed theory by taking various inventory related parameters as neutrosophic numbers. Several cases of the proposed problems are also presented. The result observed that the fractional order model in a neutrosophic environment yields significantly better results compared to integer order models in the neutrosophic environment, as well as integer or fractional order models in a crisp environment.

In the twentyfirst century, despite the existence of numerous laws and government initiatives aimed at protecting and empowering women, harassment continues to affect women across various spheres of life—both domestic and professional. As a result, women’s empowerment remains one of the most critical and urgent topics of contemporary discourse. While traditional studies have explored women’s empowerment from multiple perspectives, there has been limited application of fuzzy set theory in this domain—particularly in evaluating the degree of uncertainty involved in field-wise empowerment. To address this gap, the present study utilizes the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Complex Proportional Assessment (COPRAS) methods to assess the level of women’s empowerment in India across a range of sectors, including media, sports, defence, biotechnology, medical technology, psychology, higher education, and social work, using data compiled from diverse sources. All the data is collected in Trapezoidal Fuzzy Numbers (TrFN) to deal with the uncertainty and vagueness of the system and data sets. Given the challenges in ranking alternative empowerment options, the study applies a fuzzy Multi-Criteria Decision-Making (MCDM) approach based on key factors and their corresponding sub-factors to identify the optimal empowerment domain. The Analytic Hierarchy Process (AHP) technique is employed to determine the factor weight, fuzzy weight, and global fuzzy weight of the sub-factors. Subsequently, the fuzzy TOPSIS method is used to rank the alternative empowerment options and identify the field in which women have the greatest potential to thrive. These results are then validated through comparison with the fuzzy COPRAS technique, and the final assessment is established. To further ensure the robustness and reliability of the findings, a sensitivity analysis is conducted by selectively removing certain factors or sub-factors. The overall results provide clear insights into where and how women’s empowerment can be most effectively promoted—offering not only time-efficient decision-making but also paving the way for a more secure and equitable future for women around the world.

In recent decades, the growing global demand for energy and the depletion of conventional fossil fuel resources have intensified the need for sustainable and renewable energy alternatives. Consequently, identifying efficient renewable energy sources has become a critical challenge for policymakers and energy planners worldwide. This study evaluates major renewable energy sources, including solar, wind, tidal, hydropower, geothermal, and biomass energy, with the aim of ranking them according to their technical efficiency. To achieve this objective, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is applied within a Fermatean fuzzy framework to address uncertainty and ambiguity in expert judgments. Furthermore, a comparative analysis under different uncertainty scenarios is conducted to validate the robustness and reliability of the obtained results. The proposed approach provides a systematic decision-support framework for researchers, energy-sector authorities, and policymakers to facilitate sustainable and informed energy planning

In real-world scenarios, the neutrosophic set or neutrosophic numbers have been widely used to deal with the uncertain difference equations of the corresponding uncertain discrete dynamical system. A situation where discrete changes occur with vague information of a neutrosophic sense can be dealt with by the neutrosophic difference equation. In this paper, a new metric is defined for the neutrosophic set, and the sense of generalized Hukuhara difference for the fuzzy numbers is extended to the neutrosophic numbers. The generalized Hukuhara difference of the type-I and type-II and their corresponding neutrosophic parametric representation are discussed. The existence and uniqueness conditions to obtain a solution of the difference equation in a neutrosophic environment are argued by some theorems. The theoretical concept has been applied to the logistic difference equation in a neutrosophic environment. We have applied both the type-I and type-II Hukuhara differences to the two different generalized Hukuhara difference forms of the logistic difference equation. The equilibrium points and their corresponding stability criteria are established to perceive the effect of the Hukuhara differences. Finally, the numerical examples and their graphical portrayal are provided to recognize the intuition of the introduced theory in this paper.