Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

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Author: search.filters.author.Mathur, TrilokStart date: 2020

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Now showing 1 - 10 of 48
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    Solving extended assignment problem using stochastic DEA approach
    (IEEE, 2025-04) Agarwal, Shivi; Mathur, Trilok
    The assignment model is a particular application of linear programming problems where tasks are assigned to agents with the goal of either maximization of profit or minimization of cost (in terms of both money and time) with provided deterministic data. But in real-life cases, more than one attribute may occur. Also, all these attributes need not be deterministic; some attributes may be stochastic in nature. The existing assignment model cannot handle these types of issues. To overcome these drawbacks, the study proposes the integrated extended assignment model with stochastic theory and the data envelopment analysis (DEA) technique. To illustrate the suggested concept, a numerical example is provided.
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    Fuzzy DEA model with exogenously fixed variables for ranking of renewable energy sources
    (Springer, 2025-09) Agarwal, Shivi; Mathur, Trilok
    As the global population grows, so does the demand for energy. India, with its fast growth, industrialization, and urbanization, is struggling to meet energy needs using traditional sources. To tackle energy shortages, pollution, and climate change, it’s important to find cost-effective and environment friendly alternatives. Renewable energy sources (RESs) offer a promising solution, making it important to prioritize them. India has strong potential in technologies like solar, geothermal, hydro, biomass, wave energy, and onshore and offshore wind energy. However, prioritizing these energy options involves considering many factors, often with conflicting priorities. This study proposed a fuzzy Data Envelopment Analysis (DEA) method to prioritize renewable energy sources in India, considering exogenously fixed variables that can’t be controlled, and handling undesirable variables. The proposed model ranks RESs effectively. It is revealed from results that Offshore wind energy is found to be the most efficient, followed by onshore wind and hydro energy, while geothermal energy ranks the lowest. The proposed methodology and findings can help developing nations and policymakers make better decisions when adopting renewable energy sources.
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    An optimal criteria selection in efficiency assessment through integration of dea with rough set theory
    (Springer, 2025-09) Agarwal, Shivi; Mathur, Trilok
    Data Envelopment Analysis (DEA) is a prominent nonparametric technique used to assess the efficiency of decision-making units (DMUs) by using multi criteria. However, traditional DEA models can be significantly impacted by criteria that do not contribute significantly to the efficiency analysis, thereby reducing accuracy and discriminatory power. Additionally, for DEA models to produce reliable results, the number of DMUs should be greater than the number of criteria included. This paper introduces a Rough Data Envelopment Analysis (RDEA) approach, which integrates Rough Set Theory (RST) with DEA to effectively handle this problem. RST is used by the RDEA framework to find and remove less contributing criteria from the input and output data in efficiency analysis. RST generates lower and upper approximations which helps in identifying criteria that are not significantly contributing to the efficiency analysis. Once these criteria have eliminated from the data set, the DEA models may be utilized to provide a more accurate and reliable efficiency evaluation of DMUs. This theoretical framework leverages the capabilities of RST to streamline input and output data, enhancing the effectiveness of DEA in evaluating efficiency. Also, a numerical example is provided to show implementation of this method.
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    Analyzing unemployment dynamics: a fractional-order mathematical model
    (Wiley, 2025-03) Mathur, Trilok
    The persistent rise in unemployment rates poses a significant threat to global economic stability. Addressing this challenge effectively requires a deeper understanding of workforce dynamics, particularly through the integration of an individual's employment history into analytical models. This research introduces a fractional mathematical model, leveraging the Caputo fractional derivative and three key variables: the number of skilled unemployed individuals, the number of employed individuals, and the number of available job vacancies. The model's well-posedness and global stability are rigorously established using fixed-point theory. Additionally, the basic reproduction number is analyzed to identify critical factors that facilitate the creation of new job opportunities. Real-world data from India are employed for MATLAB simulations, offering predictions of unemployment trends in the coming years. A graphical analysis highlights the impact of the COVID-19 pandemic on unemployment rates. The model's predictive accuracy is demonstrated through error analysis, showing that fractional-order forecasts achieve less than 5% error, outperforming integer-order models in capturing the nuances of unemployment dynamics. Sensitivity analysis reveals that the employment rate is the most influential parameter; a 40% increase in this rate could lead to 192,200 additional employed individuals. The fractional-order model further exhibits superior performance metrics, including lower root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) values, alongside a higher correlation coefficient ( ). These findings underscore the model's potential to enhance the understanding and mitigation of unemployment challenges.
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    Advancements of solar energy research in the context of SDG-7 attainment: a bibliometric analysis using spar-4-slr protocol
    (IEEE, 2025-05) Agarwal, Shivi; Mathur, Trilok
    Renewable energy sources, free of environmental risks, are vital for achieving net-zero CO2 emissions and addressing climate change to meet Sustainable Development Goals. This study explores the evolution of solar energy research using bibliographic coupling and keyword co-occurrence analysis of 6,460 articles from 1988 to 2024. The findings reveal a significant increase in solar power-related publications, with China leading in research output, followed by the United States and India. Top journals include Renewable Energy and Energies, with a growing focus on Energy and Engineering. This analysis serves as a vital reference for solar energy researchers and professionals.
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    Assessment of offshore wind farm site suitability in India using GIS and MCDM methods
    (Springer, 2025-03) Agarwal, Shivi; Mathur, Trilok
    The growing demand for sustainable energy sources has prompted investigation of offshore wind farms (OfWF) as viable options. This study proposes an innovative framework combining GIS with MCDM methods to identify highly suitable sites and efficiently prioritize alternative sites for OfWF, specifically focusing on regions viable for fixed foundations within the Indian EEZ. It takes into account technical, economic, and socio-environmental criteria to identify the optimal sites for OfWF. Two types of criteria are involved: exclusion criteria, refining study area by excluding areas unsuitable for renewable energy projects, and evaluation criteria, influencing the viability of specific sites in line with defined objective. The methodology involves screening criteria from existing literature, preprocessing data through GIS, and calculating criteria weights with AHP and CRITIC methods. This is followed by ranking potential sites using TOPSIS and VIKOR, offering structured decision support. The final phase of the analysis involved evaluating the consistency between individual site rankings using the Spearman rank correlation, ensuring reliability in the ranking outcomes across selected methods. The findings suggest the top fifteen sites for installing wind farms, ranging in offshore regions from Pallam town in Kanyakumari to Kooduthalai in Tirunelveli district, Tamil Nadu. This study’s insights on offshore renewable energy site selection in India are invaluable for policymakers, investors and sustainability initiatives, offering a roadmap for a cleaner and more sustainable energy future worldwide.
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    A DEA-based approach for optimizing the extended transshipment problem
    (Elsevier, 2025-09) Agarwal, Shivi; Mathur, Trilok
    Transshipment issues represent a distinct category of transportation challenges that commonly arise in practical contexts. The conventional transshipment model typically focuses on a single variable (predominantly cost), with decision-makers endeavoring to enhance this variable. Nevertheless, in practical contexts, numerous cost-related and revenue-related variables significantly influence the transshipment process, necessitating their optimization to augment the efficacy of the transshipment strategy. To our knowledge, a deficiency exists in addressing such a transshipment problem characterized by multiple variables. To address this deficiency, the present study advances the conventional transshipment model to accommodate scenarios wherein various variables are present within the transshipment framework. To illustrate the validity of the proposed methodology, a numerical example is provided, utilizing empirical data concerning wheat production in Iran.
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    Inhomogeneous generalized fractional Bessel differential equations in complex domain
    (Elsevier, 2026-03) Mathur, Trilok; Agarwal, Shivi
    This paper explores inhomogeneous generalized fractional-order Bessel differential equations in the complex domain with arbitrary-order δ () using Riemann-Liouville (R-L) fractional operators. The study establishes the existence of holomorphic solutions through the power series method, considering the concept of radius of convergence. Conditions for the unique existence of holomorphic solutions in the complex domain are identified using fixed point theory and the Rouche theorem. Additionally, the paper demonstrates that the solution, particularly for infinite series of fractional power, satisfies the generalized Ulam-Hyers stability. Furthermore, when , the solution to the inhomogeneous Bessel differential equation takes the form of Bessel functions of the first kind, denoted as .
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    Fractional-order crime propagation model: a comparison between logistic and exponential growth
    (Springer, 2024-11) Mathur, Trilok
    Everyone is affected by crime in some manner. Criminal activity spreads through peer influence and is contagious. Several mathematical models for predicting crime transmission have been proposed in various studies. However, these models do not account for an individual’s logistic development, which is required to describe criminal behavior changes. As a result, this research present a fractional-order mathematical model of crime transmission that considers the logistic growth of law-abiding people. The existence and stability of the crime-free and crime persistence equilibrium have been investigated using the Routh-Hurwitz criterion. We also investigated the incidence of transcritical bifurcation in the proposed model system, including law enforcement. Numerical simulations have been preformed to validate the analytical findings, further supporting our qualitative conclusions and establish the role of different crucial parameters and variables used in the proposed model. The model with logistic growth outperforms the traditional one (exponential model). The results reveal that offenders survive as long as the coefficient of law enforcement remains below a specific threshold value. The criminals start vanishing once this value is achieved. The findings demonstrate that the offenders may persist if isolation and conversion rates remain low.
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    Performance evaluation of public transport sector with missing data
    (Springer, 2024-07) Agarwal, Shivi; Mathur, Trilok
    Efficiency analysis is vital for decision-making in service sectors such as public transport and public health, aiding policy formulation and understanding competition. This study focuses on evaluating the efficiency of India's public transport sector, particularly State Road Transport Undertakings (SRTUs), utilizing Data Envelopment Analysis (DEA). However, a key challenge in real-life efficiency analysis is the unavailability or absence of certain data points. To address this issue, the study proposes the integration of DEA models and fuzzy numbers. By incorporating non-symmetrical fuzzy data, the study measures the efficiency of SRTUs and provides a ranking based on fuzzy efficiency.