MS or Mphil

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3-Total edge mean cordial labeling of some classes of graphs
(UMT Lahore, 2018-07-19) Fakhir Aslam
3-Total edge mean cordial labeling of subdivision of some standard classes of graphs
(UMT Lahore, 2020) Zurnab Zulfiqar
Our task in this thesis is to focus on 3-total edge mean cordial (3-TEMC) labeling of the subdivision of some standard classes of graphs. We study the subdivision of comb graph, double comb graph, ladder graph, triangular graph, double triangular graph, prism graph and n-sunlet graph in the context of 3-TEMC labeling.
3-Total edge product cordial labeling of some new classes of graphs
(UMT Lahore, 2016-03-14) Madiha Saqlain
Our aim in this thesis is to study 3-total edge product cordial (3-TEPC) labeling of some new classes of graphs. We study ladder graph, wheel graph, m isomorphic copies of n cycle graph and Dutch windmill graph in the context of 3-TEPC labeling. We also studied 3-TEPC labeling of some particular examples of graph operations like corona graphs and subdivision graphs.
3-total edge product cordial labeling of some standard classes of graphs and convex polytopes
(UMT Lahore, 2017) Umer Ali
In this thesis, our task is to study 3-total edge product cordial (3-TEPC) labeling of some standard classes of graphs and convex polytopes graphs. We discuss web graph, book graph, ower graph and some families of convex polytopes in the context of 3-TEPC labeling.
4-Total edge mean cordial labeling of some standard classes of graphs
(UMT Lahore, 2018-07-27) Hafiz M Tariq Mahmood
In this thesis, we introduce new labeling and called it as k-total edge mean cordial (k-TEMC) labeling of graphs, which is a generalization of edge mean cordial labeling (see [9]). We discussed path graph, ladder graph, comb graph, double comb graph, cycle graph, wheel graph, sun-let graph, helm graph, gear graph and prism graph in the context of k-TEMC labeling for k = 4.
4-Total edge mean cordial labeling of some classes of convex polytopes
(UMT Lahore, 2019-11-07) Fakhra Malik Awan
In this thesis, we study the type of graph labeling known as k-total edge mean cordial (k-TEMC) labeling of graphs introduced by F. Aslam at al. (see [2]), which is a generalization of edge mean cordial labeling (see [17]). We discussed some classes of convex polytopes graphs and their different combinations in the context of k-TEPC labeling for k = 4
4-total edge product cordial labeling of some standard classes of graphs
(UMT Lahore, 2019-02-22) Rushba Rushin
In this thesis, we define new labeling and named it 4-total edge product cordial labeling (4-TEPC) of graphs, which is a generalization of product cordial labeling. We discussed some convex polytope graphs, book graph and flower graph in the context of k-TEPC labeling for k = 4.
4-total edge product cordial labeling of some standard classes of graphs
(UMT Lahore, 2018) Javeed Iqbal
Our task in this thesis is focuses on 4-total edge product cordial (4-TEPC) labeling of some standard classes of graphs and the main aim of the study is to discuss path graph, cycle graph, wheel graph, helm graph, banana tree graph, recracker graph, gear graph and tadpole graph in the context of 4-TEPC labeling.
4-total edge product cordial labeling of the subdivision of some classes of graphs
(UMT Lahore, 2019-08-02) Hina Nawaz
Our task in this thesis focuses on 4-total edge product cordial (4-TEPC) labeling of the subdivision of some standard classes of graphs, and the main aim of the study is to discuss prism graph, wheel graph, book graph, banana tree graph, recracker graph, and star graph in the context of 4-TEPC labeling.
4-total mean cordial labeling of some convex polytopes
(UMT Lahore, 2018) Nelofar Shami
In this thesis, we study k-total mean cordial (k-TMC) labeling of graphs (see [2]), which is a generalization of mean cordial labeling (see [14]). We discussed different convex polytopes in the context of k-TMC labeling for k = 4.
4-total prime cordial labeling of subdivision of some standard classes of graphs
(UMT Lahore, 2020) Sharoon Anjum
Our task in this thesis is to focus on 4-total prime cordial (4-TPC) labeling of the subdivision of some standard classes of graphs. We study the subdivision of star, comb, double comb, ladder, and triangular ladder graphs in the context of 4-TPC labeling.
A decision framework for ranking electronic voting machines using (m, n)-rung orthopair fuzzy soft sets.
(UMT Lahore, 2025-07-17) Rukhsar Hamid
The purpose of this thesis is to develop a new concept of possibility (m,n)-rung orthopair fuzzy soft set ((m,n)-rofs), which is an expansion of traditional fuzzy set theory. Electronic voting machines related to elections (evms) are becoming more and more reliant on voting; therefore, it is important to have a strong and trustworthy methodology to evaluate them. The results of the study can improve the overall quality of electronic voting machines (evms) in the future and provide valuable information to voters and election officials. This research proposes an effective decision-making approach for evaluating electronic voting machines (evms) using the (m, n)-rofs with a possibility setting based on aggregation operators. Here, the incorporation of possibility settings and aggregation operators enhance the decision-making process by systematically integrating various criteria and expert opinions. To make the possibility (m,n)-rofss acceptable for multi argument scenarios, this study modifies its current structure. Thus, we first create the basic idea of a possibility (m,n)-rofss. To demonstrate the possibilities of (m,n) rung orthopair fuzzy soft sets, an example is given that shows how several models of electronic voting machines can be assessed using the approach according to established standards. Moreover, using the suggested aggregation operators as a basis, we suggest a method for p-(m,n)-ropfss to address decision-making problems, including known possibility data. These aggregation operators are useful to make research more subjective, and they can also provide a comprehensive evaluation. The foundation of our madm approach is the p (m,n)-rofssga or p (m,n)-rofssaa operators, which take contention relationships into account. Furthermore, sensitivity and comparative analyses are provided in the end, along with a real-life example to illustrate the feasibility of the proposed methods. Their inclusion not only strengthens the method but allows experts to make a cohesive decision-making process. These analyses are helpful in assessing the reliability and stability of the process of evaluation when faced with varying levels of uncertainty. The evaluation of these machines is conducted based on several critical criteria: security, usability, auditability, initial purchase cost and maintenance cost. This algorithm works well to figure out whether a specific electronic voting machine (evm) is appropriate to use in an election, which will ultimately be a great innovation in the election system of any government. Overall, this method’s actual use shows how adaptable and successful it is at handling challenging decision-making situations. It emphasizes how crucial it is to use contemporary methods to enhance decision-making procedures and guarantee the smooth and dependable operation of vital systems, such as voting mechanisms. This research allows both election officials and voters to understand the performance and sustainability of electronic voting machines during the election. The insights will be beneficial for stakeholders in the electoral process, policymakers, and election officials. It adds to the ongoing discussion about electoral technology and provides information for decision-making processes targeted at improving the credibility, accessibility, and integrity of us elections by analyzing the effectiveness and factors related to these electronic voting systems.
A deep learning approach to analysis the Covid-19 disease spread in population
(UMT Lahore, 2023) Touseef Afzal
The susceptible, exposed, infected, hospitalized, recovered (SEIHR) model, a frequently employed framework for explaining the dynamics of the novel coronavirus (COVID-19), has been thoroughly examined, and I describe that study in my thesis. Our main interest is in the numerical solutions of this model, especially when using various step sizes with two well-known numerical methods, the RK-4 method and the Euler method. Our findings show a clear pattern in these numerical approaches’ behavior. Particularly, the Euler and Runge-Kutta Four Order (RK-4) approach both consistently produce accurate results when the step size is set to one, demonstrating their dependability in capturing the complex dynamics of the SEIHR model. Larger step sizes, though, provide a serious obstacle. Both the Euler and the RK-4 methods show this crucial shortcoming in such situations, failing to generate valid solutions and instead deviating from the desired results. In order to overcome this limitation, investigate a new approach that involves using a neural network technique to solve the SEIHR model. Our research yields a startling and encouraging finding: the neural network consistently produces precise solutions across a wide variety of step sizes. This exceptional robustness of the neural network method highlights its potential as a reliable substitute for solving the SEIHR model, especially when handling bigger step sizes. This study highlights the importance it is to using the right numerical techniques when working with intricate epidemiological models like the SEIHR model. Additionally, our study opens up a fruitful path for expanding our knowledge of the dynamics of the novel coronavirus and other infectious disorders. When bigger step sizes are required, the neural network approach proves to be an exceptionally useful tool. This finding has enormous potential for improving our capacity to forecast infectious disease behavior and, ultimately, to support public health decision-making and pandemic management.
A development of multi – polar interval valued fuzzy soft set with applications
(UMT Lahore, 2020) Rimsha Zofishan
The similarity measure for the fuzzy system plays a very important role in dealing with problems that recognize ambiguous information but are unable to deal with the complexity and ambiguity of multi-polar interval-valued information issues. To minimize this gap, a certain distance between two multi-polar interval-valued fuzzy soft sets (mIVF soft-set) will be defined in this study. A new distance-based similarity measure (Sim. M) IVFS, some basic operations like union, intersection, complement, and difference will be proposed. An application that the suggested Sim. M IVFS typeset can recognize various objects belonging to the same family that will be demonstrated for understanding.
A generalization of nadler fixed point result in hausdorff double controlled metric type space
(UMT Lahore, 1-8-2022) Muhammad Tariq
In 2020, Nayab Alamgir [9] showed that every controlled metric type space (; q) induces a Hausdorff controlled metric type space on the class of closed subsets of which is also complete if (; q) is complete. He also defined multivalued almost F-contractions on Hausdorff controlled metric type spaces and proved some fixed point results. In this thesis, we will show that every double controlled metric type space makes a Hausdorff double controlled metric type space (H; CD()) where CD() is the collection of all non-empty closed subsets of and if (; q) is complete then (H; CD()) is also complete. We will also demonstrate multivalued almost F-contractions on Hausdorff double controlled metric type space and we will derive a few fixed point results.
A mathematical framework of optimal agriculture planning via MCDM approach.
(UMT Lahore, 2024-07-08) Misbah Khan
Agriculture undoubtedly plays a profound and irreplaceable role in the economy of Pakistan, being the cornerstone of livelihood that not only ensures food security for the nation but also serves as the main source of employment for countless people in various regions. The importance of the sector is further emphasized by its significant contribution to export earnings, which supports the stability and growth of Pakistan's economy. In addition, agriculture is an important livelihood for rural communities, providing essential livelihood support and acting as a catalyst for poverty alleviation across the country. In light of the evolving agricultural landscape, plant selection decision-making has emerged as a critical issue that requires increased attention and strategic planning to maximize productivity and sustainable results. This trend underlines the increasing complexity and importance of agricultural practices in Pakistan, highlighting the need for informed decisions and innovative approaches to improve the overall efficiency of the sector and the economic impact of the country. In light of our plant selection study, extensive mathematical modeling was used to delve into the complexity of this real-world challenge. This comprehensive analysis paved the way for the formulation of a multi-criteria decision making (MCDM) framework that sheds light on various aspects of the problem at hand. A combination of survey data and information from various online sources was carefully collected to gather the data needed for this study. As a result of extensive research and scientific work, a decision matrix was created that provides valuable insights into the collected data. In this study, advanced multi-criteria decision-making tools such as fuzzy TOPSIS were used to explore different options and accurately evaluate the criteria affecting crop selection. The area of operations research that encompasses MCDM methodologies is primarily concerned with the careful evaluation, comparative ranking and final selection of alternatives based on a number of different and often conflicting criteria. In this case, MCDM methodology is applied using Analytic Hierarchy Process (AHP) with TOPSIS techniques. The use of AHP precisely determines the relative weight of criteria, while the TOPSIS method effectively ranks alternatives according to their effectiveness against established standards. Programming techniques abstract xv are judiciously applied to analyze the results and determine the most appropriate crop for a given scenario. Optimal agricultural planning in Kasur, Pakistan requires a thorough evaluation of crop choices, resource allocation and sustainability factors on a one-abstract xvi hectare plot of land. The main objective is to maximize productivity while ensuring efficient use of resources and long-term environmental sustainability. Agriculture plays a crucial role in food security and environmental management, which emphasizes the importance of agricultural productivity and sustainability. The research focuses on the development of an adapted agricultural plan for a one-hectare plot of land in Kasur, Pakistan. The goal is to optimize productivity through efficient allocation of resources and promote long-term environmental health. The evaluation process includes a number of different aspects such as crop selection, resource allocation considerations and sustainability metrics such as water supply, soil quality maintenance and biodiversity conservation. Combining a multi-objective optimization approach, the research aims to find the ideal crop mix, irrigation schedule and fertilizer application strategy that together promote maximum productivity and sustainability. Ultimately, the results will be a valuable blueprint for smallholder farmers in Kasur, providing them with the tools they need to improve agricultural practices, improve economic prospects, and create a more active and sustainable food system within the region.
A new operational matrix in Caputo sense for Vieta-Lucas polynomial with application to fractional differential equations
(UMT Lahore, 2021-05-05) Zulfiqar Ahmad Noor
Fractional calculus, being a generalization of integer-order calculus, has been an emerging field of research in the last few decades. Many physical models and engineering processes are elegantly modeled by fractional differential equations (FDEs). For example, a model on the nonlinear oscillation of earthquakes can be best described with fractional derivatives [49], and the fluid-dynamic models with fractional derivatives [50] help to remove the inadequacy arising from the assumption of continuum traffic flow. Such fractional order differential problems (FODPs) appear in almost every field of science. This leads to a strong motivation for researchers to develop reliable and efficient numerical methods to find the approximate solutions of FODPs. There are several methods used in the literature to find the approximate solution of FODPs. In this thesis, we have used the operational matrices to reduce the FDEs to a system of algebraic equations, which are then easily solved using any computational software. In this thesis, we develop a numerical method based on the operational matrices of Shifted Vieta-Lucas polynomials (VLPs) for solving FDEs. We derive a new operational matrix of the fractional order derivatives in the Caputo sense, which is then used with the collocation method to reduce the FDEs to a system of algebraic equations. Several numerical examples are given to show the accuracy of this method. These examples show that the obtained results are aligned with the analytical solutions in both linear and non-linear FDEs.
A novel approach to Q-rung orthopair fuzzy multi-attribute decision-making based on Q-rung orthopair fuzzy entropy
(UMT Lahore, 2023-03-11) TAYYABA AZAM
Using Q-rung orthopair fuzzy sets provides a useful tool for dealing with uncertain or imprecise expert knowledge, which can greatly enhance the decision-making process. This work presents a fresh approach for quantifying the degree of fuzziness inherent in Q-rung orthopair fuzzy sets, known as Q-rung orthopair fuzzy entropy. Entropy is a concept from information theory that measures the uncertainty or randomness in a system. In the context of Q-rung orthopair fuzzy sets, entropy can help us understand how fuzzy or unclear the knowledge represented by these sets is. The higher the entropy, the more uncertain or fuzzy the knowledge; high entropy in Q-rung orthopair fuzzy sets suggests a lack of clarity or precision in the information they convey. By quantifying this fuzziness with Q-rung orthopair fuzzy entropy, decision-makers can gain insights into the reliability and precision of the knowledge they're working with. This allows for more informed decision-making processes, as it considers the inherent uncertainty in the information available. Q-rung orthopair fuzzy sets can represent uncertain knowledge, and calculating the Q-rung orthopair fuzzy entropy can assess just how fuzzy or uncertain this knowledge is. This insight can help weigh the risks and make a more informed investment decision. Q-rung orthopair fuzzy sets provide a valuable framework for handling uncertain or imprecise knowledge, and the introduction of Q-rung orthopair fuzzy entropy offers a method to measure the level of fuzziness within these sets. This allows decision-makers to better understand and navigate the uncertainty inherent in their knowledge, ultimately leading to more informed and strong decision-making processes. Furthermore, this work explores how this innovative entropy measure can be practically applied in creating a unique decision-making framework for situations involving multiple attributes, using Dempster-Shafer theory. In this approach, criteria are assigned weights based on the entropy of Q-rung orthopair fuzzy sets, where each fuzzy number offers supporting evidence. Using these criterion weights, the framework then calculates the weighted average evidence for different options. To illustrate the methodology, this work presents a detailed application and algorithm for selecting the most suitable investor in a business context, employing Q-rung orthopair fuzzy sets. This practical example demonstrates the relevance and effectiveness of the proposed decision-making approach. To sum up, this study introduces Q-rung orthopair fuzzy entropy as a novel metric for measuring fuzziness within Q-ROFSs, and utilizes it to develop a distinctive decision-making framework grounded in Dempster-Shafer theory. By determining criterion weights from the entropy of Q-rung orthopair fuzzy sets, the methodology enables the assessment of alternative options through a weighted average evidence calculation. Finally, the approach is applied to the selection of an optimal investor in a business setting, showcasing its practical applicability and efficiency and selection of appropriate suture material in medical. In surgical procedures, selecting the appropriate suture material is crucial for ensuring optimal patient outcomes. By employing Q-rung orthopair fuzzy sets, doctors can effectively navigate the complexities of choosing the right suture material among various factors such as tissue type, wound location, and patient characteristics.
A real-life MCDM problem of selecting a university in the UK for post-graduate studies
(UMT Lahore, 2022-10-29) Zulaikha Aftab Sheikh
Education is the finest investment one can make as it serves as a cornerstone for a better future. Higher education offers opportunities for individuals to thrive and compete with the challenges of the modern era. Highly educated individuals with diverse experience are more likely to achieve high-paying jobs. Every student who is pursuing higher education wants his degree to be affiliated with some well-established institute. One can only gain a successful career if he has some remarkable research included in his resume. Mathematical science is particularly one of the most complex and advanced degrees. Most students, especially from third-world countries, choose the United Kingdom to pursue their post-graduate (master’s and doctoral) degrees. The reason behind this, most countries are way behind in the latest research and up-to-date applications of mathematical sciences, while the United Kingdom has a well-regarded center of advanced research institutions. Lack of educational infrastructure, research centers, and funding are the most common issues that urge students to abandon their own country in pursuit of a better future. Therefore, selecting a university in the UK is a big challenge for students. To overcome this challenge, mathematical modeling for selecting a university is performed to solve this real-life problem, resulting in a multi-criteria-decision-making (MCDM) problem. Data for this problem has been arranged from the university’s websites. In this study, MCDM techniques are used to assess the standards taken into account while selecting a university. Two popular MCDM techniques are used: Analytical Hierarchy Process (AHP) is used to calculate the weights for each qualitative and quantitative criterion, and another technique namely VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) is used to rank the alternatives of problem. The outcomes are very promising, programming code for the AHP and fuzzy VIKOR algorithms is also implemented in order to broaden the work application to time series analysis and the creation of algorithms for graph theory, machine learning, pattern recognition, and artificial intelligence.
A study of Casson fluid flow on the Riga plate using Prabhakar fractional derivative
(UMT Lahore, 2024-04-04) Khola Zainab
Complex problems in mathematical modeling and analysis arise when fluid flow occurs on solid surfaces, particularly when external influences are present. This thesis delves into the complexities of Casson fluid flow on a Riga plate that undergoes acceleration, resulting in the generation of convective flow. The focal point of the investigation lies in employing Prabhakar fractional derivatives to explore the stability of fractional differential equations governing the system. The governing equations are constructed by including Fourier and Fick’s laws into the mathematical framework, paving the way for an extensive investigation of the fluid dynamics. Our comprehension of fractional order systems is improved by the clever method of incorporating Prabhakar fractional derivatives into the study of Casson fluid flow on an accelerating Riga plate. Through the use of Fourier and Fick’s laws to derive governing equations, we create a complete framework that captures the complex interactions between fluid dynamics and plate motion. Next, Prabhakar fractional derivatives become important since they are the most flexible for dealing with non-local and non-singular occurrences. This decision is crucial for stability analysis since it clarifies the long-term behavior of the system. Moreover, it facilitates a refined investigation of non-local effects, offering an enhanced comprehension of the fundamental principles of physics. To solve the derived fractional partial differential equations, a two pronged approach is adopted. Firstly, the Laplace transform is employed to convert the equations into ordinary differential equations (ODEs), facilitating a more tractable analytical solution. This step showcases the versatility of the Laplace transform in simplifying complex mathematical expressions. Secondly, the obtained ODEs are solved to yield both analytical and semi-analytical solutions, providing a comprehensive understanding of the system’s behavior. Zakian’s numerical method plays a pivotal role in handling the inverse Laplace transform, particularly for the velocity component. This numerical approach ensures the accuracy of solutions for concentration and temperature, offering a bridge between the analytical and numerical realms. The numerical method adds a layer of validation to the obtained results, confirming the efficacy of the mathematical framework in describing the intricate interplay between Casson fluid flow and the accelerating Riga plate. To comprehend the complex interactions between many elements and the flow behavior, a wide range of parameter variations are investigated. The Casson parameter, mass Grash ̈of number, Prandtl number, Grash ̈of number, modified Hartmann number Ha, fractional parameters, magnetic parameter M, and Schmidt number are among the critical parameters whose systematic variation and graphical representation provide a visual roadmap to understand their respective effects on Casson fluid flow dynamics. These graphs are useful tools that capture the subtle way in which the system reacts to changes in parameters. This thorough investigation of a broad range of parameters reveals nuanced impacts and interdependencies, promoting a thorough comprehension of how every component affects the complex dance of fluid dynamics on the accelerating Riga plate. Such comprehensive understandings are crucial for real world applications and decision making procedures. In addition to adding to our theoretical knowledge of casson fluid dynamics, this research provides useful information that may be applied in engineering and industrial settings. Future research into more complex fluid solid interactions and the application of fractional calculus to complex system modeling are made possible by the discoveries.

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