2023

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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 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 theoretical approach towards interval-valued neutrosophic fuzzy soft set like structures with applications
(UMT Lahore, 2023) Kinza Kareem
This study analyses structures that are similar to interval-valued neutrosophic fuzzy soft set (IVNFSS), presenting a thorough theoretical foundation and demonstrating their practical application. This research demonstrates the inherent limits of soft sets, neutrosophic sets, and fuzzy sets, which led to the development of IVNFSS and IVNFHSS as a revolutionary method for dealing with imprecise and uncertain information. Soft sets, neutrosophic sets, and fuzzy sets have historically handled uncertainty. The theoretical framework is meticulously built, starting with a thorough literature analysis that highlights the shortcomings of current approaches and establishes the need for IVNFSS and IVNFHSS. The algebraic structures, mathematical operations, and features of IVNFSS and IVNFHSS are defined methodically, revealing the resilience and elegance of their underlying mathematics. The results of this study highlight the flexibility and effectiveness of IVNFSS and IVNFHSS. The research exhibits crucial theoretical features including union, intersection, complement, and De Morgan’s laws in the context of IVNFSS and IVNFHSS by thorough investigation. Furthermore, practical applications of IVNFSS and IVNFHSS are illuminated through illustrative examples and compelling case studies, providing tangible evidence of its effectiveness in domains like decision-making, pattern recognition, and expert systems. These findings highlight IVNFFSS’s tremendous potential as a useful tool for addressing real-world problems characterized by uncertainty and imprecision. The study advises a further investigation of IVNFSS and IVNFHSS across several domains, including artificial intelligence, data mining, and decision support systems, in light of these insightful findings. The research also urges the creation of software tools and algorithms to speed up the use of IVNFSS based techniques, enabling more effective and broad use. Academic and industrial cooperation is urged to make it easier to incorporate IVNFSS and IVNFHSS into real-world applications, thereby improving decision-making in both academic research and practical situations. In addition to providing a solid theoretical foundation for interval-valued neutrosophic fuzzy soft set-like structures, this paper also highlights how they have the potential to fundamentally alter how uncertainty is managed in a variety of applications and practitioners may open the way for more precise and robust decision-making processes by adopting IVNFSS-based methodologies, ushering in a new age of tackling complex, real-world situations rife with uncertainty and ambiguity.
An innovative approach to passport quality assessment based on possibility Q-rung orthopair fuzzy hypersoft so.
(UMT Lahore, 2023-06) Mubashir Ali
This research article aims to evaluate the quality of passports issued by different countries. Passport quality assessment plays a critical rule in ensuring secure and efficient international travel. By leveraging this novel framework, we address the limitations of existing methods and provide a comprehensive and accurate evaluation of passport quality. Our proposed PQROFHS (possibility q-rung orthopair fuzzy hypersoft set) based framework integrates various attributes related to passport quality, considering the inherent uncertainties and imprecisions associated with each attribute. Through extensive experimentation, we demonstrate the superior performance of our approach, achieving higher accuracy, reliability, and consistency compared to traditional methods. The flexibility of the PQROFHS framework allows for a nuanced representation of uncertainty, enabling informed decision-making in real-world scenarios. The implementation of our approach holds significant potential in enhancing global travel security, streamlining immigration processes, and facilitating seamless international travel experiences. For this, an explanatory example of a real-world problem is presented to demonstrate the suggested approach.
Analysis of Jeffrey fluid with generalized boundary conditions via Prabhakar fractional approach
(UMT Lahore, 2023) Syed Mohsin Raza Shirazi
This theoretical investigation aims to generalize the idea of fractionalized Jeffrey fluid flow present in this research work. Exact analysis of MHD natural convective flow of the Jeffrey fluid to derive analytical solutions with the non-integer order derivative Prabhakar fractional operator with non-singular type kernel along with application of generalized laws namely Ficks and Fouriers are reported here. This fractional operator has multi-parameter generalized Mittag-Leffler kernel. The fluid flow is elaborated near an infinitely vertical plate with characteristic velocity u0. The modeling of the considered problem is done in terms of the partial differential equations together with generalized boundary conditions. Appropriate sets of variables are introduced to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also in the form of special functions. The pertinent parameters’ influence such as Pr, Gm, Sc, and Gr on the fluid flow is brought under consideration to reveal interesting results. In comparison, we noticed the Prabhakar-like non-integer approach shows better results than the existing operators in the literature, and graphs are drawn to show the results. Also, results are obtained in a limiting sense such as second grade fluid, Newtonian fluid in fractionalized form, as well as Jeffrey and viscous fluid models for classical form from Prabhakar-like non-integer Jeffrey fluid model.
Analytical solutions of fractional partial differential equations for the second grade fluid flow.
(UMT Lahore, 2023) Maira Anwar
This thesis deals with unsteady flow of second grade fluid over an infinite plate. The governing equations for flow are developed through constitutive relations. Then classical model extended to fractional order model with power law fractional differential operator. The Laplace transform (LT) method, which is expressed in terms of series that meet the boundary conditions, is used to discover the analytical solutions. Some graphs are shown to illustrate the physical significance of flow parameters. Recent results from the existing literature are also recovered to validate.
Analytical solutions of non-Newtonian fluid flow containing hybrid nanoparticles with different fractional operators.
(UMT Lahore, 2023-07-17) Mubarra Abbas
The present study deals with the fractional model of unsteady and the incompressible MHD Brinkman fluid between vertical plates. For this problem we use the Caputo, Caputo-Fabrizio, Antangna Baleanu and Prabhakar fractional derivatives with suitable boundary conditions. The non dimensional equations solved by Laplace transform method. The solution of energy and momentum are balances in terms of series form. We have also discussed the influence of the memory parameters on the temperature and velocity field. The mathematical outcomes for temperature and velocity field are introduced graphically for different parameters. We also draw some comparisons between different fractional derivatives in order to see more memory of the temperature and velocity.
Applications of bipolar soft sets on BCK-modules
(UMT Lahore, 2023) Madeeha Ilyas
The notion of BCK-module was established as an action of BCK-algebras on abelian groups. On the other hand bipolar soft sets have been developed to equip the notion of soft set with a polarity. In this thesis the notion of bipolar soft sets is applied on the notion of BCK-module and thereby the novel idea of bipolar soft BCK-module is introduced. In this regard, the fundamental operations on bipolar soft BCK-modules have been defined and discussed for various attributes. These operations included union, intersection, addition, complement and cartesian product of bipolar soft BCK-modules. Further, the notion of bipolar soft BCK-submodules is introduced and discussed for fundamental properties.
Artificial neural network-based numerical modeling of virus transmission in computer networks
(UMT Lahore, 2023) Haseeb Hussain Awaisi
In this thesis, artificial neural networks (NN) are used to predict virus transmission patterns in computer networks, introducing a new and data-driven strategy for improving network security. This is a difficult challenge because of how complicated the model is in real life. By training the neural networks (NN) on historical network data and virus transmission records, the model learns to recognize underlying patterns and factors that influence the spread of viruses in a network environment. By contrasting the efficiency of neural networks with traditional numerical techniques for resolving complex equations, this study explores a novel viewpoint. To illustrate the potential of the neural network-based technique in defining viral transmission via computer networks, specifically employ the Susceptible, Exposed, Infected, and Removed (SEIR) model. The neural network methodology is compared to widely used numerical methods like the Euler method and the Fourth Order Runge-Kutta method (RK-4) in this study on the dynamics of viral propagation through computer networks. The numerical methods, Euler and RK-4, are really good at staying stable and providing correct answers, but they run into issues with certain step sizes. Once the step size gets too big, both Euler and RK-4 stop working correctly. However, the neural network method works consistently for all step sizes. The importance of this study is seen in its comparison of the Euler and RK-4, and neural network approaches. The neural network method stands out as the best option since it continuously produces estimates that are more accurate, no matter the circumstance. The work highlights the capacity of neural networks to provide more accurate results, highlighting their promising role in boosting network security against emerging cyber threats, even though numerical approaches still serve their purpose well.
Classes of cycle related graphs with constant edge metric dimension
(UMT Lahore, 2023-01-19) Adeem Ahmad Bashir
Graph theory serves as a powerful tool for understanding the structural intricacies of various systems, and in this thesis, we delve into the complex dimensions of this mathematical domain. Specifically, our exploration centers around the concept of edge metric dimension within connected graphs, aiming to unravel its complexities and implications. We begin by defining a connected graph R = (V (R), E(R)), where each vertex m, n ∈ V (R) is associated with the minimum path length d(m, n). This fundamental metric provides the basis for understanding the spatial relationships between different nodes in the graph. Extending our inquiry to edges, let e = mn ∈ E(R) be an edge, and μ ∈ V (R) be a vertex. We introduce the minimum distances d(μ, e) and d(e, μ) as crucial measures, representing the shortest paths from μ to the vertices m and n respectively, enhancing our comprehension of the graph’s connectivity. The thesis introduces an innovative idea that involves vertices μ distinguishing between edges e and e∗ based on the inequality d(e, μ) ̸ = d(e∗, μ). This introduces an additional layer of discrimination within the graph, contributing to the understanding of its topology. To systematically characterize this distinction, a set WE = {ω1, ω2, ..., ωp} within V (R) is utilized. The resulting characterization r(e/WE ) of an edge e with respect to WE becomes a p-tuple (d(e, ω1), d(e, ω2), ..., d(e, ωp)). This tuple provides a detailed representation of how the edge is identified from different vertices, surrounding the complex relationships within the graph. A key contribution of this work is the introduction of an edge metric generator WE , which serves as a set uniquely characterizing each edge in R. The minimum cardinality of this generator, referred to as the edge metric basis edim(R), becomes a key metric in our analysis. We explore into the detailed exploration of edge metric dimensions, focusing on various uni-cyclic and bi-cyclic graphs. For instance, structures like C′ M,ę,6 and C′ M,6 are examined, revealing intriguing dimensions of 2 and 3 respectively.
Computation of local fractional metric dimension of certain families of graphs
(UMT Lahore, 2023) Ayesha Badar
Metric related graph parameters have been used as effective tools in various network domains where nodal distances are the focus of study. Some of these domains include computer networking, telecommunication and electrical networking. The fractional metric dimension is a recently developed variant of the metric dimension that is commonly used for non-integral linear programming problems. In this thesis, we will compute the local fractional metric dimension (LFMD) of certain circular ladders with pendent edges and convex polytopes. Further, the obtained results are illustrated with the help of examples.
Computation of metric dimension of certain hypergraphs
(UMT Lahore, 2023-11-22) MAHNOOR ATTIQUE
In a hypergraph, the basis is the smallest set of vertices that uniquely identifies or resolves all vertices in hypergraph. The metric dimension of the hypergraph is the size of this basis, representing how many vertices are needed to distinguish all vertices from one another. This document comprises chapters focused on the computation of the metric dimension for important classes of hypergraphs, including the Hyper Star Graph, Hyper Prism Graph, Hyper Double Prism Graph, and Hyper Petersen Graph. The primary objective is to establish upper bounds on the metric dimension, with a demonstration of the uniqueness of vertex representation using resolving sets. Different hypergraphs and their specific characteristics are explored in each chapter, contributing to our understanding of graph theory and network analysis. Valuable insights into the metric dimension properties of complex graph structures are provided.
Computation of topological indices of connected graphs based on 2-distance degree
(UMT Lahore, 2023-03-06) MARYYAM SATTAR
Computing bounds of Lanzhou index for the unicyclic graphs
(UMT Lahore, 2023) Farwa Zafar
A topological index being a graph theoretic parameter plays a role of function for the assignment of a numerical value to a molecular graph which predicts the several physical and chemical properties of the underlying molecular graph such as heat of evaporation, critical temperature, surface tension, boiling point, octanol-water partition coefficient, density and flash points. For a (molecular) graph Y, the Lanzhou index (Lz-index) is obtained by the sum of (f)&(f) over all the vertices, where (f) and (f) are degrees of the vertex f in Y and its complement Y respectively. Let 2 be a class of unicyclic graphs (same order and size) such that each graph of this class has order and å leaves (vertices of degree one). In this thesis, we compute the lower and upper bounds of Lz-index for each unicyclic graph in the class of graphs 24. Moreover, we characterize the extremal graphs with respect to Lz-index in the same class of graphs.
Computing connection zagreb indices of molecular structures
(UMT Lahore, 2023) Alam Shair
CA topological index (TI) is a function that associates a numeric number to the under-studied molecular graph. Molecular descriptors play a fundamental role in the study of mathematical chemistry, especially quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR). In this thesis, we computed the first Zagreb index, second Zagreb index, modified first, modified second, modified third and modified fourth Zagreb indices, first multiplicative, second multiplicative, third multiplicative and fourth multiplicative Zagreb indices and modified first, modified second and modified third multiplicative Zagreb indices based on connection Zagreb indices of molecular structures such as carbon nanotubes.
Computing fractional metric dimension of networks under operations
(UMT Lahore, 2023) Samreena Qaiser; M. Farhan Tahir; M. Mahib
Graph theory has received a lot of interest in recent years because of its many applications in domains including computational science, social networking sites, and communication networks. Graph theory has received a lot of interest in recent years because of its many applications in domains including information technology, networking platforms, and communication networks. The goal of this study is to look at local resolving sets in the complementing graph of sunflower networks. Sunflower networks, which are well-known graph topologies, are made up of a core vertex known as the sunflower center, which is linked to multiple unique petals. The complementary graph of the sunflower network, which is formed by swapping edges and non-edges, provides an interesting study field for analyzing graph features. Local resolving sets are vertices subsets that can independently determines the labels of every other vertices within a given distance. Let h=(j(h), k(h)) be a connected and finite graph. In this project, we are going to calculate the LFMD or the local fractional metric dimensions of the complement graphs of sunflower network via generating the classes ‘a’, ‘b’ and ‘ab’ class. We computed the generalized formulas for the LFMD of complementary sunflower network graphs. The entirety of the acquired results are demonstrated by the illustration of specific graphical representations pertaining to the under researched families of graphs.
Computing local fractional metric dimension of certain connected networks.
(UMT Lahore, 2023) AQSA ALEEM
Metric dimension is a useful tool for studying many distance based issues in the field of electrical networking robotics, computer networking integral programming, telecommunication and rebortic. The most recently created variant of the metric dimension know as the fractional metric dimension is widely applied to non-integrallinear programming issues. In this thesis we will compute local fractional metric dimension (LFMD) for complement of prism graph in the form lower and upper bound. The bounded and unboundedness of the obtain result is also discussed. We develop the general formulas of lower and upper bounds of local metric dimension of complement of prism graph for n ≥ 5, n ∼= 0(mod2). All the obtained results are discussed by the example of particular graph belonging to the understudied families of graph.
Cracking of stellar configuration with complexity factor
(UMT Lahore, 2023-09-15) Fizza Iqbal
In this work, the static spherically symmetric stellar system is considered. The main purpose of this work is to check the stability or instability of compact objects under the anisotropic fluid models. We explored different scenarios to configure the stability conditions. A complexity factor is used as an axillary condition. Cracking scheme is used here on compact objects. The hydrostatic equilibrium equation is obtained by manipulating Einstein Field equations. The testing of stability is analyzed by observing change in sign of different physical factors. For this we have used local perturbation scheme for analysis. The compact objects which are taken under consideration are Vela X-1, PSR 1937+ 21 and PSR 31611-2231. Cracking is observed to analyze the stability of CO. We conclude that for taken models, these compact objects are stable at every point and for each value of taken parameter.
Detecting patterns of infection-induced fertility using fermatean neutrosophic set with similarity analysis
(UMT Lahore, 2023-06) MEHAR UN NISA
Urinary tract infections (utis) pose a significant challenge globally, as they increase the risk of miscarriage and promote the growth of gram-negative bacteria. Accurately assessing susceptibility is crucial for effective diagnosis and treatment in resource-limited settings. In the field of diagnosing and treating infected patients, numerous models have been suggested in various studies. An innovative mathematical model is presented for analysing utis. To address this disease, a decision-making model is developed utilizing the fermatean neutrosophic set (fns) distance and similarity measures (sm), which is the affixed structure of the pythagorean neutrosophic set (pns) and the intuitionistic neutrosophic set (ins). The fns susceptibility model incorporates expert opinions to identify appropriate types of utis based on relevant symptoms or parameters. It calculates the distance and similarity between an ideal utis patient and the fns for the disease. This novel and forward-thinking method intends to greatly boost and enhance the diagnostic process by successfully reducing biases, errors, and inaccuracies caused by subjective assessments. The technique provides a solid decision-making framework by implementing an effective multi-attribute selection mechanism. However, it is critical to note that, while this procedure is useful, it does not intend to displace or replace existing methods for diagnosing. Rather, it should be viewed as an integrated instrument that supplements current practices, collaborating to attain the highest level of accuracy in detecting difficult illnesses. The use of this cutting-edge approach has tremendous potential to transform the handling of urinary tract infections utis, thus contributing significantly to the general enhancement of public health. A specific diagnostic table is rigorously constructed and employs a fuzzy interval of [0, 1] to aid in the proper diagnosis of utis patients. This approach enables accurate and trustworthy utis detection by adeptly leveraging powerful distance and similarity metrics within the revolutionary fermatean neutrosophic fn domain. Fns provides a robust and adaptive framework that captures the nuances of ambiguity inherent in the diagnosis of utis. It deftly depicts the fundamental issues of indeterminacy and inconsistency and the intricate interplay of insufficient medical data, a common scenario in medical environments where information shortages can impair proper diagnosis.
Development of an intelligent computing network for whooping cough like infection disease.
(UMT Lahore, 2023) Muhammad Khalil Tariq
In this thesis, the critical issues in global public health brought on by infectious diseases like whooping cough are discussed. Innovative methods for early diagnosis, monitoring, and control are required due to the rising occurrence of infectious diseases that are emerging and re-emerging. In order to do this, the author looked into the whooping cough epidemic using the SEIR model, a well-known mathematical framework in epidemiology. The study covered four different approaches to solving the SEIR model, each of which illuminated a different facet of disease transmission. The Euler approach was initially used by the author to attack the SEIR model, but as the inquiry went on, it became clear that this method had limits, especially with shifting step sizes. The author used the RK-4 method to overcome these difficulties, which improved the study and gave more precise insights into the dynamics of the disease. In addition, the Non-Standard Finite Difference (NSFD) approach was investigated, providing a nuanced viewpoint on the SEIR model. The author added artificial neural network (ANN) approaches to the research as a complement to the conventional mathematical techniques because they recognized the need for a comprehensive approach. This innovation was really helpful, especially when the earlier techniques had issues with certain step sizes. The author developed a more complete understanding of whooping cough transmission dynamics by combining ANN approaches with the SEIR model analysis. At the last, a neural network is applied for solving the SEIR model. After comparing the results of Euler, RK-4, NSFD, and Neural Network (NN), it was observed that NN is better than Euler, RK-4, and NSFD. The reason is that neural networks properly work at different step sizes, but Euler, RK-4, and NSFD are stuck at different step sizes. The neural network method stands out as the best option since it continuously produces estimates that are more accurate, no matter the circumstance. The work highlights the neural networks' capacity to provide more accurate results.

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