Browsing by Author "Dr. Madiha Khalid"

Now showing 1 - 7 of 7

Application of Ranking Heptagonal Neutrosophic Fuzzy Numbers to a Tansportation Problem
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Mudasir Nazar, Umer Farooq; CIIT/FA22-BSM-031/LHR, CIIT/FA22-BSM-59/LHR; Dr. Madiha Khalid; LHR TP 9924
This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli- cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever- aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini- mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac- terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
Application of Ranking Heptagonal Neutrosophic Fuzzy Numbers to Transportation Problem
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Mudasir Nazar (FA20-BSM-031 : Umer Farooq (FA20-BSM-059); Dr. Madiha Khalid; LHR TP 9923
This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
Application of Ranking Hexaagonal Neutrosophic Fuzzy Numbers to an Assignment Problem
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Usama Talib (FA20-BSM-044) : Zafar Iftikhar (FA20-BSM-054); Dr. Madiha Khalid; LHR TP 9920
This thesis introduces the concept of neutrosophic hexagonal numbers and presents a novel approach for their ranking. Neutrosophic hexagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic hexagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
Extended Fuzzy H-Magic Labelings of Some Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Maham Shahid; SP23-RMT-015; LHR TP 9588; Dr. Madiha Khalid
Let G⋆ = (V,E) and H = (V⋆,E⋆) be simple, finite, planar, connected and undirected graphs, where every edge of G⋆ belongs to at least one subgraph of G⋆ isomorphic to H. A fuzzy labeling graph G = (κ,τ) on G⋆ is defined by the mappings κ :V → [0,1] and τ : E →[0,1], which are one-to-one and satisfy the condition: τ(uv)
Neutrosophic Fuzzy Number Optimized Path in a Network
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Shahzaib Sajid; CIIT/SP21-BSM-029/LHR; Dr. Madiha Khalid; LHR TP 9889
Fuzzy and neutrosophic numbers are mathematical tools designed to handle un- certainty and imprecision in real-world problems. Fuzzy numbers, grounded in fuzzy set theory, represent values with gradual transitions between membership and non-membership, characterized by a membership function. These numbers effectively model uncertainty when precise values are unavailable, as seen in applications like decision-making, optimization, and engineering systems. Neutrosophic numbers extend this concept by incorporating indeterminacy into the model, a key feature of neutrosophic set theory. They consist of three components: truth (T), indeterminacy (I), and falsity (F), each of which is independently assessed. This structure enables a more nuanced representation of uncertainty, capturing scenarios where incomplete, contradictory, or vague information coexists. Both approaches play crucial roles in addressing the complexity of real-world problems where classical mathematics may fall short. While fuzzy numbers are suitable for problems with well-defined boundaries of uncertainty, neutro- sophic numbers offer superior flexibility in environments with higher levels of indeterminacy. Together, these tools have broadened the scope of uncertainty modeling across disciplines such as artificial intelligence, economics, and risk management
On Some Types of Pythagorean Fuzzy Labelings
(Library Information Services, COMSATS University, Lahore Campus, 2025) Husnain Ali; Fa23-rmt-013; Dr. Madiha Khalid; LHR TP 9761
With the extensive application of networks in every field of science such as engineering, chemistry, biology, and computer networking, the modeling of complex uncertain systems has become more prominent. Graph theory is one of the efficient mathematical methods of representing such systems in which issues of real life are described with the assistance of vertices and edges. Classical graphs are not satisfactory in models involving vagueness and indecision. Fuzzy graphs and their extensions have been developed to address these issues for their handling. Intuitionistic fuzzy graphs (IFGs) on the basis of both membership and non-membership grades provided a more versatile structure to handle uncertainty. However, the condition that the sum of membership and non-membership cannot be more than one puts a limit to their expressiveness. To solve this, Pythagorean fuzzy graphs (PFGs) have been introduced so that the sum of squares of such degrees can be less than or equal to one, thus giving a broader and more precise representation of uncertainty. In This thesis we solves the issue of converting IFGs to PFGsbydevelopingamathematicalframeworkthat preserves the graph structure but enhances its fuzzy representation capability. By using super edge magic labeling we assign unique la bels to the vertices and edges and sum should be constant. The transformation from IFG to PFGis carried out systematically. Additionally, the research explores the consequences of this change in super edge magic labeling, introducing new information on the labeling structures that can be employed on PFGs. The findings prove that PFGs not only generalize IFGs but also are more flexible and effective in graph-based modeling, particularly in scenarios where greater uncertainty and intricate relationships exist.
Shortest Path Solution of an Intuitionistic Fuzzy Network
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Aleesha; CIIT/SP21-BSM-031/LHR; Dr. Madiha Khalid; LHR TP 9891
This study focuses on solving the shortest path problem in networks where edge weights are represented as Intuitionistic Fuzzy Numbers (IFNs). Intuitionistic fuzzy sets allow the incorporation of both membership and non-membership degrees, providing a more com- prehensive representation of uncertainty compared to traditional fuzzy sets. The Floyd- Warshall algorithm, a well-established method for finding the shortest paths in weighted graphs, is adapted to work with IFNs. The algorithm operates iteratively, leveraging the properties of IFNs and appropriate fuzzy arithmetic to handle uncertainty in edge weights effectively. The proposed approach ensures that the shortest path calculations consider both the degree of certainty and uncertainty, providing a more robust solution for real- world problems involving imprecise or uncertain data. Numerical examples are presented to demonstrate the effectiveness and accuracy of the adapted algorithm, highlighting its po- tential applications in fields such as transportation, logistics, and communication networks.