Department of Mathematics

Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21

Browse

Author: search.filters.author.Dr. Madiha KhalidSubject: search.filters.subject.Mathematics

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    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)
  • No Thumbnail Available
    Item
    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
  • No Thumbnail Available
    Item
    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.