Department of Mathematics

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

Browse

Subject: search.filters.subject.Network

Search Results

Now showing 1 - 2 of 2
  • 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
    Network Analysis Using Graph Indices
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Shamsa Liaqat (CIIT/FA-BSM-010/LHR), Mahnoor (CIIT/FA20-BSM-043/LHR); Dr. Hani Shaker; LHR TP 9917
    In the digital age, social networking platforms like Twitter, LinkedIn, and Facebook have significantly influenced how individuals interact and form communities. These platforms, along with transportation networks, play crucial roles in shaping social dynamics and fa- cilitating physical mobility. This thesis employs graph theory to analyze these networks, focusing on the complexities of their interactions using Graph Indices, a mathematical framework that enhances the precision of network analysis. Graph theory provides a robust foundation for understanding the structure and flow of information within networks. This study specifically utilizes concepts such as betweenness centrality and the beta index to an- alyze network properties. Betweenness centrality identifies key influencers by measuring how often a node lies on paths between other nodes, while the beta index assesses network complexity by calculating the ratio of edges to vertices. The research encompasses a de- tailed examination of subgraphs, which reveal clusters or communities within the network, providing insights into user behavior and network dynamics. This analysis is applied to various social networks and transportation systems, demonstrating how graph indices can be used to optimize and enhance network structures. By integrating Graph Indices into graph theory, this study offers a more versatile framework for capturing social interactions’ complexities. The findings underscore the importance of mathematical tools in developing strategies for managing and leveraging social networks, leading to improved efficiency and robustness of network systems. This research not only advances theoretical understand- ing but also provides practical solutions for network analysis, paving the way for future applications in the field.