Employing the Bellman-Ford Algorithm with Score Functions to Address the Linear Diophantine Fuzzy Shortest Path Problem in Network Analysis
Vidhya Kannan, Saraswathi Appasamy · Mathematical Modelling and Engineering Problems · 2023
The realms of Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFS), and qrung Orthopair Fuzzy Sets (q-ROFSs) have found extensive applications across various disciplines, notably in resolving real-world problems.However, limitations concerning membership and non-membership grades pose challenges to these theories.Efforts to mitigate these constraints have led to the introduction of a new concept, the Linear Diophantine Fuzzy Set (LDFS), with reference parameters.This study advances the shortest path (SP) problem for Linear Diophantine Fuzzy graphs.An innovative method for constructing direct network graphs within a Linear Diophantine Fuzzy (LDF) context is proposed.Distances or costs between nodes are encapsulated by Linear Diophantine Fuzzy numbers.The principal contribution of this investigation lies in proposing a novel approach to solving the Linear Fuzzy Diophantine Fuzzy shortest path problem using the Bellman-Ford algorithm for optimal solution attainment.Usage of the score function enables the comparison and identification of the minimum arc value between nodes.The proposed algorithm's validity is demonstrated through a numerical example, and a comparison with existing methodologies underscores the benefits of the proposed algorithm.