Applying the Dijkstra Algorithm to Solve a Linear Diophantine Fuzzy Environment

Abstract

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify the shortest path (SP) problem for linear Diophantine fuzzy graphs. Linear Diophantine fuzzy numbers (LDFNs) are used to represent the weights associated with arcs. The main goal of the presented work is to create a solution technique for directed network graphs by introducing linear Diophantine fuzzy (LDF) optimality constraints. The weights of distinct routes are calculated using an improved score function (SF) with the arc values represented by LDFNs. The conventional Dijkstra method is further modified to find the arc weights of the linear Diophantine fuzzy shortest path (LDFSP) and coterminal LDFSP based on these enhanced score functions and optimality requirements. A comparative analysis was carried out with the current approaches demonstrating the benefits of the new algorithm. Finally, to validate the possible use of the proposed technique, a small-sized telecommunication network is presented.

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

“…1 provides a brief overview of the comparison between IFS, PyFS, q-ROFS, and LDFS. LDFS has its unique feature by incorporating the reference parameter and got many real-life applications with the help of different algorithms and operators like Dijkstra algorithm in LDFS environment [36], Einstein aggregation operators for multi-criteria decision-making [37], TOPSIS, VIKOR and Aggregation Operators [38], q-linear Diophantine fuzzy emergency decision support system [39], cosine similarity measures [40]. Also when we consider CPM/PERT got their one results and optimizes the project.…”

Improved Q-Learning Applied to Dynamic Obstacle Avoidance and Path Planning

“…Choosing the appropriate algorithm is of great significance. The Dijkstra algorithm [18] proposed by Dijkstra started scholars' pursuit of path planning algorithms. Currently, with the advent of the intelligent era, a large number of scholars have conducted a variety of research investigations on path planning algorithms and have developed many common intelligent algorithms with strong computing power, such as genetic algorithm [19], particle swarm optimization [20], artificial neural networks [21], reinforcement learning [22] [23] [24] [25] and the ant colony algorithm [26].…”

Experimental Analysis of a Fuzzy Scheme against a Robust Controller for a Proton Exchange Membrane Fuel Cell System

“…Usually, human knowledge is expressed through simple rules and membership functions, which can be symmetric or asymmetric [24,25]. This tool introduced by Zadeh in 1965 [26,27] has been an example of employment in decision making processes [28] and mathematical modelling [29,30]. Examples of experimental tests on a converter had been developed by Ramalu et al [31].…”