Researchers

Alaa Jony and Shawki Al Rashed

Published in

Al-Baath University Journal, Volume 45, Issue 6, April 2023.

Abstract

In this paper, we present a study of the problem of sending and receiving information on a probability communication network, using some useful tools from commutative algebra and algebraic geometry. Then we transferred the fundamental theory of network coding from the classical case to the general case, i.e. the Fuzzy case, after developing the necessary concepts for this generalization.

Then we set a necessary and sufficient condition for the coding problem to be solvable depending on the nature of the set of polynomials defining the coding problem on a given fuzzy communication network.

Accordingly, we presented some results about the solvability, i.e. the ability to complete the transmission process successfully, and then we found a relationship between the solvability of the encoding problem and the dimension of the space  ) using Grobner Bases, also we define a fuzzy coding and a fuzzy communication network as an application for this study.

Keywords: Network Coding – Fuzzy Set – Fuzzy Graph – Fuzzy Map.

Link to full paper

https://albaath-univ.edu.sy/journal/index.php/BUJB/article/view/2179/2074