Qualitative Behavior of Bidimensional Rational Fuzzy Difference Equations

This paper aims to extend the research conducted by Yalçınkaya et al. on one-dimensional dynamics, specifically, their work titled “Qualitative behavior of a higher-order fuzzy difference equation.†The purpose of this study is to expand the analysis of fuzzy difference equations into a bidimensional framework. Our research question focuses on understanding how the qualitative behavior of bidimensional fuzzy systems, described by the given fuzzy difference equations, compares to the one-dimensional case. We investigate a system described by the following equations:  ∀i≥0,Pi+1=r1Pi−lr2+r3∠j=0lQi−j, Qi+1=s1Qi−ls2+s3∠j=0lPi−j,where Pi and Qi are sequences of positive fuzzy numbers, while rj and sj for j=1,2,3 denote positive fuzzy numbers. The initial conditions P−j and Q−j,j=0,…,l are fuzzy. To validate our results, we present two illustrative examples demonstrating the effectiveness of the outcomes. Our findings reveal novel insights into the qualitative behavior of bidimensional fuzzy systems, extending the understanding of these systems beyond the one-dimensional case. The results are significant as they provide a deeper understanding of the dynamics of fuzzy systems in a multidimensional context, which has implications for further theoretical research and practical applications in various fields where fuzzy systems are used.MSC2020 Classification:03E72, 39A10, 39A30