Qualitative Analysis of A Third-order Fuzzy Riccati Difference Equation

Abstract In this article, the well-posedness of a generalized discrete-time Riccati model with a fuzzy environment is studied. Initially, relying on the theory of fuzzy sets and the arithmetic operations for fuzzy numbers, the generalized discrete-time Riccati model with a fuzzy environment is reformulated into the common difference equations, incorporating parameters with a value scope confined between 0 and 1. Secondly, the proof of the existence and uniqueness of solutions for the common difference equations is accomplished using a blend of iterative strategies, inductive proofs, and inequality manipulations. At the same time, the stability of the equilibrium solution of p + q + r = 1 in a special case is discussed according to the linearized equation theory. Thus, the well-posedness of the generalized discrete-time Riccati model with a fuzzy environment is proven.