Uncertain stochastic hybrid zero-sum games based on forward uncertain difference equations and backward stochastic difference equations.

We investigate the interplay between forward uncertain difference equations and backward stochastic difference equations, which belong to distinct mathematical frameworks: uncertainty theory and probability theory, respectively. By establishing the connections between uncertain expectation, probabilistic expectation, and chance expectation, we develop the chance theory framework for analyzing uncertain stochastic hybrid zero-sum games constrained by both forward uncertain difference equations and backward stochastic difference equations. Through an equivalent transformation, we convert these games into deterministic difference equation solving problems. By backward-solving the difference equations and applying mathematical induction, analytical expressions for the equilibrium solutions of two types of uncertain stochastic hybrid zero-sum games are obtained. Furthermore, we explore solution methods for zero-sum games with different operational orders of uncertain and probabilistic expectations and highlight the fundamental differences through numerical examples. • Present uncertain stochastic hybrid zero-sum games of forward and backward systems. • Chance theory framework aids analysis of uncertain stochastic hybrid zero-sum games. • Transforms these games into deterministic difference equation solving problems. • Explores solution methods for games with different expectation operational orders. • Provides numerical examples to illustrate effectiveness of solution methods. [ABSTRACT FROM AUTHOR]