Fuzzy Cognitive Modeling of Psychological Well Being and Social Interaction

Human internal states such as happiness, stress, trust, and perceived social position are inherently imprecise and are better represented as graded cognitive quantities rather than exact numerical measurements. This work develops a fully mathematical framework in which such states are modeled as fuzzy variables evolving within a nonlinear dynamical system. Each state is represented through a membership function taking values in the unit interval, and their mutual influences are described through a weighted interaction matrix defining a cognitive network. The resulting system forms a bounded continuous self mapping on a compact convex set, allowing rigorous analysis of equilibrium existence and stability. A global well being functional is constructed as a defuzzified aggregate of component states, and the decision behavior is linked to this index through a probabilistic choice mechanism. The framework unifies fuzzy set theory, nonlinear dynamics, and decision modeling into a single structure that permits analytical investigation of how changes in social and economic conditions propagate through cognitive interactions to alter collective mental states. The study establishes theoretical foundations for mathematically analyzing vague psychological perceptions and social influences without imposing artificial numerical precision.