Description
This monograph develops a unified theoretical framework in which uncertainty is reinterpreted as a structured, dynamic, and geometric object. Moving beyond classical probability theory, where uncertainty is represented by distributions over atomic states, the work begins by identifying the limitations of Shannon entropy and its generalizations (Rényi, Tsallis) in contexts involving ambiguity, partial knowledge, and structural indeterminacy. The theory is extended through Evidence Theory (Dempster–Shafer), where uncertainty is defined over subsets of outcomes via basic probability assignments (BPA). Within this setting, Deng entropy is introduced as a measure that captures both distributional uncertainty and structural imprecision. This entropy serves as a critical bridge, revealing that uncertainty is not only probabilistic but also inherently configurational. Building on this insight, the monograph reinterprets entropy as a functional over configuration space, leading to the definition of a global potential—PTK (Potential of Total Knowledge). This transformation enables the formulation of belief as a field evolving under entropy-derived forces. The configuration space, initially combinatorial, is shown to admit a geometric structure with metrics, curvature, and trajectories, allowing uncertainty to be analyzed as a dynamical system.