Some Research Problems in Uncertainty Theory

TLDR

The paper extends uncertainty theory by introducing a product measure axiom, an operational law for independent uncertain variables, and a concept of entropy for continuous uncertain variables. It proposes a new uncertain calculus based on uncertainty theory and applies it to uncertain differential equations, finance, control, filtering, and dynamical systems. c.

Abstract

In addition to the four axioms of uncertainty theory, this paper presents the flfth axiom called product measure axiom. This paper also gives an operational law of independent uncertain variables and a concept of entropy of continuous uncertain variables. Based on the uncertainty theory, a new uncertain calculus is proposed and applied to uncertain difierential equation, flnance, control, flltering and dynamical systems. Finally, an uncertain inference will be presented. c