Uncertainty Theory

This book shows applications of uncertainty theory to scheduling, logistics, data mining, control, and finance. Something is called random if its frequency of occurrence is known. Otherwise, it is called uncertain. The outcome of tossing a coin is an example of randomness since the frequency that the coin will come up heads is known. The outcome of a falling cake is an example of uncertainty since the frequency that the cake will land butter-side down is unknown. In order to rationally deal with those phenomena, there exist two mathematical systems, one is probability theory and the other is uncertainty theory. Probability theory is a branch of mathematics concerned with the analysis of random phenomena, while uncertainty theory is a branch of mathematics concerned with the analysis of uncertain phenomena. In order to use them to handle some quantity (e.g., stock price) in practice, the first action is to produce a distribution function representing the possibility that the quantity falls into the left side of the current point. If you believe the distribution function is close enough to the future frequency, then you should use probability theory. Otherwise, you have to use uncertainty theory. Numerous empirical studies show that the real world is far from frequency stability. This fact makes the distribution function obtained in practice usually deviate from the future frequency even when numerous observed data are available, and consequently provides a motivation to learn and use uncertainty theory. This is an introductory textbook on uncertainty theory, uncertain statistics, uncertain programming, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation.