Abstract
Uncertain measure, which is used to indicate the degree of belief that an uncertain event may occur, is a set function satisfying the normality, duality, and subadditivity axioms. Although the tools of uncertain measure, uncertainty space, and uncertain variable have been well developed and became the foundations of uncertainty theory, there is no study on how to construct the uncertainty space for an uncertain variable, which seriously hinders the applications of uncertainty theory in practice. In this paper, we propose an expert knowledge-based construction approach for uncertainty space with maximum-mean uncertain measure, which takes the maximum and mean operations on confidence function.
Highlights
Uncertainty theory introduced by Liu [1] is a branch of nonadditive measure theory for describing human uncertainty
Uncertainty theory has become a branch of axiomatic mathematics for modeling human uncertainty, and it has been well developed and applied to uncertain programming [2], uncertain statistics [3], uncertain risk analysis [4], uncertain set [5], uncertain logic [6], uncertain inference [7,8], uncertain process [9], uncertain renewal process [10], uncertain calculus [11], uncertain differential equation [12], uncertain finance [13], and so on
The purpose of this paper is to provide a general construction approach for uncertainty space with maximum-mean uncertain measure based on the expert knowledge
Summary
Uncertainty theory introduced by Liu [1] is a branch of nonadditive measure theory for describing human uncertainty. Uncertain measure, which is used to indicate the degree of belief that an uncertain event may occur, was defined in [1] as a set function satisfying the normality, duality, and subadditivity axioms. Uncertain variable is used to represent quantity with uncertainty, which was defined in [1] as a measurable function from uncertainty space to the set of real numbers.
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