Abstract
Entropy is usually used to measure the uncertainty of uncertain random variables. It has been defined by logarithmic entropy with chance theory. However, this logarithmic entropy sometimes fails to measure the uncertainty of some uncertain random variables. In order to solve this problem, this paper proposes two types of entropy for uncertain random variables: sine entropy and partial sine entropy, and studies some of their properties. Some important properties of sine entropy and partial sine entropy, such as translation invariance and positive linearity, are obtained. In addition, the calculation formulas of sine entropy and partial sine entropy of uncertain random variables are given.
Highlights
Liu [8] proposed a concept of logarithmic entropy of uncertain variables
We review some basic concepts of chance theory
A function ξ is called an uncertain random variable if it is from a chance space (Γ, L, M) × (Ω, A, Pr) to the set of real numbers such that {ξ ∈ B} is an event in L × A for any Borel set B of real numbers
Summary
Liu [8] proposed some formulas by uncertainty distribution for calculating variance and moment. Liu [8] proposed a concept of logarithmic entropy of uncertain variables. Liu [19] proposed and studied the basic concepts of chance measure, which is a monotonically increasing set function and satisfies selfduality. Liu [19] put forward some basic concepts, including uncertain random variable, and its chance distribution and digital features, etc. In order to further improve this problem, this paper will propose two new entropies for uncertain random variables, namely sine entropy and partial sine entropy, and discuss their properties.
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