Fuzzy Optimization and Decision Making

, Volume 14, Issue 1, pp 57–76

# Some results of moments of uncertain variable through inverse uncertainty distribution

• Yuhong Sheng
• Samarjit Kar
Article

## Abstract

Uncertainty theory is a branch of axiomatic mathematics for modeling belief degrees. This theory provides a new mathematical tool for indeterminacy phenomena. Uncertain variable is a fundamental concept in uncertainty theory and used to represent quantities with uncertainty. There are some important characteristics about uncertain variables. The expected value of uncertain variable is its average value in the sense of uncertain measure and represents the size of uncertain variable. The variance of uncertain variable provides a degree of the spread of the distribution around its expected value. The moments are some other important characteristics of an uncertain variable. In order to describe the moment of uncertain variable, this paper provides a new formula using inverse uncertainty distribution. Several practical examples are provided to calculate the moments using inverse uncertainty distribution. In addition, some new formulas are derived to calculate the central moments of uncertain variables through uncertainty distribution and inverse uncertainty distribution.

## Keywords

Uncertainty theory Uncertain variable Inverse uncertainty distribution Moments

## Notes

### Acknowledgments

This work was supported by National Natural Science Foundation of China Grants Nos. 61273044 and 91224008.

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