# Elliptic entropy of uncertain set and its applications

Elliptic entropy of uncertain set and its applications Entropy is commonly used as a way to measure the uncertainty of random variables. In uncertain set theory, a concept of entropy for uncertain sets has been defined by using logarithm. However, such an entropy fails to measure the uncertain degree of some uncertain sets. This paper aims at proposing a concept of elliptic entropy for uncertain sets and investigating its properties such as translation invariance and positive linearity. It also provides some formulas for calculating the elliptic entropy via inverse membership functions. Additionally, elliptic relative entropy for uncertain sets is presented as a measure of the difference between two membership functions, and some applications are considered in portfolio selection and clustering. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Intelligent Systems Wiley

# Elliptic entropy of uncertain set and its applications

, Volume 33 (4) – Jan 1, 2018
22 pages

/lp/wiley/elliptic-entropy-of-uncertain-set-and-its-applications-xQSXZMpXnz
Publisher
Wiley Subscription Services, Inc., A Wiley Company
ISSN
0884-8173
eISSN
1098-111X
D.O.I.
10.1002/int.21970
Publisher site
See Article on Publisher Site

### Abstract

Entropy is commonly used as a way to measure the uncertainty of random variables. In uncertain set theory, a concept of entropy for uncertain sets has been defined by using logarithm. However, such an entropy fails to measure the uncertain degree of some uncertain sets. This paper aims at proposing a concept of elliptic entropy for uncertain sets and investigating its properties such as translation invariance and positive linearity. It also provides some formulas for calculating the elliptic entropy via inverse membership functions. Additionally, elliptic relative entropy for uncertain sets is presented as a measure of the difference between two membership functions, and some applications are considered in portfolio selection and clustering.

### Journal

International Journal of Intelligent SystemsWiley

Published: Jan 1, 2018

Keywords: ; ; ;

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