Elliptic entropy of uncertain set and its applications. Issue 4 (30th January 2018)

• Record Type: Journal Article
• Authors: Gao, Rong; Ralescu, Dan A.
• Is Part Of: International journal of intelligent systems. Volume 33:Issue 4(2018)
• Page Start: 836
• Page End: 857
• Publication Date: 2018-01-30
• Subjects: entropy -- relative entropy -- uncertain set -- uncertainty theory; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; 006.3
• DOI: 10.1002/int.21970
• Languages: English
• ISSNs: 0884-8173

Abstract

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.