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Elliptic entropy of uncertain set and its applications
Author(s) -
Gao Rong,
Ralescu Dan A.
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21970
Subject(s) - joint entropy , entropy (arrow of time) , mathematics , logarithm , transfer entropy , information diagram , maximum entropy probability distribution , joint quantum entropy , mathematical optimization , principle of maximum entropy , maximum entropy thermodynamics , mathematical analysis , statistics , physics , quantum mechanics
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.