Journal of Statistical Theory and Applications

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Volume 17, Issue 4, December 2018, Pages 627 - 635

Interval-valued uncertainty based on entropy and Dempster–Shafer theory

Authors
F. Khalaj1, E. Pasha2, *, R. Tavakkoli-Moghaddam3, 4, M. Khalaj5
1Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
3School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
4LCFC, Arts et Métier Paris Tech, Metz, France
5Department of Industrial Engineering, Robat Karim Branch, Islamic Azad University, Tehran, Iran
*

Corresponding author. Emails: pashaeinollah@yahoo.com; pasha@khu.ac.ir

Received 2 August 2017, Accepted 20 November 2017, Available Online 31 December 2018.
DOI
10.2991/jsta.2018.17.4.5How to use a DOI?
Keywords
Epistemic uncertainty; Aleatory uncertainty; Shannon entropy; Dempster–Shafer theory; Upper and lower bounds
Abstract

This paper presents a new structure as a simple method at two uncertainties (i.e., aleatory and epistemic) that result from variabilities inherent in nature and a lack of knowledge. Aleatory and epistemic uncertainties use the concept of the entropy and Dempster–Shafer (D–S) theory, respectively. Accordingly, we propose the generalized Shannon entropy in the D–S theory as a measure of uncertainty. This theory has been originated in the work of Dempster on the use of probabilities with upper and lower bounds. We describe the framework of our approach to assess upper and lower uncertainty bounds for each state of a system. In this process, the uncertainty bound is calculated with the generalized Shannon entropy in the D–S theory in different states of these systems. The probabilities of each state are interval values. In the current study, the effect of epistemic uncertainty is considered between events with respect to the non-probabilistic method (e.g., D–S theory) and the aleatory uncertainty is evaluated by using an entropy index over probability distributions through interval-valued bounds. Therefore, identification of total uncertainties shows the efficiency of uncertainty quantification.

Copyright
© 2018 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Statistical Theory and Applications
Volume-Issue
17 - 4
Pages
627 - 635
Publication Date
2018/12/31
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.2018.17.4.5How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - F. Khalaj
AU  - E. Pasha
AU  - R. Tavakkoli-Moghaddam
AU  - M. Khalaj
PY  - 2018
DA  - 2018/12/31
TI  - Interval-Valued Uncertainty Based on Entropy and Dempster–Shafer Theory
JO  - Journal of Statistical Theory and Applications
SP  - 627
EP  - 635
VL  - 17
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.4.5
DO  - 10.2991/jsta.2018.17.4.5
ID  - Khalaj2018
ER  -