Possibility transformation of the sum of two symmetric unimodal independent/comonotone random variables

DOI

10.2991/eusflat.2013.93How to use a DOI?

Keywords

Possibility theory uncertainty propagation maximum specificity principle independence comonotonicity

Abstract

The paper extends author’s previous works on a proba-bility/possibility transformation based on a maximum specificity principle to the case of the sum of two iden-tical unimodal symmetric random variables. This trans-formation requires the knowledge of the dependency relationship between the two added variables. In fact, the comonotone case is closely related to the Zadeh’s extension principle. It often leads to the worst case in terms of specificity of the corresponding possibility dis-tribution, but it may arise that the independent case is worse than the comonotone case, e.g. for symmetric Pa-reto probability distributions. When no knowledge about the dependence is available, a least specific pos-sibility distribution can be obtained from Fréchet bounds.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Gilles Mauris
PY  - 2013/08
DA  - 2013/08
TI  - Possibility transformation of the sum of two symmetric unimodal independent/comonotone random variables
BT  - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 653
EP  - 659
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.93
DO  - 10.2991/eusflat.2013.93
ID  - Mauris2013/08
ER  -