Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)

A fuzzy extension of explanatory relations based on mathematical morphology

Authors
Jamal Atif, Isabelle Bloch, Felix Distel, Hudelot Celine
Corresponding Author
Jamal Atif
Available Online August 2013.
DOI
https://doi.org/10.2991/eusflat.2013.41How to use a DOI?
Keywords
Propositional logic with fuzzy models Fuzzy mathematical morphology Explanatory relations Fuzzy abduction
Abstract
In this paper, we build upon previous work defining explanatory relations based on mathematical morphology operators on logical formulas in propositional logics. We propose to extend such relations to the case where the set of models of a formula is fuzzy, as a first step towards morphological fuzzy abduction. The membership degrees may represent degrees of satisfaction of the formula, preferences, vague information for instance related to a partially observed situation, imprecise knowledge, etc. The proposed explanatory relations are based on successive fuzzy erosions of the set of models, conditionally to a theory, while the maximum membership degree in the results remains higher than a threshold. Two explanatory relations are proposed, one based on the erosion of the conjunction of the theory and the formula to be explained, and the other based on the erosion of the theory, while remaining consistent with the formula at least to some degree. Extensions of the rationality postulates introduced by Pino-Perez and Uzcategui are proposed. As in the classical crisp case, we show that the second explanatory relation exhibits stronger properties than the first one.
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Proceedings
8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2013
ISBN
978-90786-77-78-9
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2013.41How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Jamal Atif
AU  - Isabelle Bloch
AU  - Felix Distel
AU  - Hudelot Celine
PY  - 2013/08
DA  - 2013/08
TI  - A fuzzy extension of explanatory relations based on mathematical morphology
BT  - 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 284
EP  - 291
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.41
DO  - https://doi.org/10.2991/eusflat.2013.41
ID  - Atif2013/08
ER  -