TY - GEN
T1 - A fuzzy extension of explanatory relations based on mathematical morphology
AU - Atif, Jamal
AU - Bloch, Isabelle
AU - Distel, Felix
AU - Hudelot, Céline
PY - 2013/12/1
Y1 - 2013/12/1
N2 - 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
AB - 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
KW - Explanatory relations
KW - Fuzzy abduction
KW - Fuzzy mathematical morphology
KW - Propositional logic with fuzzy models
UR - https://www.scopus.com/pages/publications/84891802021
M3 - Conference contribution
AN - SCOPUS:84891802021
SN - 9781629932194
T3 - 8th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2013 - Advances in Intelligent Systems Research
SP - 244
EP - 251
BT - 8th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2013 - Advances in Intelligent Systems Research
T2 - 8th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2013
Y2 - 11 September 2013 through 13 September 2013
ER -