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Min-max inference for Possibilistic Rule-Based System

Abstract : In this paper, we explore the min-max inference mechanism of any rule-based system of n if-then possibilistic rules. We establish an additive formula for the output possibility distribution obtained by the inference. From this result, we deduce the corresponding possibility and necessity measures. Moreover, we give necessary and sufficient conditions for the normalization of the output possibility distribution. As application of our results, we tackle the case of a cascade of two if-then possibilistic rules sets and establish an input-output relation between the two min-max equation systems. Finally, we associate to the cascade construction an explicit min-max neural network.
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Submitted on : Tuesday, April 19, 2022 - 5:45:13 PM
Last modification on : Saturday, April 23, 2022 - 3:29:52 AM


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Ismaïl Baaj, Jean-Philippe Poli, Wassila Ouerdane, Nicolas Maudet. Min-max inference for Possibilistic Rule-Based System. 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Jul 2021, Luxembourg, Luxembourg. pp.9494506, ⟨10.1109/FUZZ45933.2021.9494506⟩. ⟨hal-03408909⟩



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