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Double-linear fuzzy interpolation method

Abstract : In this paper, we present an original fuzzy interpolation method. In contrast to existing approaches, our method is able to always construct an interpolated fuzzy interval without a need of a special step dedicated to the ''standardization'' of non-viable solutions, which fractures the sense of the interpolation. In fact, these ''standardization'' steps imply that, for instance, a point obtained from the interpolation of the upper limit (right side) of the fuzzy sets, is used to build the lower limit (left side) of the interpolated conclusion, breaking the underlying hypothesis of (linear) graduality. To achieve the direct interpolation, our method is based on the deviation of the observation from the expected linearly interpolated solution and constrains of the constructed solution between extreme cases. We illustrate and discuss the behavior of our method by comparison to other well-known fuzzy interpolation methods.
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Marcin Detyniecki, Christophe Marsala, Maria Rifqi. Double-linear fuzzy interpolation method. IEEE International Conference on Fuzzy Systems FUZZIEEE'2011, Jun 2011, Taipei, Taiwan. pp.455-462, ⟨10.1109/FUZZY.2011.6007693⟩. ⟨hal-00687670⟩