Defining the standard Boolean operations on fuzzy Booleans with the compositional rule of inference (CRI) or Zadeh's extension principle gives counter-intuitive results. We introduce and motivate a slight adaptation of the CRI, which only effects the results for non-normal fuzzy sets. It is shown that the adapted CRI gives the expected results for the standard Boolean operations on fuzzy Booleans. As a second application, we show that the adapted CRI enables a don't-care value in approximate reasoning. From the close connection between the CRI and Zadeh's extension principle, we derive an adaptation of the extension principle, which, like the modified CRI, also gives the expected Boolean operations on fuzzy Booleans.
|Title of host publication||Theoretical Advances and Applications of Fuzzy Logic and Soft Computing|
|Place of Publication||Berlin Heidelberg, Germany|
|Number of pages||8|
|Publication status||Published - 2007|
|Name||Advances in Soft Computing|
- SE-SC: Soft Computing applied to Software Engineering