On the difference between traditional and deductive fuzzy logic

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Libor Běhounek
Title: On the difference between traditional and deductive fuzzy logic
Journal: Fuzzy Sets and Systems
Volume 159
Number 10
Pages: 1153-1164
Year: 2008
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Author's comment

The paper delimits the area of logic-based fuzzy mathematics more narrowly than an earlier paper From fuzzy logic to fuzzy mathematics: a methodological manifesto, which (following the optimism of Hájek's 1998 monograph) assumed that formal fuzzy logic can give foundations to all fuzzy mathematics. However, it turned out that traditional fuzzy mathematics actually deals with too many different phenomena and is in fact composed of several completely different parts. The field in which the logic-based approach is most fruitful is marked by a clear interpretation of membership degrees as degrees of truth (preserved under inference), while other areas of fuzzy mathematics work with a mixture of other notions of `degrees' (often not clarified enough). Naturally, logic-based methods apply less straightforwardly to such fields, even though formal fuzzy logic can sometimes help there as well. The paper therefore presents rather a more precise delimitation of the area of research than a retreat from the foundational program. -- LBehounek 16:35, 2 September 2008 (CEST)