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Title of article :
On triangular norms and uninorms definable in image Original Research Article
Author/Authors :
Enrico Marchioni، نويسنده , , Franco Montagna، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
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Abstract :
In this paper, we investigate the definability of classes of t-norms and uninorms in the logic image. In particular we provide a complete characterization of definable continuous t-norms, weak nilpotent minimum t-norms, conjunctive uninorms continuous on [0, 1), and idempotent conjunctive uninorms, and give both positive and negative results concerning definability of left-continuous t-norms (and uninorms). We show that the class of definable uninorms is closed under construction methods as annihilation, rotation and rotation–annihilation. Moreover, we prove that every logic based on a definable uninorm is in PSPACE, and that any finitely axiomatizable logic based on a class of definable uninorms is decidable. Finally we show that the Uninorm Mingle Logic (UML) and the Basic Uninorm Logic (BUL) are finitely strongly standard complete w.r.t. the related class of definable left-continuous conjunctive uninorms.
Keywords :
Fuzzy logics , Left-continuous uninorms , Decidability , Complexity , Semialgebraic sets , Left-continuous t-norms
Journal title :
International Journal of Approximate Reasoning
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