Rotation-invariant t-norms: Where triple rotation and rotation-annihilation meet

Generalizing the notion of a zoom of a t-norm not only allows to extend the triple rotation method and its corresponding decomposition, but also allows to describe the interface between the triple rotation method and the rotation(-annihilation) method. An alternative view on the partition behind the rotation(-annihilation) method is required to make both methods compatible. Besides zooms we also use contour lines and the companion of a t-norm to concisely formulate the results.

[1]  B. Baets,et al.  Orthosymmetrical monotone functions , 2007 .

[2]  Sándor Jenei,et al.  Structure of left-continuous triangular norms with strong induced negations. (III): Construction and decomposition , 2002, Fuzzy Sets Syst..

[3]  Bernard De Baets,et al.  The triple rotation method for constructing t-norms , 2007, Fuzzy Sets Syst..

[4]  Liu Lianzhen,et al.  Involutive monoidal t‐norm based logic and R0 logic , 2004 .

[5]  Bernard De Baets,et al.  A contour view on uninorm properties , 2006, Kybernetika.

[6]  Bernard De Baets,et al.  On the structure of left-continuous t-norms that have a continuous contour line , 2007, Fuzzy Sets Syst..

[7]  Lluis Godo,et al.  Monoidal t-norm based logic: towards a logic for left-continuous t-norms , 2001, Fuzzy Sets Syst..

[8]  Bernard De Baets,et al.  Rotation-invariant t-norms: The rotation invariance property revisited , 2009, Fuzzy Sets Syst..

[9]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[10]  Sándor Jenei,et al.  A note on the ordinal sum theorem and its consequence for the construction of triangular norms , 2002, Fuzzy Sets Syst..

[11]  Li Kaitai,et al.  Involutive monoidal t-norm based logic and R 0 logic , 2004 .

[12]  Radko Mesiar,et al.  Different Types Of Continuity Of Triangular Norms Revisited , 2005 .

[13]  Sándor Jenei,et al.  New family of triangular norms via contrapositive symmetrization of residuated implications , 2000, Fuzzy Sets Syst..

[14]  Jun Li,et al.  A conditionally cancellative left-continuous t-norm is not necessarily continuous , 2006, Fuzzy Sets Syst..

[15]  K. Maes,et al.  Rotation-invariant T-norms , 2007 .

[16]  Franco Montagna,et al.  On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic , 2002, Stud Logica.

[17]  Sándor Jenei,et al.  A characterization theorem on the rotation construction for triangular norms , 2003, Fuzzy Sets Syst..

[18]  Sándor Jenei,et al.  How to construct left-continuous triangular norms--state of the art , 2004, Fuzzy Sets Syst..

[19]  Sándor Jenei,et al.  Structure of left-continuous triangular norms with strong induced negations (II) Rotation-annihilation construction , 2001, J. Appl. Non Class. Logics.

[20]  Sándor Jenei,et al.  Structure of left-continuous triangular norms with strong induced negations (I) Rotation construction , 2000, J. Appl. Non Class. Logics.

[21]  Zhi-Hong Yi,et al.  Generalizations to the constructions of t-norms: Rotation(-annihilation) construction , 2008, Fuzzy Sets Syst..