# On some geometric transformation of t-norms.

• Volume: 5, Issue: 1, page 57-67
• ISSN: 1134-5632

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## Abstract

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Given a triangular norm T, its t-reverse T*, introduced by C. Kimberling (Publ. Math. Debrecen 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have T** = T is completely solved. The t-reverses of ordinal sums of t-norms are investigated and a complete description of continuous, self-reverse t-norms is given, leading to a new characterization of the continuous t-norms T such that the function G(x,y) = x + y - T(x,y) is a t-conorm, a problem originally studied by M.J. Frank (Aequationes Math. 19, 194-226, 1979). Finally, some open problems are formulated.

## How to cite

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Klement, Erich Peter, Mesiar, Radko, and Pap, Endre. "On some geometric transformation of t-norms.." Mathware and Soft Computing 5.1 (1998): 57-67. <http://eudml.org/doc/39122>.

@article{Klement1998,
abstract = {Given a triangular norm T, its t-reverse T*, introduced by C. Kimberling (Publ. Math. Debrecen 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have T** = T is completely solved. The t-reverses of ordinal sums of t-norms are investigated and a complete description of continuous, self-reverse t-norms is given, leading to a new characterization of the continuous t-norms T such that the function G(x,y) = x + y - T(x,y) is a t-conorm, a problem originally studied by M.J. Frank (Aequationes Math. 19, 194-226, 1979). Finally, some open problems are formulated.},
author = {Klement, Erich Peter, Mesiar, Radko, Pap, Endre},
journal = {Mathware and Soft Computing},
keywords = {Norma triangular; Espacio normado probabilístico; Espacios métricos; Lógica difusa; triangular norm; t-reverse; invert; ordinal sums; self-reverse t-norms; continuous t-norms; t-conorm},
language = {eng},
number = {1},
pages = {57-67},
title = {On some geometric transformation of t-norms.},
url = {http://eudml.org/doc/39122},
volume = {5},
year = {1998},
}

TY - JOUR
AU - Klement, Erich Peter
AU - Pap, Endre
TI - On some geometric transformation of t-norms.
JO - Mathware and Soft Computing
PY - 1998
VL - 5
IS - 1
SP - 57
EP - 67
AB - Given a triangular norm T, its t-reverse T*, introduced by C. Kimberling (Publ. Math. Debrecen 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have T** = T is completely solved. The t-reverses of ordinal sums of t-norms are investigated and a complete description of continuous, self-reverse t-norms is given, leading to a new characterization of the continuous t-norms T such that the function G(x,y) = x + y - T(x,y) is a t-conorm, a problem originally studied by M.J. Frank (Aequationes Math. 19, 194-226, 1979). Finally, some open problems are formulated.
LA - eng
KW - Norma triangular; Espacio normado probabilístico; Espacios métricos; Lógica difusa; triangular norm; t-reverse; invert; ordinal sums; self-reverse t-norms; continuous t-norms; t-conorm
UR - http://eudml.org/doc/39122
ER -

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