# On some geometric transformation of t-norms.

Erich Peter Klement; Radko Mesiar; Endre Pap

Mathware and Soft Computing (1998)

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

## Access Full Article

top## Abstract

top## How to cite

topKlement, 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 - Mesiar, Radko

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 -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.