Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms

被引：74

作者：

Klement, EP ^{[1
]}

Mesiar, R

Pap, E

机构：

[1] Johannes Kepler Univ Linz, Dept Algebra Stochast & Knowledge Based Math Syst, A-4040 Linz, Austria

[2] Slovak Univ Technol Bratislava, Dept Math, Fac Civil Engn, SK-81368 Bratislava, Slovakia

[3] SAS, Inst Math, SK-81473 Bratislava, Slovakia

[4] Univ Novi Sad, Inst Math, YU-21000 Novi Sad, Yugoslavia

来源：

FUZZY SETS AND SYSTEMS | 1999年 / 104卷 / 01期

关键词：

triangular norm; fully ordered semigroup; quasi-inverse; pseudo-inverse;

D O I：

10.1016/S0165-0114(98)00252-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Several properties of quasi- and pseudo-inverses of a non-decreasing real function are discussed. Based on a result of Schweizer and Sklar, for a given triangular norm T and non-decreasing function f a construction method leading to a commutative, fully ordered semigroup on the unit interval is given. A similar construction based on the pseudo-inverse implies that the resulting operation will be bounded from above by the minimum, but then the associativity may be violated. Several sufficient conditions for constructing new t-norms from a given one and a non-decreasing function f, based on its quasi-inverses and on its pseudo-inverse, respectively, are discussed, together with illustrative examples. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

引用

页码：3 / 13

页数：11

共 43 条

[1] A note to a construction of t-norms based on pseudo-inverses of monotone functions
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