On Generalized Mulholland Inequality and Dominance on Nilpotent Triangular Norms

被引：0

作者：

Petrik, Milan ^{[1
,2
]}

机构：

[1] Czech Univ Life Sci, Fac Engn, Dept Math, Prague, Czech Republic

[2] Acad Sci Czech Republ, Inst Comp Sci, Prague, Czech Republic

来源：

2017 JOINT 17TH WORLD CONGRESS OF INTERNATIONAL FUZZY SYSTEMS ASSOCIATION AND 9TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (IFSA-SCIS) | 2017年

关键词：

DOMINATION; FAMILIES;

D O I：

暂无

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The paper is focused on the generalized Mulholland inequality and its connection with the dominance relation defined on the set of continuous Archimedean triangular norms. A counter-example is provided showing that the set of the solutions of the generalized Mulholland inequality is not closed with respect to compositions and that the dominance relation is not transitive on the set of nilpotent triangular norms.

引用

页数：6

共 50 条

[1] Dominance on continuous Archimedean triangular norms and generalized Mulholland inequality
Petrik, Milan
[J]. FUZZY SETS AND SYSTEMS, 2021, 403 : 88 - 100
[2] Dominance on strict triangular norms and Mulholland inequality
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[J]. FUZZY SETS AND SYSTEMS, 2018, 335 : 3 - 17
[3] On Mulholland Inequality and Dominance of Strict Triangular Norms
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[J]. AGGREGATION FUNCTIONS IN THEORY AND IN PRACTISE, 2013, 228 : 187 - 195
[4] A note on a nilpotent lower bound of nilpotent triangular norms
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[J]. FUZZY SETS AND SYSTEMS, 1999, 104 (01) : 27 - 34
[5] Convex combinations of nilpotent triangular norms
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Sarkoci, Peter
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 350 (01) : 271 - 275
[6] Dominance is not transitive on continuous triangular norms
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[J]. Aequationes mathematicae, 2008, 75 : 201 - 207
[7] Dominance is not transitive on continuous triangular norms
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[J]. AEQUATIONES MATHEMATICAE, 2008, 75 (03) : 201 - 207
[8] A generalization of the Mulholland inequality for continuous Archimedean t-norms
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[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (02) : 607 - 614
[9] Distributive equations of implications based on nilpotent triangular norms
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[J]. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2010, 51 (08) : 984 - 992
[10] A note on a nilpotent lower bound of nilpotent triangular norms (vol 104, pg 27, 1999)
Mesiar, R
[J]. FUZZY SETS AND SYSTEMS, 1999, 104 (01) : 137 - 137

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