On the relationship between positive semi-definite matrices and t-norms

Recasens J.

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On the relationship between positive semi-definite matrices and t-norms

机译：On the relationship between positive semi-definite matrices and t-norms

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? 2021 Elsevier B.V.In this work the positive semi-definiteness of symmetric matrices with non-negative entries and positive entries on the diagonal will be analyzed by using the Yager's family of t-norms. It can always be assumed that such an n×n matrix corresponds to a reflexive and symmetric fuzzy relation A on a set of cardinality n and the main result of this paper states that if A is transitive with respect to a specific t-norm Tλ of Yager's family with λ depending on n, then A is positive semi-definite. This constitutes a surprising novel application of t-norms to an a priori unrelated field such as linear algebra. The result will be applied to give alternative proofs of the following two important facts. ? Every min-indistinguishability operator on a finite set has a positive semi-definite matrix. ? Every pseudoultrametric on a finite set is Euclidean. The reciprocal of the main result is not true but some results concerning this issue are studied.

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来源
《Fuzzy sets and systems》 |2022年第5期|26-37|共12页
作者
Recasens J.;
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作者单位

Dept. Tecnologia de l'Arquitectura ETS Arquitectura del Vallès Universitat Politècnica de Catalunya;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
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关键词
Embeddability of metric spaces; Euclidean metric space; Indistinguishability operator; Positive definite matrix; Positive semi-definite matrix; Proximity relation; Tolerance relation; Transitivity; Yager's family of t-norms;

On the relationship between positive semi-definite matrices and t-norms

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