Characterizing Positive Definite Matrices with t-norms

DOI

10.2991/eusflat-19.2019.14How to use a DOI?

Keywords

Positive definite matrix Indistinguishability operator Yager's family of t-norms

Abstract

In this work symmetric positive definite matrices with non-negative entries will be characterized by using the Yager's family of t-norms. It can always be assumed that such an n X n matrix corresponds to a reflexive and symmetric fuzzy relation A on a set of cardinality n and then A is positive definite if and only if it is transitive with respect to a specific t-norm T_λ of Yager's family with λ depending on n. The result will be applied to give alternative proofs of the following two facts:
•Every min-indistinguishability operator on a finite set has a positive definite matrix.
•Every ultrametric on a finite set is Euclidean.

Copyright

© 2019, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jordi Recasens
PY  - 2019/08
DA  - 2019/08
TI  - Characterizing Positive Definite Matrices with t-norms
BT  - Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
PB  - Atlantis Press
SP  - 91
EP  - 95
SN  - 2589-6644
UR  - https://doi.org/10.2991/eusflat-19.2019.14
DO  - 10.2991/eusflat-19.2019.14
ID  - Recasens2019/08
ER  -