Characterizing quasi-metric aggregation functions

ABSTRACT

In this paper, we study those functions that allows us to combine a family of quasi-metrics, defined all of them on the same set, into a single one, which will be called quasi-metric aggregation functions. In particular, we characterize the quasi-metric aggregation functions and, in addition, we discuss a few of their properties. Moreover, a few methods to discard those functions that are useless as quasi-metric aggregation functions are introduced. Throughout the paper, different examples justify and illustrate the results presented. Finally, two possible fields where the developed theory can be useful are exposed.

KEYWORDS:

• Quasi-metric space
• aggregation
• subadditive function
• monotone function
• triangle triplet

Acknowledgments

This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Juan-José Miñana http://orcid.org/0000-0001-9835-0700

Oscar Valero http://orcid.org/0000-0003-4710-1338

Additional information

Funding

The authors acknowledge financial support from Spanish Ministry of Science, Innovation and Universities [grant number PGC2018-095709-B-C21] and AEI/FEDER, UE funds. This work is also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direcció General d'Innovació i Recerca, Govern de les Illes Balears) and by project ROBINS. The latter has received research funding from the EU H2020 framework [grant number GA 779776].

Notes on contributors

Juan-José Miñana

Juan-José Miñana is graduated in Mathematics by the University of Valencia from 2010. Then, in 2015, he obtained a PhD in Mathematics by the Polytechnical University of Valencia. Since September of 2018, he is Associate Professor (tenure track) in the Department of Mathematics and Computer Science at Balearic Islands University. His research interest includes different topics related to both Pure and Applied Mathematics. In particular, his research has focused in Fuzzy Mathematics and its applications to Computer Science, Artificial Intelligence, Engineering and Economics. He has been the author of more than 30 research papers and has contributed as a reviewer in different scientific journals. He is member of the research group MOTIBO of the Balearic Islands University.

Oscar Valero

Oscar Valero Sierra received a BS degree and a Ms degree in Mathematics by the University of Valencia in 2000. Later on, in 2003, he received a Ph.D. in Mathematics by the Polytechnical University of Valencia. He was a visiting researcher at ‘Center for Efficiency-Oriented Languages’ which belongs to the Computer Science Department at National University of Ireland. He is currently an Associate Professor in the Department of Mathematics and Computer Science at Balearic Islands University. So far, he has taught lectures on bachelor's degrees in Engineering, Business Administration, Economics and Mathematics. His research activity focus on Mathematical Models applied to Computer Science, Artificial Intelligence, Engineering and Economics. In this direction, he has published more than 110 papers and he serves as a member of editorial board of 8 journals. A detailed information about his research activity can be viewed at http://www.uib.eu/research/groups/grup/MOTIBO/