Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

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Fuzzy Relations and Monometrics: Some Correspondences

Authors
Megha Gupta, Balasubramaniam Jayaram
Corresponding Author
Balasubramaniam Jayaram
Available Online 30 August 2021.
DOI
10.2991/asum.k.210827.084How to use a DOI?
Keywords
Betweenness relation, Monometric, Fuzzy relations, Non Strict T-transitivity
Abstract

Fuzzy relations that are not T -transitive have not merited as much scrutiny as their T - transitive counterparts. Recently monometrics on a given betweenness set, or a B-set, has garnered a lot of attention, especially for their role in decision making and penalty based data aggregation. In this work, we show that from non strict T -transitive relations one can obtain both betweenness relations, satisfying various types of transitivities, and monometrics on them. In fact, it can be shown that the natural or canonical betweenness obtained from a given distance function can be seen as being obtained from an appropriate non strict T-transitive similarity relation. Further, a typical practical problem in this context is that of obtaining a monometric on a given B-set. Our investigations show that there exists a one-one correspondence between non strict T - transitive similarity relations and monometrics defined on the given B-set. This study, thus, shows the usefulness of non strict T - transitive fuzzy relations as much as their T - transitive counterparts.

Copyright
© 2021, 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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Volume Title
Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
Series
Atlantis Studies in Uncertainty Modelling
Publication Date
30 August 2021
ISBN
978-94-6239-423-0
ISSN
2589-6644
DOI
10.2991/asum.k.210827.084How to use a DOI?
Copyright
© 2021, 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/).

Cite this article

risenwbib
TY  - CONF
AU  - Megha Gupta
AU  - Balasubramaniam Jayaram
PY  - 2021
DA  - 2021/08/30
TI  - Fuzzy Relations and Monometrics: Some Correspondences
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 624
EP  - 630
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.084
DO  - 10.2991/asum.k.210827.084
ID  - Gupta2021
ER  -