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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Order Based on Non-Associative Operations

Authors
Kavit Nanavati, Balasubramaniam Jayaram
Corresponding Author
Balasubramaniam Jayaram
Available Online 30 August 2021.
DOI
10.2991/asum.k.210827.091How to use a DOI?
Keywords
Non-Associative Operations, Posets, Lattices, Copulas, Fuzzy Implications
Abstract

Recently there have been many works studying orders obtained from fuzzy logic connectives, using the relation proposed in [12]. However, almost all of these works have dealt only with associative operations. In this work, we investigate the conditions under which the above relation leads to a partial order even when the operation is non-associative, i.e., in the setting of a groupoid instead of a semigroup. We begin by presenting the necessary and sufficient conditions towards the same. Following this we study the major non-associative aggregation operations, viz., semi-copulas, fuzzy implications, overlapping and grouping functions. Our investigations show that even appropriate non-associative functions can lead to interesting order-theoretic structures on the underlying set.

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.210827.091How 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  - Kavit Nanavati
AU  - Balasubramaniam Jayaram
PY  - 2021
DA  - 2021/08/30
TI  - Order Based on Non-Associative Operations
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  - 675
EP  - 681
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.091
DO  - 10.2991/asum.k.210827.091
ID  - Nanavati2021
ER  -