Orders from Uninorms on Bounded Lattices: Some Perspectives

DOI

10.2991/asum.k.210827.085How to use a DOI?

Keywords

Uninorms, T-norms, Bounded Lattice, Posets, Quasi-Projectivity

Abstract

Recently many works have proposed different ways of obtaining orders from associative fuzzy logic operations. While the order ⊑ investigated by Karaçal and Kesicioğlu [10] was modified in [6] to obtain orders on uninorms, this order relation was based on the sub-domains of the arguments. Recently in [9], a property called Quasi-Projectivity (QP) was shown to be important to obtain an order from the relation investigated in [10] and showed that all t-norms, t-conorms and nullnorms satisfy (QP) giving rise to posets, when the underlying domain is [0, 1], while not all classes of uninorms satisfied (QP). Many constructions of uninorms U exist on bounded lattices, which unlike [0, 1], may neither be total nor complete. In this work, we investigate the satisfaction of (QP) for these constructions. Our study shows that interestingly, almost all existing constructions satisfy (QP) and hence give rise to posets. Further, the orders obtained based on ⊑ and ≼ differ majorly, with the ⊑ relation consistently giving rise to richer order-theoretic structures. This study further merits attention since it offers an alternate perspective - that a uninorm U on a lattice (𝕃, ≤) can be made to be seen as a t-norm on the U -poset obtained (𝕃, ⊑U).

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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TY  - CONF
AU  - Vikash Kumar Gupta
AU  - Balasubramaniam Jayaram
PY  - 2021
DA  - 2021/08/30
TI  - Orders from Uninorms on Bounded Lattices: Some Perspectives
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  - 631
EP  - 638
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.085
DO  - 10.2991/asum.k.210827.085
ID  - Gupta2021
ER  -