Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: Ω-Algebras
Journal: Proceedings - 2015 IEEE Symposium Series on Computational Intelligence, SSCI 2015
First page: 971
Last page: 975
Conference: IEEE Symposium Series on Computational Intelligence, SSCI 2015; Cape Town; South Africa; 8 December 2015 through 10 December 2015
Issue Date: 1-Jan-2015
Rank: M33
ISBN: 978-147997560-0
DOI: 10.1109/SSCI.2015.141
In the framework of Omega-sets, where Omega is a complete lattice, we generalize the notion of an (universal) algebra, and we investigate its basic properties. Our techniques belong to the theory of lattice-valued (fuzzy) structures and we use cut-sets. An Omega-Algebra is equipped with an Omega-valued equality instead of the classical one. We investigate identities and their satisfiability by these new structures. We prove that a set of identities holds on an Omega-Algebra if and only if the cut-sub algebras over the corresponding cut-congruences of the Omega-valued equality satisfy the same identities in the classical setting.
Publisher: IEEE
Project: Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”

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