|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||Abstract:||
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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