| 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 |
| 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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