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https://open.uns.ac.rs/handle/123456789/20023
Title: | Ω-groups in the language of Ω-groupoids | Authors: | Šešelja Branimir Tepavčević Andreja |
Issue Date: | 2019 | Journal: | Fuzzy Sets and Systems | Abstract: | © 2019 Elsevier B.V. We introduce Ω-groups as particular Ω-groupoids, a structure with a single binary operation and an Ω-equality replacing the classical one. The membership values belong to a complete lattice Ω. We analyze and compare languages in which such structures can be introduced. We prove the equivalence of approaches to Ω-groups as algebras with three operations and those in the language of Ω-groupoids. We also introduce a wider class of Ω-groups, so called weak Ω-groups for which different neutral elements and different inverses of the same member are equal up to the Ω-equality. For all these, quotient structures with respect to cuts of the Ω-equality are classical groups. We present basic features of Ω-groups in the language with one binary operation. As an application, we show that linear equations can be uniquely (up to Ω-equality) solved in these structures. | URI: | https://open.uns.ac.rs/handle/123456789/20023 | ISSN: | 0165-0114 | DOI: | 10.1016/j.fss.2019.08.007 |
Appears in Collections: | PMF Publikacije/Publications |
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