Authors: | Šešelja, Branimir Tepavčević, Andreja |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Ω-groups in the language of Ω-groupoids | Journal: | Fuzzy Sets and Systems | Volume: | 397 | First page: | 152 | Last page: | 167 | Issue Date: | 15-Oct-2020 | Rank: | M21a | ISSN: | 0165-0114 | DOI: | 10.1016/j.fss.2019.08.007 | Abstract: | 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. |
Keywords: | Group | Lattice-valued groupoid | Ω-algebra | Ω-group | Ω-set | Publisher: | Elsevier | Project: | Development of methods of computation and information processing: theory and applications Provincial Secretariat for Higher Education and Scientific Research AP Vojvodina, grant “Computational intelligence and relational equations in forensics”, Grant No. 142-451-3642/2017-01 |
Show full item record
SCOPUSTM
Citations
3
checked on Sep 15, 2024
Page view(s)
8
checked on Sep 16, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.