Name
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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.fss.2019.08.007 | Fuzzy Sets and Systems |
Keywords | DocType | Volume |
Lattice-valued groupoid,Group,Ω-set,Ω-algebra,Ω-group | Journal | 397 |
ISSN | Citations | PageRank |
0165-0114 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Branimir Šešelja | 1 | 170 | 23.33 |
| Andreja Tepavčevic | 2 | 39 | 8.83 |