Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)

On Isomorphism Theorems for MI-groups

Authors
Michal Holcapek, Michaela Wrublova, Martin Stepnicka
Corresponding Author
Michal Holcapek
Available Online August 2013.
DOI
https://doi.org/10.2991/eusflat.2013.114How to use a DOI?
Keywords
Many identities groups Fuzzy numbers Isomorphism theorems
Abstract
The theory of MI-algebras (``Many Identities''-algebras) has been introduced by M. Holcapek and M. Stepnicka recently. These structures motivated by an algebraic formalizations of distinct arithmetics of fuzzy numbers, generalize the standard structures (monoids, groups, fields etc.) by employing a whole set of identity-like elements called pseudoidentitites. This leads to natural questions which properties of classical algebraic structures related to arithmetics of crisp numbers are preserved also in the case of MI-structures. This paper focuses on MI-groups, particularly on the properties of their homomorphisms. We show that three crucial theorems of isomorphism that are valid in the classical case, are under some conditions also valid in the theory of MI-groups.
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Proceedings
8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2013
ISBN
978-90786-77-78-9
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2013.114How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Michal Holcapek
AU  - Michaela Wrublova
AU  - Martin Stepnicka
PY  - 2013/08
DA  - 2013/08
TI  - On Isomorphism Theorems for MI-groups
BT  - 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.114
DO  - https://doi.org/10.2991/eusflat.2013.114
ID  - Holcapek2013/08
ER  -