On Isomorphism Theorems for MI-groups (original) (raw)
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
Authors
Michal Holcapek, Michaela Wrublova, Martin Stepnicka
Available Online August 2013.
DOI
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.
Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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 - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13) PB - Atlantis Press SP - 804 EP - 811 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2013.114 DO - 10.2991/eusflat.2013.114 ID - Holcapek2013/08 ER -