Rough semigroups and rough fuzzy semigroups based on fuzzy ideals

Qiumei Wang, and Jianming Zhan. "Rough semigroups and rough fuzzy semigroups based on fuzzy ideals." Open Mathematics 14.1 (2016): 1114-1121. <http://eudml.org/doc/288075>.

@article{QiumeiWang2016,
abstract = {In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.},
author = {Qiumei Wang, Jianming Zhan},
journal = {Open Mathematics},
keywords = {Fuzzy ideal; t-level set; Rough semigroup; Rough fuzzy semigroup; Rough (prime) ideal; Rough fuzzy (prime) ideal; fuzzy ideal; $t$-level set; rough semigroup; rough fuzzy semigroup; rough (prime) ideal; rough fuzzy (prime) ideal},
language = {eng},
number = {1},
pages = {1114-1121},
title = {Rough semigroups and rough fuzzy semigroups based on fuzzy ideals},
url = {http://eudml.org/doc/288075},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Qiumei Wang
AU - Jianming Zhan
TI - Rough semigroups and rough fuzzy semigroups based on fuzzy ideals
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 1114
EP - 1121
AB - In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.
LA - eng
KW - Fuzzy ideal; t-level set; Rough semigroup; Rough fuzzy semigroup; Rough (prime) ideal; Rough fuzzy (prime) ideal; fuzzy ideal; $t$-level set; rough semigroup; rough fuzzy semigroup; rough (prime) ideal; rough fuzzy (prime) ideal
UR - http://eudml.org/doc/288075
ER -