TY - JOUR
TI - Hypersemigroups and Fuzzy Hypersemigroups
PY - 2017/11/02
Y2 - 2024/10/13
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 10
IS - 5
LA - en
UR - https://www.ejpam.com/index.php/ejpam/article/view/3049
SP - 929-945
AB - The aim is to show that the theory of hypersemigroups and the theory of fuzzy hypersemigroups are parallel to each other, in the following sense: An hypersemigroup$H$ is intra-regular, for example, if and only if $A\cap B\subseteq B*A$ for every right ideal $A$ and every left ideal $B$ of $H$. And an hypersemigroup$H$ is intra-regular if and only if $f\wedge g\preceq g\circ f$ for every fuzzy right ideal $f$ and every fuzzy left ideal $g$ of $H$. An hypersemigroup$H$ is left quasi-regular if and only if $A\cap B\subseteq A*B$ for every ideal $A$ and every nonempty subset $B$ of $H$. And an hypersemigroup$H$ is left quasi-regular if and only if $f\wedge g\preceq f\circ g$ for every fuzzy ideal $f$ and every fuzzy subset $g$ of $H$.
ER -