### AIMS Mathematics

2021, Issue 7: 7367-7385. doi: 10.3934/math.2021432
Research article

# Intersectional soft gamma ideals of ordered gamma semigroups

• Received: 23 December 2020 Accepted: 25 April 2021 Published: 30 April 2021
• MSC : 08Axx, 08A72, 16Wxx

• In contemporary mathematics, parameterization tool like soft set theory precisely tackle complex problems of economics and engineering. In this paper, we demonstrate a novel approach of soft set theory i.e., intersectional soft (int-soft) sets of an ordered $\Gamma$ -semigroup $S$ and develop int-soft left (resp. right) $\Gamma$-ideals of $S.$ Various classes like $\Gamma$-regular, left $\Gamma$-simple, right $\Gamma$-simple and some semilattices of an ordered $\Gamma$-semigroup $S$ are characterize through int-soft left (resp. right) $\Gamma$-ideals of $S.$ Particularly, a $\Gamma$-regular ordered $\Gamma$-semigroup $S$ is a left $\Gamma$-simple if and only if every int-soft left $\Gamma$-ideal $f_{A}$ of $S$ is a constant function. Also, $S$ is a semilattice of left (resp. right) $\Gamma$-simple $\Gamma$-semigroup if and only if for every int-soft left (resp. right) $\Gamma$-ideal $f_{A}$ of $S,$ $f_{A}\left(a\right) = f_{A}\left(a\alpha a\right)$ and $f_{A}\left(a\alpha b\right) = f_{A}\left(b\alpha a\right)$ for all $a, b\in S$ and $\alpha \in \Gamma$ hold.

Citation: Faiz Muhammad Khan, Tian-Chuan Sun, Asghar Khan, Muhammad Junaid, Anwarud Din. Intersectional soft gamma ideals of ordered gamma semigroups[J]. AIMS Mathematics, 2021, 6(7): 7367-7385. doi: 10.3934/math.2021432

### Related Papers:

• In contemporary mathematics, parameterization tool like soft set theory precisely tackle complex problems of economics and engineering. In this paper, we demonstrate a novel approach of soft set theory i.e., intersectional soft (int-soft) sets of an ordered $\Gamma$ -semigroup $S$ and develop int-soft left (resp. right) $\Gamma$-ideals of $S.$ Various classes like $\Gamma$-regular, left $\Gamma$-simple, right $\Gamma$-simple and some semilattices of an ordered $\Gamma$-semigroup $S$ are characterize through int-soft left (resp. right) $\Gamma$-ideals of $S.$ Particularly, a $\Gamma$-regular ordered $\Gamma$-semigroup $S$ is a left $\Gamma$-simple if and only if every int-soft left $\Gamma$-ideal $f_{A}$ of $S$ is a constant function. Also, $S$ is a semilattice of left (resp. right) $\Gamma$-simple $\Gamma$-semigroup if and only if for every int-soft left (resp. right) $\Gamma$-ideal $f_{A}$ of $S,$ $f_{A}\left(a\right) = f_{A}\left(a\alpha a\right)$ and $f_{A}\left(a\alpha b\right) = f_{A}\left(b\alpha a\right)$ for all $a, b\in S$ and $\alpha \in \Gamma$ hold.

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