  The aim of this paper is twofold. In the first part, we consider twisted
Rota-Baxter operators on associative algebras that were introduced by Uchino as
a noncommutative analogue of twisted Poisson structures. We construct an
$L_\infty$-algebra whose Maurer-Cartan elements are given by twisted
Rota-Baxter operators. This leads to cohomology associated to a twisted
Rota-Baxter operator. This cohomology can be seen as the Hochschild cohomology
of a certain associative algebra with coefficients in a suitable bimodule. We
study deformations of twisted Rota-Baxter operators by means of the
above-defined cohomology. Application is given to Reynolds operators. In the
second part, we consider NS-algebras of Leroux that are related to twisted
Rota-Baxter operators in the same way dendriform algebras are related to
Rota-Baxter operators. We define cohomology of NS-algebras using multiplicative
operads and study their deformations in terms of the cohomology.
