  Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial
Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial
Gelfand models for semigroup algebras of some finite semigroups, which include
the symmetric inverse semigroup, the dual symmetric inverse semigroup, the
maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and
the factor power of the symmetric group. Furthermore we extend the Gelfand
model for the semigroup algebras of the symmetric inverse semigroup to a
Gelfand model for the $q$-rook monoid algebra.
