According to an answer to my askubuntu question I managed to switch from xkb input into iBus one. I have installed via iBus the English, Greek and Japaneese (Anthy) keyboard language.
But when I type in Greek no Greek letters are shown, but I can easily type Japanese via Anthy and English as well.
The iBus setting are as the following screenshot shows:

The command dconf list /org/mate/desktop/peripherals/keyboard/ shows the following result:
numlock-state
Whilst the /etc/default/keyboard has the following settings:
# KEYBOARD CONFIGURATION FILE
# Consult the keyboard(5) manual page.
XKBMODEL="pc105"
XKBLAYOUT="us"
XKBVARIANT=""
XKBOPTIONS=""
BACKSPACE="guess"
Event changing into the following settings has no effect whatsoever:
# KEYBOARD CONFIGURATION FILE
# Consult the keyboard(5) manual page.
XKBMODEL="pc105"
XKBLAYOUT="us,gr"
XKBVARIANT=""
XKBOPTIONS=""
BACKSPACE="guess"
So how I can enable iBus to manage the Greek layout as well? I need iBus because I find it convenient using the Anthy Japanese input instead of the mozc one.