Turkey was founded on a former Roman territory, approximately one thousand years ago. Very often, they called their state, their territory and even themselves “Roman” (Rum, in Turkish): Roman Saltanate, Rum Seljuk, Rum Province…
Today, only southeastern corner of Turkey is middle eastern. The rest is rather eastern European (Balkan, in particular). Turkish people (culture, traditions, habits) are much like Greeks, Romanians, Serbs, Bosnians, Albanians and Macedonians.
Some people think that Turkey was a middle eastern country and after the westernization revolutions it became different. This is not true. It was always different. It was a Balkan country, in negative or positive aspect, and still is.
And interesting that today the most difficult part in integrating to the rest of country is the southeastern part of Turkey: PKK terrorism, tribal structure, feudal institutions, poverty etc…