Specifying the question more clearly would spoil the point. Simply, theoretically, can you create a world by imagining it? Even though it may consist of elements (such as yourself) located in this world, that doesn't have to negate the possibility.
Fitology
Writers of all kinds (poets, screenwriters, novelists, etc) do this for a living.
The idea that thoughts (imagined events) can become 'physical' is a staple premise for science-fiction stories, and also features strongly in the 'fantasy' category of fiction.
The people involved in the creation of movies are often very motivated by the notion that they are making an imaginary world 'come alive'.
Anonymous
The perceived world would only exist in the individuals mind, therefore it would exist, but since we are limited creatures and can't actually create something tangible, I would question the sanity of the person. Also the definition of "world" would need to be established.
Nickname
Mental Health is an interesting category for the questions. Good job Yahoo.
?
Yes. Only if you're considered crazy. People do it often when writing books though.
Anonymous
It can be done in lucid dreaming, and therefore by people who are highly suggestible, and knowledgeable about autosuggestion / self hypnosis.
View my comprehensive previous answer about autosuggestion / self hypnosis at http://au.answers.yahoo.com/question/index?qid=20131225013553AALfDFw and my answer about lucid dreaming at http://au.answers.yahoo.com/question/index?qid=20110919231009AA7QY0R
Much would depend on your inherent abilities, and application, but either or both may be worth trying.