Final answer:
The statement relates to Borderline Personality Disorder (BPD) due to its reference to shallow, fleeting interpersonal relationships serving dependency needs. This aligns with the characteristics of BPD which includes unstable relationships and intense emotional experiences.
Step-by-step explanation:
The statement 'Interpersonal relationships tend to be shallow and fleeting, serving the dependency needs of the disordered individual' may describe several personality disorders. However, considering the context and specifics of dependency needs, along with shallow and fleeting relationships, a strong case can be made for Borderline Personality Disorder (BPD).
Narcissistic Personality Disorder, on the other hand, is generally marked by an inflated self-image and deep need for admiration, rather than shallow relationships to meet dependency needs. Histrionic Personality Disorder involves excessive emotionality and attention-seeking behavior, which does not directly imply the same kind of dependency needs described.