Ungerer & Schmid (1996) use the term vagueness with reference to the transition zone consituting the boundary of an entity in a part-whole perspective. That is, vagueness is when the boundary between one part of a gestalt and another part of the same gestalt is gradual or otherwise not clear cut.
For instance, it is difficult to tell exactly where the foot of a mountain begins and ends and establish the boundaries between it and the mountain on the one hand and the valley on the other hand. Another case is a human knee inasmuch as it is difficult to set a clear dividing line between it and the thigh on the one hand and the shin on the other hand.
Vagueness should not be mistaken for fuzziness. Fuzziness applies to the boundary between one category and another, while vagueness applies to the boundary between one entity and another both of which are parts of the same whole.
- Ungerer, Friedrich & Hans-Jörg Schmid (1996). An Introduction to Cognitive Linguistics. London: Longman.