The correct answer is A. Increases with increase in velocity with respect to an observer.
According to special relativity, the mass of a particle increases with increase in velocity with respect to an observer. This is because the faster a particle moves, the more energy it has, and the more energy it has, the more mass it has. This is known as the mass-energy equivalence, which is expressed by the equation $E = mc^2$.
Option B is incorrect because the mass of a particle does not decrease with increase in velocity. Option C is incorrect because the mass of a particle does not decrease with decrease in velocity. Option D is incorrect because the mass of a particle is not independent of its velocity.