Question

Why does the mass change when any object is accelerated at or near to the speed of light?? Does this mass increase or decrease??

Answer 1

The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference.
What actually changes at relativistic speeds is the dynamical law that relates momentum and energy depend with the velocity (which was already written). Let me put it this way: trying to ascribe the modification of the dynamical law to a changing mass is the same as trying to explain non-Euclidean geometry by redefining ππ!

There is a point of view, that under the term "the mass" one must mean "the rest mass".

From that point of view there is obviously no dependence of the (rest) mass on the speed of an object. And, therefore, the mass of an object does not increase when its speed increases.

The correct (from that point of view) way to talk about the phenomenon is to say that with increase of the speed of an object you need more and more energy in order to make it move faster.

Of course there is no fundamental controversy between this point of view and that of many books and articles. But the usage of the concept of "relativistic mass" makes things much more complicated, even if it was introduced in pursuit of simplicity.

Hope it helps!