Powers of indistinguishability operators

The application of a t-norm more than one time to the same object can be seen as the modelization of a semantic reinforcement of it. From a mathematical viewpoint, this operation can be seen as powers. Depending on the properties the t-norm fulfills several interesting properties emerge. This work will study what is the effect of the application of powers to indistinguishability operators, sets of extensionals, upper and lower approximations. It will be proved that there is a tight relation between the powers of an indistinguishability and their respective sets of extensionals, upper and lower approximations, and how this can be interpreted from a semantic point of view.