Contamination-free measures and algebraic operations

An open concept of rough evolution and an axiomatic approach to granules was also developed in [1] by the present author. Subsequently the concepts were used in the formal framework of rough Y-systems (RYS) for developing on granular correspondences in [2]. These have since been used for a new approach towards comparison of rough algebraic semantics across different semantic domains by way of correspondences that preserve rough evolution and try to avoid contamination. In this research paper, we propose methods and semantics for handling possibly contaminated operations and structured bigness. These would also be of natural interest for relative consistency of one collection of knowledge relative other.