Rough Randomness and its Application

A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable artificial intelligence and machine learning). In this research, new concepts of rough randomness that are neither stochastic nor based on properties of strings are introduced by the present author. Her concepts are intended to capture a wide variety of rough processes (applicable to both static and dynamic data), construct related models, and explore the validity of other machine learning algorithms. The last mentioned is restricted to soft/hard clustering algorithms in this paper. Two new computationally efficient algebraically-justified algorithms for soft and hard cluster validation that involve rough random functions are additionally proposed in this research. A class of rough random functions termed large-minded reasoners have a central role in these.