Using generalised Łukasiewicz’s t-norm to represent and improve fuzzy rough approximations

Triangular norms are a generalisation of the classical two-valued conjunction. They were originally introduced for definition of the probabilistic (statistical) metric spaces as a generalisation of the classical triangle inequality for ordinary metric spaces. The next investigations were related with axiomatic of these norms. In this paper, a new t-norm is proposed which is generalisation of the Łukaszewicz’s norm. Some selected properties of this generalised t-norm are first presented. Next , it is shown a possibility of generalisation of the notions of lower and upper approximations used in fuzzy rough sets and also of obtaining better such approximations.