Fuzzy covering based rough sets revisited

In this paper we review four fuzzy extensions of the so-called tight pair of covering based rough set approximation operators. Furthermore, we propose two new extensions of the tight pair: for the first model, we apply the technique of representation by levels to define the approximation operators, while the second model is an intuitive extension of the crisp operators. For the six models, we study which theoretical properties they satisfy. Moreover, we discuss interrelationships between the models