An Analysis of Generalised Approximate Equalities Based on Rough Fuzzy Sets

Three types of rough equalities were introduced by Novotny and Pawlak ([7, 8,9]), which take care of approximate equalities of sets. These sets may not be equal in the usual sense. These notions were generalized by Tripathy, Mitra and Ojha ([12]), who introduced the concepts of rough equivalences of sets. These approximate equalities of sets capture equality of the concerned sets at a higher level than their corresponding rough equalities. Some more properties were proved in [13]. Two more approximate equalities were introduced by Tripathy [11] and comparative analysis of their efficiency was provided. In this paper, we generalise these approximate equalities by considering rough fuzzy sets instead of only rough sets. A concept of leveled approximate equality is introduced and properties are studied. We also provide suitable examples to illustrate the applications of the new notions and provide an analysis of their relative efficiency.