In this paper, we introduce a generalization of rough set theory using topological structures generated by any binary general relation. The class of all after-composed sets and the class of all fore-composed sets defined here are used to generate two topological spaces. These topologies are used to approximate sets topologically. Lower and upper approximations are defined topologically and some of their properties are studied using these topologies. Also, membership, equality, inclusion relations and power set notions in the generalized approximation space are studied. Many differences are shown between notions of ordinary set theory and notions of rough set theory. These notions introduced in this work are good future work to knowledge discovery and data mining.

In this paper, we introduced a new probability distribution named as inverse power Maxwell distribution. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in modeling upside-down lifetime data. Some statistical properties of this distribution are derived. In estimation viewpoint, five methods are used for estimating the unknown parameters of the distribution and these methods are performed through the simulation study. Finally, two real data sets were analyzed to illustrate the applicability of the proposed distribution, proving that it fits each real data set much better than some other existing distributions.