In generalized rough set covering reduction theory, it is necessary to find a new measure to knowledge and rough set because the upper and lower approximations of rough sets are determined by their covering reduction. In this paper, information entropy is introduced to discuss the rough entropy of knowledge and the roughness of rough set, based on generalized rough set covering reduction. A new...

‎We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares‎. ‎We examine several statistics of these point sets‎, ‎such as the electrostatic potential‎, ‎Ripley's function‎, ‎the variance of the number of points in random spherical caps‎, ‎and the covering radius‎. ‎Some of the results are conditional on t...

In 2009, Peter Cameron introduced a common generalization of various classes of combinatorial designs such as balanced incomplete block designs, resolvable designs and orthogonal arrays. Generalized covering and packing designs can be defined in analogous way. These objects bring into this framework further classes of designs, including covering and packing arrays, Howell designs, monogamous cy...

The design of nature reserves is becoming, more and more, a crucial task for ensuring the conservation endangered wildlife. In order to guarantee preservation species general ecological functioning, designed must typically verify series spatial requirements. Among required characteristics, practitioners researchers have pointed out two aspects: (i) connectivity, so as avoid fragmentation, (ii) ...