On algebrai̇c sum, Mi̇nkowski̇ di̇fference of sets and appli̇cati̇ons

In this study, algebraic sum and Minkowski difference operations which are defined on the family of subsets of R^n are presented. Some important properties of these operations are proved. In addition, volume of algebraical sum of convex sets is formulated in plane and in space by using line integral and surface integral, respectively. Moreover, a method which provides movement of a robot through barriers is given. At the end, dilation and erosion operations of computer graphs are expressed by means of algebraic sum and Minkowski difference.