The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...

This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional lambda calculus. Then, some syntactic sugar, a system of combinatory logic, and the fixed point theorem are described. The final section introduces a topology...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

The routing problem for shared path protection in multi-domain optical mesh networks is difficult due to the lack of complete and global knowledge on the network topology and bandwidth allocation. To overcome this difficulty, we propose an aggregated network modeling by overestimation with a two-step routing strategy. In the first step, a rough routing solution is sketched in a compact network ...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

The routing problem for shared path protection in multidomain optical mesh networks is difficult due to the lack of complete and global knowledge on the network topology and bandwidth allocation. To overcome this difficulty, we propose an aggregated network modeling by overestimation and a two-step routing strategy. In the first step, a rough routing solution is sketched in a compact network wh...

In this paper, we introduce a new method to generate a mesh from a 3D sketch. The latter can be considered as a skeleton that defines the global shape of the object to model. To induce a natural adjacency, for further topological control, this inner structure is a set of voxels connected using the 26-neighborhood. Two important features are supported by the resulting surface: it is a multiresol...

This study provides a numerical approach to evaluate the effect of sample sizes on fluid flow through single rough-walled fracture. The fracture was generated by using mathematical statistics. Its aperture follows normal distribution along large-size plane dimensions 20 m × m, and from this plane, series fractures with different were extracted. Then, two-dimensional (2D) Reynolds equation solve...