New rough approximations for n-cycles and n-paths

In this paper, we continue the study of a finite simple undirected graph through the rough set techniques introduced by Pawlak in the early 80's. In this sense, we focus on the Boolean information system induced from a circle or a line graph with n vertices and, for such graphs, we provide a complete description of the rough membership function and some results on the positive regions and the attribute dependency function.

[1]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[2]  D. Petrassi On Some Numbers Related to Extremal Combinatorial Sum Problems , 2014 .

[3]  Giampiero Chiaselotti,et al.  Rough Sets for n-Cycles and n-Paths , 2016 .

[4]  Gianpiero Cattaneo,et al.  Non Uniform Cellular Automata Description of Signed Partition Versions of Ice and Sand Pile Models , 2014, ACRI.

[5]  Davide Ciucci,et al.  Simple Undirected Graphs as Formal Contexts , 2015, ICFCA.

[6]  Giampiero Chiaselotti,et al.  A Class of lattices and boolean functions related to a Manickam-Mikl\ , 2010, 1004.1724.

[7]  Z. Toroczkai,et al.  Proximity networks and epidemics , 2007 .

[8]  Juan A. Aledo,et al.  Parallel dynamical systems over directed dependency graphs , 2012, Appl. Math. Comput..

[9]  P. Hogeweg Cellular automata as a paradigm for ecological modeling , 1988 .

[10]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[11]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[12]  Giampiero Chiaselotti,et al.  Sand Piles Models of Signed Partitions with Piles , 2013 .

[13]  Giuseppe Marino,et al.  Parallel Rank of Two Sandpile Models of Signed Integer Partitions , 2013, J. Appl. Math..

[14]  Giampiero Chiaselotti,et al.  Parallel and sequential dynamics of two discrete models of signed integer partitions , 2014, Appl. Math. Comput..

[15]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[16]  William J. Keith,et al.  Two Self-Dual Lattices of Signed Integer Partitions , 2014 .

[17]  Michael Schreckenberg,et al.  Two lane traffic simulations using cellular automata , 1995, cond-mat/9512119.

[18]  Juan A. Aledo,et al.  Parallel Dynamical Systems over Graphs and Related Topics: A Survey , 2015, J. Appl. Math..

[19]  Giuseppe Marino,et al.  A natural extension of the Young partition lattice , 2015 .

[20]  Giuseppe Marino,et al.  A Discrete Dynamical Model of Signed Partitions , 2013, J. Appl. Math..

[21]  Zdzislaw Pawlak,et al.  Information systems theoretical foundations , 1981, Inf. Syst..

[22]  Juan A. Aledo,et al.  Parallel dynamical systems over special digraph classes , 2013, Int. J. Comput. Math..

[23]  Juan A. Aledo,et al.  Parallel discrete dynamical systems on maxterm and minterm Boolean functions , 2012, Math. Comput. Model..

[24]  Juan A. Aledo,et al.  Parallel discrete dynamical systems on independent local functions , 2013, J. Comput. Appl. Math..

[25]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..