Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Matroidal approaches to rough sets via closure operators

AbstractThis paper studies rough sets from the operator-oriented view by matroidal approaches. We firstly investigate some kinds of closure operators and conclude that the Pawlak upper approximation operator is just a topological and matroidal closure operator. Then we characterize the Pawlak upper approximation operator in terms of the closure operator in Pawlak matroids, which are first defined in this paper, and are generalized to fundamental matroids when partitions are generalized to coverings. A new covering-based rough set model is then proposed based on fundamental matroids and properties of this model are studied. Lastly, we refer to the abstract approximation space, whose original definition is modified to get a one-to-one correspondence between closure systems (operators) and concrete models of abstract approximation spaces. We finally examine the relations of four kinds of abstract approximation spaces, which correspond exactly to the relations of closure systems

Multi-criterion two-sided matching of Public-Private Partnership infrastructure projects: Criteria and methods

Two kinds of evaluative criteria are associated with Public-Private Partnership (PPP) infrastructure projects, i.e., private evaluative criteria and public evaluative criteria. These evaluative criteria are inversely related, that is, the higher the public benefits; the lower the private surplus. To balance evaluative criteria in the Two-Sided Matching (TSM) decision, this paper develops a quantitative matching decision model to select an optimal matching scheme for PPP infrastructure projects based on the Hesitant Fuzzy Set (HFS) under unknown evaluative criterion weights. In the model, HFS is introduced to describe values of the evaluative criteria and multi-criterion information is fully considered given by groups. The optimal model is built and solved by maximizing the whole deviation of each criterion so that the evaluative criterion weights are determined objectively. Then, the match-degree of the two sides is calculated and a multi-objective optimization model is introduced to select an optimal matching scheme v ia a min-max approach. The results provide new insights and implications of the influence on evaluative criteria in the TSM decision

Gestión pública y el delito de trata de personas en una institución pública, Lima Norte, 2022

La investigación tuvo como objetivo general, Identificar la contribución de la Gestión Pública a solucionar el delito de Trata de Personas en una Institución Pública, Lima Norte, 2022. Para ello se estableció un enfoque de tesis cualitativo, con un tipo de investigación básica y con diseño fenomenológico, siendo que se tomaron las opiniones de seis expertos en la materia de la tesis, asimismo el instrumento utilizado fue la guía de entrevista, por lo que la técnica que se utilizo fue la entrevista, sobre la conclusión del objetivo general de la investigación, se indica que la Gestión Pública contribuye a solucionar el delito de Trata de Personas de manera mínima en una Institución Pública, Lima Norte, 2022. En ese sentido, la gestión pública afronta un ciclópeo reto contra la Trata de Personas, debido a que hasta el momento no se ha prestado la atención debida para enfrentar esta lucha, considerando que este delito es parte de otros