A Relative Tolerance Relation of Rough Set (RTRS) for potential fish yields in Indonesia

The sea is essential to life on earth, including regulating the climate, producing oxygen, providing medicines, providing habitats for marine animals, and feeding millions of people. It must be ensured that the sea continues to meet the needs of life without sacrificing the people of future generations. The sea regulates the planet’s climate and is a significant source of nutrients. The sea becomes an essential part of global commerce, while the contents of the ocean become the solution of human energy needs today and the future. The wealth and potential of the sea as a source of energy for humans today and the future needs to be mapped and described to provide a picture of marine potential to all concerned. As part of the government, the Ministry of Marine Affairs and Fisheries is responsible for the process of formulating, determining, and implementing policies in the field of marine and fisheries based on the results of mapping and extracting information from existing conditions. The results of this information can be used to predict the marine potential in a marine area. This prediction process can be developed using data-mining techniques such as applying the association rule by looking at the relationship between the quantity of fish based on the plankton abundance index. However, this association rules data-mining techniques that require complete data, which are data sets with no missing values to generate interesting rules for detection systems. The problem is often that required marine data are not available or that marine data are available, but they contain incomplete data. To address this problem, this paper introduces a Relative Tolerance Relation of Rough Set (RTRS). Novelty RTRS differs from previous rough approaches that use tolerance relationships, nonsymmetric equation relationships, and limited tolerance relationships. The RTRS approach is based on a limited tolerance relationship considering the relative precision between two objects; therefore, this is the first job to use relative precision. In addition, this paper presents the mathematical approach of the RTRS and compares it with other existing approaches using the marine real dataset to classify the marine potential level of the region. The results show that the proposed approach is better than the existing approach in terms of accuracy

Knowledge reduction of dynamic covering decision information systems with varying attribute values

Knowledge reduction of dynamic covering information systems involves with the time in practical situations. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings because of varying attribute values. Then we present incremental algorithms of constructing the second and sixth approximations of sets by using characteristic matrices. We employ experimental results to illustrate that the incremental approaches are effective to calculate approximations of sets in dynamic covering information systems. Finally, we perform knowledge reduction of dynamic covering information systems with the incremental approaches

Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page