Fuzzy-Rough Set Bireducts for Data Reduction

A Feature Discretization Method Based on Fuzzy Rough Sets for High-Resolution Remote Sensing Big Data Under Linear Spectral Model

“…Since these two schemes have the same number of intervals, we can judge the results by comparing η 1 and η 2 . From (19) and (11) and ( 14 (reserving four decimal places) can be found. In the same way, η 2 ≈ 0.8087. η 2 > η 1 , i.e., the average approximation precision of all the fuzzy sets obtained by the second discretization scheme was higher than that of the first scheme, which is consistent with the conclusion of Section III-C.…”

“…Rough set theory was used to encode domain knowledge to reform the structure of granular neural network, which enhanced the performance of progressive granular neural network (PGNN) model for the classification of remote sensing images [13]. The fuzzy rough set is considered to be a more powerful uncertainty analysis model for big data than either fuzzy or rough sets [14]- [19]. This model introduces a fuzzy set on the basis of a rough set, and describes the relationship between the pixels by a similarity relation instead of the equivalent relation of a rough set.…”

“…In view of the above problems, we propose a discretization method called the fuzzy-rough-set-based genetic algorithm (FRSGA) for high-resolution satellite remote sensing of big data. Our innovation points to the article are as follows: (1) different from the current discretization methods, which are based on the assumption that one pixel only corresponds to the spectral information of a single object, the influence of uncertainty caused by a mixed spectrum is fully considered in our method, each category of ground object in high-resolution remote sensing image is regarded as a fuzzy set, and the Euclidean distance between pixels is calculated according to the pixel values on each band to obtain the fuzzy relation matrix on the set of pixels; (2) based on the rough set model in the original work, the membership degree of pixels to each category is determined through linear decomposition, and the individual fitness function based on a fuzzy rough model [19] is established; (3) in contrast to the conventional genetic operations in the previous work [20], chaotic mapping is employed to generate the initial population of adaptive genetic algorithm [30] to select discrete breakpoints, and MapReduce [31] is used to calculate the fitness of all individuals of the population in parallel, hence obtaining the optimal discretization scheme in the minimum time. We compared our method with mainstream discretization methods on the authentic remote sensing datasets.…”

The Role of Spatial Context Information in the Generalization of Geographic Information: Using Reducts to Indicate Relevant Attributes

“…There is number of basic researches about rough sets theories being conducted, like relating rough sets with testors [38]. They are also very interesting approaches using bireducts based on fuzzy-rough sets which allow for a reduction of dimensionality and data size at the same time [39]. However those research have rather theoretical and mathematical character, there is a wide group of others which concern the implementations in various field of science, industry and business.…”

Fuzzy Rough Programming Models: An Expected Value Perspective

“…Its inception provides a reliable theory base for the following research. So far, this theory has been investigated from the views of theory and practice, for example, a more general concept of a fuzzy rough set [14][15][16][17], the constructive definition of fuzzy rough approximation operators [18,19], feature selection [20][21][22], as well as a wide range of applications in attribute and data reduction [23,24], multi-attribute decision making [25], and so on. Unlike the fuzzy rough set, Liu [26] put forward a fuzzy rough variable (FRV) in 2002.…”