rough set theory
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To reduce the incidence of cerebrovascular disease and mortality, identifying the risks of cerebrovascular disease in advance and taking certain preventive measures are significant. This article was aimed to investigate the risk factors of cerebrovascular disease (CVD) in the primary prevention, and to build an early warning model based on the existing technology. The authors use the information entropy algorithm of rough set theory to establish the index system suitable for early warning model. Then, using the limited Boltzmann machine and direction propagation algorithm, the depth trust network is established by building and stacking RBM, and the back propagation is used to fine-tune the parameters of the network at the top layer. Compared with the LM-BP early-warning model, the deep confidence network model is more effective than traditional artificial neural network, which can help to identify the risk of cerebrovascular disease in advance and promote the primary prevention.

In this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system and study three functions of the Shannon type, which characterize the dependence in the worst case of the minimum depth of a decision tree solving a problem on the number of attributes in the problem description. The considered three functions correspond to (i) decision trees using attributes, (ii) decision trees using hypotheses (an analog of equivalence queries from exact learning), and (iii) decision trees using both attributes and hypotheses. The first function has two possible types of behavior: logarithmic and linear (this result follows from more general results published by the author earlier). The second and the third functions have three possible types of behavior: constant, logarithmic, and linear (these results were published by the author earlier without proofs that are given in the present paper). Based on the obtained results, we divided the set of all infinite binary information systems into four complexity classes. In each class, the type of behavior for each of the considered three functions does not change.

The original K-nearest neighbour ( KNN) algorithm was meant to classify homogeneous complete data, that is, data with only numerical features whose values exist completely. Thus, it faces problems when used with heterogeneous incomplete (HI) data, which has also categorical features and is plagued with missing values. Many solutions have been proposed over the years but most have pitfalls. For example, some solve heterogeneity by converting categorical features into numerical ones, inflicting structural damage. Others solve incompleteness by imputation or elimination, causing semantic disturbance. Almost all use the same K for all query objects, leading to misclassification. In the present work, we introduce KNNHI, a KNN-based algorithm for HI data classification that avoids all these pitfalls. Leveraging rough set theory, KNNHI preserves both categorical and numerical features, leaves missing values untouched and uses a different K for each query. The end result is an accurate classifier, as demonstrated by extensive experimentation on nine datasets mostly from the University of California Irvine repository, using a 10-fold cross-validation technique. We show that KNNHI outperforms six recently published KNN-based algorithms, in terms of precision, recall, accuracy and F-Score. In addition to its function as a mighty classifier, KNNHI can also serve as a K calculator, helping KNN-based algorithms that use a single K value for all queries that find the best such value. Sure enough, we show how four such algorithms improve their performance using the K obtained by KNNHI. Finally, KNNHI exhibits impressive resilience to the degree of incompleteness, degree of heterogeneity and the metric used to measure distance.

Traditional financial data storage methods are prone to data leakage and narrow data coverage. Therefore, this paper proposes a dynamic and secure storage method of financial data based on cloud platform.In order to improve the ability of enterprise data management, the paper constructs a financial cloud computing platform, mining financial data by rough set theory, and analyzing the results of frequent pattern mining of financial data by fuzzy attribute characteristics.According to the granularity theory, the financial data is classified and processed, and the CSA cloud risk model is established to realize the dynamic and secure storage of financial data.The experimental results show that. The maximum data storage delay of this method is no more than 4.1 s, the maximum data leakage risk coefficient is no more than 0.5, the number of data types can reach 30, and the data storage coverage is improved.

<abstract><p>In the philosophy of rough set theory, the methodologies of rough soft sets and rough fuzzy sets have been being examined to be efficient mathematical tools to deal with unpredictability. The basic of approximations in rough set theory is based on equivalence relations. In the aftermath, such theory is extended by arbitrary binary relations and fuzzy relations for more wide approximation spaces. In recent years, the notion of picture hesitant fuzzy relations by Mathew et al. can be considered as a novel extension of fuzzy relations. Then this paper proposes extended approximations into rough soft sets and rough fuzzy sets from the viewpoint of its. We give corresponding examples to illustrate the correctness of such approximations. The relationships between the set-valued picture hesitant fuzzy relations with the upper (resp., lower) rough approximations of soft sets and fuzzy sets are investigated. Especially, it is shown that every non-rough soft set and non-rough fuzzy set can be induced by set-valued picture hesitant fuzzy reflexive relations and set-valued picture hesitant fuzzy antisymmetric relations. By processing the approximations and advantages in the new existing tools, some terms and products have been applied to semigroups. Then, we provide attractive results of upper (resp., lower) rough approximations of prime idealistic soft semigroups over semigroups and fuzzy prime ideals of semigroups induced by set-valued picture hesitant fuzzy relations on semigroups.</p></abstract>

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the ɛ- constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker’s optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameter ɛ are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.

Rough Set Theory (RST) is an essential mathematical tool to deal with imprecise, inconsistent, incomplete information and knowledge Rough Some algebra structures, such as groups, rings, and modules, have been presented on rough set theory. The sub-exact sequence is a generalization of the exact sequence. In this paper, we introduce the notion of a sub-exact sequence of groups. Furthermore, we give some properties of the rough group and rough sub-exact sequence of groups. 

Proportional Feature Rough Selector (PFRS) merupakan sebuah metode seleksi fitur yang dikembangkan berdasarkan Rough Set Theory (RST). Pengembangan ini dilakukan dengan merinci pembagian wilayah dalam set data menjadi beberapa bagian penting yaitu lower approximation, upper approximation dan boundary region. PFRS memanfaatkan boundary region untuk menemukan wilayah yang lebih kecil yaitu Member Section (MS) dan Non-Member Section (NMS). Namun PFRS masih hanya digunakan dalam seleksi fitur pada klasifikasi biner dengan tipe data teks. PFRS ini juga dikembangkan tanpa memperhatikan hubungan antar fitur, sehingga PFRS memiliki potensi untuk ditingkatkan dengan mempertimbangkan korelasi antar fitur dalam set data. Untuk itu, penelitian ini bertujuan untuk melakukan penyesuaian PFRS untuk bisa diterapkan pada klasifikasi multi-label dengan data campuran yakni data teks dan data bukan teks serta mempertimbangkan korelasi antar fitur untuk meningkatkan performa klasifikasi multi-label. Pengujian dilakukan pada set data publik yaitu 515k Hotel Reviews dan Netflix TV Shows. Set data ini diuji dengan menggunakan empat metode klasifikasi yaitu DT, KNN, NB dan SVM. Penelitian ini membandingkan penerapan seleksi fitur PFRS pada data multi-label dengan pengembangan PFRS yaitu dengan mempertimbangkan korelasi. Hasil penelitian menunjukkan bahwa penggunaan PFRS berhasil meningkatkan performa klasifikasi. Dengan mempertimbangkan korelasi, PFRS menghasilkan peningkatan akurasi hingga 23,76%. Pengembangan PFRS juga menunjukkan peningkatan kecepatan yang signifikan pada semua metode klasifikasi sehingga pengembangan PFRS dengan mempertimbangkan korelasi mampu memberikan kontribusi dalam meningkatkan performa klasifikasi.