Introduction to Classical Rough Set Based APIs Library

Rough set theory for the interval-valued fuzzy information systems

The definition of basic rough sets [3] depends upon either a single equivalence relation defined on a universe or several equivalence relations defined over the universe, taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. Extending this notion, a rough set model based on multi-granulations (MGRS) was introduced in [5]. In this approach, approximations of sets were defined through multiple equivalence relations on the universe and their properties were investigated. Using hybridization of fuzzy set [13] with rough set the concept of rough fuzzy set was introduced by Dubois and Prade [1]. Recently, a Rough Fuzzy Set Model was introduced and studied by Wu and Kou [12], which is based on Multiple Granulation. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [10]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [11]. In this paper we introduce incomplete multigranulation on rough fuzzy sets, study their basic properties and extend the topological properties in [11] to this context. Our findings are true for both complete and incomplete fuzzy rough set models based upon multi granulation.KeywordsRough SetsFuzzy rough setsequivalence relationstolerance relationstype of rough setsmulti granular fuzzy rough sets

Soft rough fuzzy sets and soft fuzzy rough sets

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft---rough fuzzy sets, which extends Dubois and Prade's rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Molodtsov (Comput Math Appl 37:19–31, 1999 [6]) initiated a novel concept called soft sets, a new mathematical tool for dealing with uncertainties. It has been found that fuzzy sets, rough sets, and soft sets are closely related concepts (Aktas and Cagman in Inf Sci 1(77):2726–2735, 2007 [1]). Research works on soft sets are very active and progressing rapidly in these years. In 2001, Maji et al. (J Fuzzy Math 9(3):589–602, 2001 [5]) proposed the idea of intuitionistic fuzzy soft set theory and established some results on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (Int J Gen Syst 17:191–209, 1990 [3]) introduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al. (Soft Compt 14:899–911, 2009 [4]) introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model called soft rough fuzzy sets which is the extension of Dubois and Prade’s rough fuzzy sets. The aim of this chapter is to consider lower and upper soft rough intuitionistic fuzzy approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space) and obtain a new hybrid model called soft rough intuitionistic fuzzy sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

Local rough set: A solution to rough data analysis in big data

A generalization of the original idea of rough sets and variable precision rough sets is introduced. This generalization is based on the concept of absolute and relative rough membership. Similarly to variable precision rough set model, the generalization called parameterized rough set model, is aimed at modeling data relationships expressed in terms of frequency distribution rather than in terms of a full inclusion relation used in the classical rough set approach. However, differently from variable precision rough set model, one or more parameters modeling the degree to which the condition attribute values confirm the decision attribute value, are considered. The properties of this extended model are investigated and compared to the classical rough set model and the variable precision rough set model.

Six-Set Approximation Theorem of neighborhood related rough sets

Based on rough set and basic theory of data fusion, the data fusion algorithm combining rough set theory and BP neural network is studied. Since rough set theory can effectively simplify information, cut down the tagged dimension . This paper will be rough set theory and neural networks combined, using channel capacity of knowledge relative reduction algorithms to simplify the input information. Rough set theory is first used to process the sample data, and eliminate the redundant information, then reduce the scale of neural network, improve the identification rate, and improve the efficiency of the whole data fusion system. The effectiveness of the improved algorithm is demonstrated by an example compared with the traditional neural network system.

With the requirements of the power load predicting accuracy becoming higher and higher, and the actual power load is also a complex nonlinear system limited by various uncertain factors. Given only considering the influence of a single model on the load forecasting, the predicting accuracy is absolutely not high under the comprehensive effects of multiple factors. Ensuring to make the electrical model satisfy the requirements, there is access to improving the accuracy of load predicting results through analysis of the relationship between load and multiple factors in power load forecasting. This paper combines the rough set theory with information fusion, firstly a decision table of attributes is established on the basis of historical datum, for the purpose of simplifying the attribute index in mining to obtain important information. Following step is to rank the importance of the factors influencing the load according to the degree of effect, with grouping these sorted factors into attributes combination and using the same kind of load forecasting method to predict each combination's own results, and finally all groups of the predicting results are integrated by fusion, where then final predicting result can be obtained. The results of the algorithmic example show that groups of predicting results integrated based on information fusion theory are better than the results got through any casual single attribute combination. And fusion results are a combined action of a variety of related factors, enhancing the favorable trend, where at the same time it has reduced the uncertainty brought by multiple factor comprehensive effect. Based on information fusion the predicting results are helpful to reduce the prediction error, which is feasible and effective. With the explosive growth on the amount of in today's information age, the wave of data is coming, fast and furious. The era of big proposes a new challenge for the development in electricity industry. With the advance of electricity industry, intelligence, automation and interaction will bring many datum casing electrical big generation. Due to the numerous index of power load forecasting, different goals of all kinds of power load forecasting, even with the same kind of theory, the forecast model to predict no matter from the form, content or effect also vary widely. The load in the medium and long-term prediction of power system is greatly influenced by economy, society and meteorology factors and other uncertainties, etc. How to extract the key factor from multiple factors and reduce the results' uncertainty arising from the comprehensive effect of multiple factors, and improving the precision has been becoming a serious problem to be solved. Aiming at these problems, the paper based on the literature (8) proposing medium-and long- term load forecasting based on partial least squares regression analysis, an more optimized and advanced method is put forward to improve accuracy of prediction. The rough set theory and information fusion are introduced into the model, which respectively advance pre-processing and optimize the integration of multiple sets of results after prediction, in order to reduce uncertainty caused by varieties factors affecting and improve accuracy of forecasting results. II. THE ROUGH SET THEORY In the era of big data, on account of the characteristics on grid volume, which is large amount, variety type, and more speed, the traditional attribute simplified methods have been unable to complete the pre-processing on electrical big data. To this end the paper proposes a method on power big simplified processing based on cloud computing technology. The rough set theory which offers a new way for mining, is a new mathematical tool to deal with uncertain and imprecise problems. In this paper, rough sets method is used in power load forecasting to analyze the dependence of load on each factor and the importance of various properties in condition attribute set. In the decision system R={U, A}, the rough set divides A(attribute) into two categories C and D, where C is condition attribute, D is decision attribute, and U is domain. The ternary collection R={U,C,D} is known as a decision-making system. An important application of rough set in the analysis is to find the dependence among attributes from a known decision system R={U,C,D}. The dependency is defined as follows.

In this paper, we study the application of fuzzy set theory, genetic algorithms and rough set theory techniques to the control of the rectifier. A fuzzy adaptive control scheme with the aid of rough set theory via genetic algorithms (GAs) finding the center parameters in place of the classical control is proposed. On the one hand, genetic algorithm gets optimal parameters of an accurate domain model, which tunes the scaling factors of fuzzy adaptive control but is hardly established in a non-liner system. On the other hand, fuzzy adaptive control deals with the dynamics and complexity of responses from rectifier of a HVDC system in the operation points, by adjusting its control parameters with the aid of rough tuner adaptively. Our study includes a brief introduction to fuzzy control and rough set algorithms, both theory and application. We also evaluate the performance of rough fuzzy control by simulation in the paper. The focus of our experiments is on the constant current control in rectifier side of HVDC system. The result shows there are many improvements offered by the fuzzy control scheme based on rough set theory in comparison with the only fuzzy control scheme in the rectifier side of HVDC system.

In order to solve problems of blurry of innovation process for the moment and practical dilemma in enterprises' development in competition, this article pays close attention to the tacit knowledge management of independent innovation based on rough sets (RS) theory. The rough characters of innovation knowledge sources are analyzed, and it accordingly comes to the conclusion that methods based on RS theory is compatible to the forepart matter, namely, the tacit knowledge study of independent innovation. Relative knowledge of innovation and RS theory is reviewed, and accordingly, an applied analysis with a RS toolkit is demonstrated as a revisit to the initiate period of independent innovation matter. The analysis is concluded with revelatory strategy of tacit knowledge management in context of independent innovation, of which information systems construction and information collection is instantly needed for presently independent innovation enterprises.

Rough function is one of interesting new directions of the classical Pawlak rough set theory. This paper presents a generalized rough function with one variable under the framework of classical Pawlak rough set theory. In the definition of generalized rough function, we extend the domain of the classical rough function from the general natural number set to integer set, and then the rough function with one variable defined on an integer set is obtained. After that, we investigate the basic properties of the proposed rough function with one variable base on the classical function analysis theory in detail. Furthermore, some interesting results about the rough function with one variable over integer set are given and the relationship between the existing literatures is discussed. The contribution of this is twofold: one is present a new concept of rough function with one variable over the integer set. Another is of enriches the basis of theory of classical Pawlak rough set and also extends the areas of the applications.

Neighborhood rough set theory is an important method for dealing with uncertainty, fuzziness and undefined objects, and neighborhood rough set theory based on binary relation is studied by scholars a lot. However, most of the current research is used to deal with equivalent binary relations or other binary relations with stringent condition, which has been unable to meet the rapid development of data. This paper proposes a new multi-granulation rough set that can deal with general binary relations based on the C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</inf> neighborhoods, and verifies its related properties. At the same −time, it has richer meanings through weighted methods. Theoretical analysis and practical examples show that this rough set has better ability to process data. Finally, a weighted attribute reduction algorithm is designed based on the significant function under the general binary relation. The experimental results show that this rough set can handle complex data well. The research in this paper develops the theory of classical rough sets, and provides a theoretical basis for the knowledge acquisition of information systems under the general binary relation.

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes.