Grey Correlation Evaluation Based on Rough Set in Combat Effectiveness for Avionics System

Soft rough fuzzy sets and soft fuzzy rough sets

Rough set theory for the interval-valued fuzzy information systems

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.

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.

Along with the status and function increase of satellite navigation system in information-age war, a new method of combat effectiveness evaluation-rough fuzzy sets(RFS) theory is proposed which is based on rough sets and fuzzy sets theory. The algorithm of the RFS theory is analyzed and designed, and effectiveness evaluation index system of satellite navigation system is established. And then, by an example, combat effectiveness of satellite navigation system is evaluated by RFS and decision rules are also given. The theory provides a new idea for evaluation and decision of satellite navigation system.

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

It is important for us to evaluate each trainee’s ability with the aim of improving BDAR training efficiency. The typical assessment methods include fuzzy evaluation, gray correlation evaluation, neural network and so on. All of these methods are not able to make full use of the historical information. Determining membership function in first two methods is not easy. And ANN needs a lot of data sample which is difficult to obtain in BDAR training. So we can’t use these methods to model the assessment of personnel BDAR ability. Then we introduce Bayesian Stochastic Assessment Method which can deal well with the nonlinear and random problem. Each indexes’ standard is given according to the characteristics of BDAR training. A modified normal distribution which can make full use of historical information was put forward to determine the prior probability. And the poster probability is determined by distance method.

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XVI includes extensions of papers from the Rough Sets and Knowledge Technology Conference which was held in Banff, Canada, in October 2011. In addition this book contains a long paper based on a PhD thesis. The papers cover both theory and applications of rough, fuzzy and near sets. They offer a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century.

Researchers in science and engineering face various obstacles due to a lack of specific and full data. Many different approaches have been devised to deal with these restrictive requirements, but two notable schools of thought are the fuzzy set (FS) theory and the rough set (RS) theory, both of which have spawned many extensions and hybridizations. Although RS theory originated from an indiscernibility relation (also known as an equivalence relation in mathematics), emphasis rapidly shifted to similarity or coverings (and their fuzzy analogues). Many other hybrid schemes were suggested with this goal in mind. The gap between those concepts shrank because to this thorough analysis. Fuzzy set theory is a legitimate way to convey the ambiguity of assessment data, yet it is still inadequate for dealing with certain intricate problems in the actual world. In reality, decision makers will undoubtedly provide different kinds of ambiguous and nuanced assessments. Atanassov’s intuitionistic fuzzy set theory broadened the application of fuzzy set theory by imbuing it with an element of uncertainty. Sometimes in real life, you have to deal with a neutral element on top of the indeterminate one. Picture fuzzy sets were developed specifically for this purpose. Membership roles may be positive, neutral, or negative/refusal. In contrast, hesitant fuzzy sets and its hybrid models are useful when decision makers are on the fence about which option to choose. As a binary relation on a set, a graph is symmetric. It is a staple in mathematical modelling and is used in almost every scientific and technological discipline. Graph theory has been essential in the mathematical modelling and subsequent resolution of several real-world situations. Information about connections between things is often best represented using graph theory, which uses vertices to stand in for the items and edges for the relationships between them. The suggested dynamic algorithm is better to the static approach in dealing with the multidimensional dynamic changes of the hybrid incomplete decision system, according to a series of experiments carried out on nine UCI datasets.

PurposeThe purpose of this paper is to introduce the elementary concepts and fundamental principles of grey systems and the main components of grey systems theory. Also to discuss the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.Design/methodology/approachThe characteristics of unascertained systems including incomplete information and inaccuracies in data are analysed and four uncertain theories: probability statistics, fuzzy mathematics, grey system and rough set theory are compared. The scientific principle of simplicity and how precise models suffer from inaccuracies are also shown.FindingsThe four uncertain theories, probability statistics, fuzzy mathematics, grey system and rough set theory are examined with different research objects, different basic sets, different methods and procedures, different data requirements, different emphasis, different objectives and different characteristics.Practical implicationsThe scientific principle of simplicity and how precise models suffer from inaccuracies are shown. So, precise models are not necessarily an effective means to deal with complex matters, especially in the case that the available information is incomplete and the collected data inaccurate.Originality/valueThe elementary concepts and fundamental principles of grey systems and the main components of grey systems theory are introduced briefly. The reader is given a general picture of grey systems theory as a new method for studying problems where partial information is known, partial information is unknown; especially for uncertain systems with few data points and poor information.

Load forecasting is key for the optimal control of heating, ventilating, and air-conditioning. However, accurate forecasting modeling requires the ability of selecting relevant factors so that the influences of the irrelevant factors can be reduced substantially. This paper presents a novel hybrid method combining rough set theory and support vector machine network (RSSV). Rough set (RS) theory is applied to find the relevant factors of the load, which are used as the inputs of support vector machine (SVM) to predict cooling load. To improve the accuracy and enhance the robustness of load forecasting results, a general load prediction model synthesizing multi-RSSV (MRSSV) is presented so as to make full use of redundant information. Optimum principle is employed to deduce the weights of each RSSV model. Actual prediction results for a real HVAC system show that the MRSSV forecasting model, whose relative error turned out to be within 4%, may be better than those models using individual RSSV, recursive least squares (RLS), and autoregressive integrated moving average (ARIMA). In addition, individual RSSV forecasting results are also better than that of ARIMA.