# Rough Set

## Top PDF Rough Set: ### A New Method of Translating Covering Rough Set into Classical Rough Set

Abstract. Binary relational rough sets enrich the applicable scope of classic rough set, but they lose some excellent properties. Therefore, covering translates to partition has become one of the key points in the study of covering approximate spaces. However, the existing translation methods have some shortcomings, such as the inconsistency between the partitions translated by covering and covering reduction, the inconsistency between the monotonicity of the covering and the translated partition, and the limited application of the translation method, and so on. In view of this situation, the basic requirements for covering translate partition are put forward, and then the concepts of transposed and symmetric classes are defined. On this basis, the translation method is proposed which gets over the shortcomings of the existing methods, and the effectiveness of the way is proved theoretically. At the same time, in consideration of the situation that practical data cannot form a single coverage, the new method is extended to the multi-covering approximate space by the minimum description of multi-covering elements. ### BAT ALGORITHM FOR ROUGH SET ATTRIBUTE REDUCTION

This formula denotes the classification quality and feature subset length have different importance. We adopt this approach based on the work done in [10, 23], they states that classification quality is more significance than the size of subset, as a result both parameters have been set as follow: δ = 0.9, φ = 0.1. The high δ guarantees that the best position is at least a real rough set reduction. The quality of each position is calculated according to equation 8, the goal is to maximize fitness values. Fig. 2 presents the pseudo-code for BAAR. ### A Rough Set View on Bayes Theorem

It is seen clearly from Examples 1 and 2 the difference between Bayesian data analysis and the rough set approach. In the Bayesian inference, the data are used to update prior knowledge (probability) into a posterior probability, whereas rough sets are used to understand what the data tell us. ### A Variable Precision Fuzzy Rough Set Approach to a Fuzzy Rough Decision Table

Abstract. In a real world, non-empty boundaries between classes may be both rough and fuzzy. In order to make decision in fuzzy approximation space, a fuzzy VPRS (variable precision rough set) approach is proposed based on substitution of the indiscernibility relation by a fuzzy indiscernibility relation in the rough approximation of decision classes, which can obtain probabilistic rules from fuzzy decision tables. Some set theoretic properties of the proposed approach are discussed. ### Quantization of Rough Set Based Attribute Reduction

impossible to check the correctness of assumption in practice. In contrast, rough set can hold complete analy- sis, since it considers missing value as “everything is possible” [8, 9]. Rough set is proposed by Pawlak  as a mathematical theory of set approximation, which is now widely used in information system. In order to find the solution of incomplete system by rough set, tolerance relation is defined through relaxing the equivalence rela- tion [8,11]. It is a NP-hard problem to find an optimal solution. Heuristic approaches have been proposed, keep- ing the positive region of target decision unchanged  or employing conditional entropy to obtain a solution . Each method aims at some basic requirement ac- cording to their mechanisms of reduction, so no one can give a fair evaluation among these methods. ### Autonomous clustering using rough set theory

This paper proposes an autonomous methodology for extracting knowledge and relationships from mixed attribute data in the form of coarse clusters which reflect important global properties of the data. The resultant clustering technique is presented as a simple algorithm and modified tools from rough set theory are used to form the classes. By virtue of the fact that rough set theory reflects global data properties, the clustering solution is unaffected by local discrepancies. This then has the advantages of (a) avoiding the generation of too many small and unrepresentative clusters and (b) leading to a coarse clustering of the universe. Furthermore, the reliance of the traditional clustering techniques on local optimality paves the way for a number of different clustering solutions and scope for distorted results. ### Rough Set Approach in Machine Learning: A Review

Secondly, a rough set rule induction algorithm generates decision rules, which can reveal profound knowledge and provide new insights . For example, Tsumoto introduced an approach to knowledge acquisition, which induced probabilistic rules based on rough set theory (PRIMEROSE) and developed a program that extracts rules for an expert system from a clinical database. Tsumoto also proposed PRIMEROSE4.5 (Probabilistic Rule Induction Method based on Rough Sets Ver 4.5) as an extension of earlier version of PRIMEROSE4 reported by Tsumoto. In the earlier work of Tsumoto, only rigid set- inclusion relations were considered for grouping, while rough- inclusion relations were introduced in the second approach, allowing it to outperform the earlier approach . The LEM2 algorithm was proposed to extract a minimum set of decision rules, and the rule induction algorithm was useful for both classification and medical knowledge discovery [39,53,112]. This algorithm could reveal regular and interpretable patterns of the relations between glioma MRI features and the degree of malignancy, which were helpful for medical evolution. ### Chikungunya Diagnosing using Rough Set Approach

Symptoms etc. have been gathered from internet and doctors to identify effective parameters in relation to Chikungunya diagnosis. These attributes shown in Table II. The attributes of age distribution, IgM : IgG ratio, symptoms-I, symptoms-II, seasonal distribution, platelet count and clinical features can all be considered as condition attribute, whereas the viral illness attribute is considered a decision attribute. Each row of decision table determines a decision rule, which specifies the decisions (actions) must be taken when conditions indicated by condition attributes are satisfied. Each column of the mentioned table indicates one of the characteristics (attributes) considered for the diagnosis and the last column implies the decision parameter for Chikungunya fever. Next, the data should be classified using rough set theory to analyze the information. Therefore each conditional attribute is provided as three classes low, medium and high and the decision level is also classified with low, medium and high conditions as L, M, and H respectively. The arrangement of all attributes has been undertaken to define the specified level and assigning a code to each specified attribute in the rows of the table. Table III shows the relation between the class numbers of conditional attributes of each parameter and its decision attribute. In this stage, all the cases of the conditional attributes should be checked to find the non- deterministic rule. ### A Rough Set Formalization of Quantitative Evaluation with Ambiguity

We have first proposed a model of objective quantitative evaluation for natural language processing based on rough sets, distinguishing the annotation equivalence relation (in- trinsic criteria) and the reward function (extrinsic criteria), second we presented the notion of potential performance space to describe the effect that resolving the remaining ambiguity of the hypothesis data would have on the per- formance range. We have also shown that the accuracy approximation coefficient used to quantifies the level of “roughness” of a rough set can be used to describe the amount of variability of the potential performance space corresponding to the ambiguity present in the hypothesis data. Our future work will concern using and refining our model in order to obtain, from the formal representation, ### Rough set approach for categorical data clustering

Therefore, based on these drawbacks, there is a need for improving of those techniques. In this work, a technique termed MDA (Maximum Dependency of Attributes) for categorical data clustering aimed to mine the hidden “nuggets” patterns in database is proposed. It is based on rough set theory taking into account maximal dependency of attributes in an information system. Experimental tests on small datasets, benchmark datasets and real world datasets demonstrate how such techniques can contribute to practical system, such as for supplier chain management clustering. ### Rough Set Based Opinion Mining in Tamil

ABSTRACT: - As individuals impart on the Web about their sentiments on products and services they have used, it has become important to formulate methods of automatically classifying and judging them. The task of examining such data, collectively called client feedback data, is known as opinion mining. Opinion mining consists of several steps, and different techniques have been proposed at each stage in this process. This paper basically explains such techniques that have been used for the implementation of task of opinion mining in Tamil. On the basis of this analysis we provide an overall system design for the development of opinion mining approach. In this paper, the rough set theory is useful to extract the key sentences and its feature attribute after getting the opinion from the post will be evaluated. Before this operation the pre-processing steps will be discussed for finding the entity and its attribute, on the basis of the output the rough set theory is used for avoiding the ambiguities between the word sense sentences. Using Rough set we generated the result for three class ( நேர்மறை (Positive), யாரும் (None), எதிர்மறை (Negative)) and five class ( மிகவும் சாதகமான (More Positive), நேர்மறை (Positive), யாரும் (None), மிகவும் எதிர்மறை (More Negative), எதிர்மறை (Negative)) problems. ### Fuzzy-Rough Set Bireducts for Data Reduction

The increase in the popularity of rough sets is largely the result of a series of desirable theoretical aspects. Indeed, the grouping of information into equivalence classes is intuitive and offers a certain universal appeal. Additionally, RST possesses other properties that are advantageous. Parameters are not needed, thus obviating any requirement for user input, which is subjective and potentially erroneous. RST also determines a representation of the data that is minimal. However, the primary obstacle for traditional rough set theory is that it can only be applied to crisp or discrete-valued data. This inability to handle real-valued and noisy data has led to the exploration of approaches which hybridise RST with other techniques. One of these hybridisations is fuzzy-rough sets  which offer the ability to model fuzzy uncertainty in both the conditional and decision attributes. ### Liquefaction Prediction Using Rough Set Theory

The results of the liqueed case histories appear to have an output range of 0.6-0.7, and the liquefaction prediction indices for liquefaction unlikely cases have a range of 0.3-0.4; however, there were some misclassi- cations in 5 cases in each table. The decision levels used in rough set analysis in Tables 2(a) and 2(b) are a result of real data from past earthquakes with the same classications as the simplied method proposed by Youd et al. . ### Empirical analysis of rough set categorical clustering techniques based on rough purity and value set

The RST is a viable system to deal with uncertainty in clustering process of categorical data. RST was originally a symbolic data analysis tool now being developed for cluster analysis (D¨untsch & Gediga, 2015). In rough categorical clustering, mainly the data set is expressed as the decision table by introducing a decision attribute. Most of these methods assume one or more given partitions of the data set aiming to find a cluster which best represents the data according to some predefined measure. Set approximation and reduct based methods are the two main ideas of the rough set model which are promising for applications. Tolerance rough set clustering (Ngo & Nguyen, 2004) and rough-K-Means clustering (Peters, 2006) are the examples of set approximation methods. Despite of having satisfactory results, these methods have issues as they depend on several parameters and thresholds (D¨untsch & Gediga, 2015). The reduct based methods either work as pre-processing tool or as a tool for cluster generation but the problem of time complexity has not been solved yet (D¨untsch & Gediga, 2015). ### Retrieving the Missing Information from Information Systems Using Rough Set, Covering Based Rough Set and Soft Set

Soft set theory has potential applications in many different fields which include the smoothness of functions, game theory, operations research, Riemann integration, Peron integration, probability theory, and measurement theory and so on [4, 5]. Also, application of soft set theory to the problems of medical diagnosis in medical expert system was discussed. Maji et al. gave first practical application of soft set in decision making problems. It is based on the notion of knowledge of reduction in rough set theory. N. Cagman and S. Enginoglu  defined soft matrices and their operations to construct a soft max-min decision making method which can be successfully applied to the problems that contain uncertainties. T. Herawanet al., , gave an alternative approach for attribute reduction in multi-valued information system under soft set theory. In their work they had shown that the reducts obtained using soft set are equivalent with Pawlak’s rough reduction. ### Concept Lattice: A rough set approach

Concept lattice is an efficient tool for knowledge representation and knowledge discovery and is applied to many fields successfully. However, in many real life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts. The hierarchical structure of formal concept (called concept lattice) represents a structural information which obtained automatically from the input data table. We deal with the problem in which how further additional information be supplied to utilize the basic object attribute data table. In this paper , we provide rough concept lattice to incorporate the rough set into the concept lattice by using equivalence relation. Some results are established to illustrate the paper. ### BAT ALGORITHM FOR ROUGH SET ATTRIBUTE REDUCTION

Keywords: Permanent Magnet Synchronous Motor PMSM, Modeling and Simulation, Extended Kalman Filter EKF, Vector Control 1... With the development of the power electronics, micro-electroni[r] ### BAT ALGORITHM FOR ROUGH SET ATTRIBUTE REDUCTION

After the validation of the trained Fuzzy-ANN model, the study further examined the stock selection capability while applying to the real stock market. The whole sample set was used to generate FIS output. For those stocks with FIS output higher than 0.5 were selected to form the Hi-Value (i.e., high value) portfolio with equal weights in the portfolio (comprised of 22 stocks). The return performance of the Hi-Value portfolio was compared against the market index and the Taiwan 50 index in various time periods. The Taiwan 50 index comprises of 50 highly capitalized blue-chip stocks and it represents nearly 70% of the Taiwan stock market. To balance the evaluation in return and risk, the Sharpe ratio as Eq. (6) was also calculated to see if the Hi-Value portfolio outperformed the market index considering risk factor. The result was shown in the Table 3, and the monthly HPR of the Hi-Value portfolio was plotted to compare with the market indexes in the Figure 5.  