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.

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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.

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.

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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.

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 [10] 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 [12] or employing conditional entropy to obtain a solution [13]. 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.

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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.

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Secondly, a **rough** **set** rule induction algorithm generates decision rules, which can reveal profound knowledge and provide new insights [120]. For example, Tsumoto[115] 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[116] 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 [115]. 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.

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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.

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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,

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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.

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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.

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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 [3] which offer the ability to model fuzzy uncertainty in both the conditional and decision attributes.

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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. [8].

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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).

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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.[13] 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 [24] 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., [25], 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.

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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.

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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]

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.

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In order to mobilize students' learning initiative and active participation, improve the experimental teaching, and reduce the evaluation workload of the experiment, this paper presents [r]

Suppose the initial position is (0m, 0m), the desired position is (10m, 10m). Select the module of Constant as our input and **set** its value as 10, parameters of PID valued as p=10; i=0.01; d=3. The module of Pid1 and Pid2 are the state equation of ship’s surge and sway motion. The outputs of the simulation delegating the ship’s position are as shown in Figure 2 and Figure 3. Ship’s motion trail is as shown in Figure 4. The simulation time is 10s.