Modifications to Bayesian Rough Set Model and Rough Vague Sets

Bayesian Decision theoretic rough set has been invented by the author. In this paper the attribute reduction by the aid of Bayesian decision theoretic rough set has been studied. Lot of other methods are there for attribute reduction such as Variable precision method, probabilistic approach, Bayesian method, Pawlaks rough set method using Boolean function. But with the help of some example it is shown that Bayesian decision theoretic rough set model gives better result than other method. Lastly an example of HIV /AIDS is taken and attribute reduction is done by this new method and various other method. It is shown that this method gives better result than the previously defined methods. By this method the authors get only the reduced attribute age which is the best significant attribute. Though in Pawlak model age sex or age living status are the reduced attribute and variable precision method fails to work here. In this paper attribute reduction is done by the help of discernibility matrix after determining the positive, boundary and negative region. This model is a hybrid model of Bayesian rough set model and decision theory. So this technique gives better result than Bayesian method and decision theoretic rough set method.

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.

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set and variable precision rough set so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set, which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We, respectively, define the variable precision rough lower and upper approximations of any fuzzy set and it level set with variable precision parameter by constructive approach. Also, we present the properties of the proposed model in detail. Meanwhile, we establish the relationship between the variable precision rough approximation of a fuzzy set and the rough approximation of the level set for a fuzzy set. Furthermore, we give a new approach to uncertainty measure for variable precision rough fuzzy set established in this paper in order to overcome the limitations of the traditional methods. Finally, some numerical example are used to illuminate the validity of the conclusions given in this paper.

In order to realize a well-designed product that appeals to costumers, the product not only should meet the physical requirements of consumers but also has to satisfy their affective needs. Packaging design is an important factor of purchasing decision of consumers. Several research was explained the impact of packaging design to the children and their parents with statistical ways, but there are few approach to consider multi-values data set. This study propose Bayesian Rough Set model to deal some uncertainties and incomplete data in classification data. Bayesian Rough Set method has strength to solve vagueness in human sensory data with probabilistic approximation to identify the relation rules between human perception and product packaging design. This is also useful to handle heterogeneous population, contradictive between generalization versus customization, and uncertainty — inconsistency in market segmentation. For the case study in this research, we will investigate the effect of packaging design on luxury food (ex, chocolate, cake and so on) and instant food packaging preferences and its ability to influence costumers' buyer decision in-store. At the final result, the proposed method get better result than conventional method (Rough Set) as followed: 1) The proposed method get accuracy improvement rather than conventional method (Rough Set) as many as 12.07%, and confidence level as big as 10.61% 2) The proposed method also get calculation time improvement rather than conventional method (Rough Set), which is 81.25%.

Variable precision rough set model, as an important probabilistic approach to rough set theory, can deal with many practical problems which involve noise data and cannot be effectively handled by Pawlak's rough set model. Generally, rough set theory based knowledge reduction includes attribute reduction and attribute value reduction. Attribute reduction in variable precision rough set model has been attracted many researchers' attentions. However, attribute value reduction in variable precision rough set model was rarely discussed. In this paper, an approach to attribute value reduction in variable precision rough set model is presented, with which the redundant information in the given decision table can be effectively removed and the properties of the acquired rules, namely deterministic or probabilistic, can be preserved well.

Traditional rough set of noise data, the lack of adaptability, lack of flexibility or robustness, for the engineering data can not distinguish between equivalence classes of edge region of overlap with the collection, resulting in loss of many valuable engineering information. Strong noise in the actual engineering data over-fitting due to reduced ability to distinguish the object, its limitations limits its further application. In this paper, variable precision rough set model (VPRS, the variable precision Rough set Model), allows a certain threshold level of classification rate exists, in order to better solve the engineering data, no functional relationship between attributes of interference data classification problem, it Overcome the standard rough set model on the shortcomings of the data is too sensitive to noise, thereby enhancing the data analysis and processing robustness. Finally, simulation results show that using variable precision rough set theory to solve the data uncertainty of similar projects under the influence of the extraction is feasible.

Variable precision rough set model is the extension of rough set model, which introduce theβparameter based on the basic rough set theory, that is, allows a certain degree of misclassification rate existing. This paper presents the web mining algorithm based on variable precision rough set in e-commerce, analyzes the limitation of the reduction methods based on variable precision rough set theory. The experiment shows the CPU Time in the attribute numbers, indicating that VPRS is superior to normal algorithm in web mining in e-commerce. The experiments show the algorithm could flexibly and dynamically web mining and therefore provide a valuable addition to the field.

Variable Precision Rough Set (VPRS) model is one of the most important extensions of the Classical Rough Set (RS) theory. It employs a majority inclusion relation mechanism in order to make the Classical RS model become more fault tolerant, and therefore the generalization of the model is improved. This paper can be viewed as an extension of previous investigations on attribution reduction problem in VPRS model. In our investigation, we illustrated with examples that the previously proposed reduct definitions may spoil the hidden classification ability of a knowledge system by ignoring certian essential attributes in some circumstances. Consequently, by proposing a new ß-consistent notion, we analyze the relationship between the structures of Decision Table (DT) and different definitions of reduct in VPRS model. Then we give a new notion of /3-complement reduct that can avoid the defects of reduct notions defined in previous literatures. We also supply the method to obtain the /3- complement reduct using a decision table splitting algorithm, and finally demonstrate the feasibility of our approach with sample instances.

PurposeThe purpose of this paper is to acquire doubly variable precision‐based knowledge rules from incomplete decision tables (IDTs) in the framework of pansystems methodology. It suggests a new variable precision limited tolerance – a special pansystems relation – rough set model with precision inclusion and a reduct procedure in which it overcomes the non‐monotony in forming tolerance classes when reducing an attribute from attribute set.Design/methodology/approachThrough introducing variable precision and limited tolerance relation in IDT, it constructs symmetric binary relation, dissimilar to non‐symmetric relation proposed by others, and then forms tolerance classes. It proposes a new reduction procedure with absolute value calculation to avoid tolerance classes being non‐monotone. Using variable inclusion, it obtains lower and upper approximations with noises.FindingsTolerance classes are not monotone with the reduction of attribute from attribute set in the proposed variable precision and limited tolerance relation, but it remains symmetry. Proposed reduction procedure with absolute value calculation is a new approach in adjudging whether a reduct equals to the original whole attribute set within a error range or not.Practical implicationsUsing variable precision and limited rough set model with variable inclusion to mine deep knowledge from IDT is a paradise in knowledge discovery in dealing with non‐determinative and vague problems.Originality/valueThe formation of symmetric tolerance relation is natural. The reduction procedure with absolute value calculation is new and not similar to those existed in literatures.

An illustration of variable precision rough sets model: an analysis of the findings of the UK Monopolies and Mergers Commission

In this paper, we study variable precision rough set models based on multiple decision tables. The models can control the admissible level of classification error in each table, the ratio of supporting decision tables to all decision tables and the ratio of opposing decision tables to all decision tables. As the classical rough set model plays a key role in analysis of decision tables such as reduction, rule induction, etc., the proposed variable precision rough set models will play a key role in analysis of multiple decision tables.

Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approximation operators of vague sets based on vague relations, and investigate the basic properties of approximation operators on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transitive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.

Radar emitter information detected by multisensor system takes on uncertainty, illegibility and contradiction. In real reconnaissance environment, the patterns of radar classes often overlap, the accurate classification of the Pawlak rough set model restricts its application in the real world. In order to solve emitter recognition problem, a new method of finding decision rules is presented to classify radar emitter from the new point of view of variable precision rough set. This method is according to dependent degree of decision attributes on condition attributes. The decision rules proposed are more straightforward. At last, example of recognizing the radar emitter purposes is selected. During the experiment, discretization is conducted on extracted index data of radar emitter and metrical radar characteristic parameter firstly. Then, positive region of each condition attribute are calculated under the given error parameter, which is the basis of decision rules. Experimental results demonstrate this new radar emitter recognition method by finding decision rules based on variable precision rough set model is effective and feasibility

We present a novel approach to understanding the concepts of the theory of rough sets in terms of the inverse probabilities derivable from data. It is related to the Bayes factor known from the Bayesian hypothesis testing methods. The proposed Rough Bayesian model (RB) does not require information about the prior and posterior probabilities in case they are not provided in a confirmable way. We discuss RB with respect to its correspondence to the original Rough Set model (RS) introduced by Pawlak and Variable Precision Rough Set model (VPRS) introduced by Ziarko. We pay a special attention on RB’s capability to deal with multi-decision problems. We also propose a method for distributed data storage relevant to computational needs of our approach.KeywordsRough SetsProbabilitiesBayes Factor

Six-Set Approximation Theorem of neighborhood related rough sets