Narrow Results

This paper explores the topological aspects of algebras determined by rough sets. It is well known that the lattice structure of rough sets is characterized by the lattices of the form $2^I$ ×$3^J$. We show that algebras determined by the rough sets are characterized by the condition “any chain of completely prime filters has at most two elements”. We introduce the notion of rough topological space in which the basic open set has at most two elements. We further provide representations of rough topological spaces in terms of topologies determined by algebras of rough sets.

A methodology for using rough sets theory for preference modeling in decision problem is presented in this paper. We will introduce a new method where neural network systems and rough sets theory are completely integrated into a hybrid system and are used cooperatively for decision and classification support. At the first glance, the two methods we discuss have not much in common. But, in spite of the differences between them, it is interesting to try to incorporate both into one combined system, and apply it in the building of a decision support system.

We purpose to find a new beneficial method for accelerating the Decision-Making and classifier support applied on imprecise data. This acceleration can be done by integration between Rough Sets theory, which gives us the minimal set of decision rules, and the Cellular Neural Networks. Our method depends on Genetic Algorithms for designing the cloning template for more accuracy. Some illustrative examples are given to demonstrate the effectiveness of the proposed method, whose advantages and limitations are also discussed.

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

Data mining currently is a vital and core process because of advances in the technology, and numerous other forms of data. As an essential and significant constituent of data mining, classification has also become vital and a sought-after-option for research. Over the years, as various soft computing tools have been proven to be more complimentary than competitive, many hybrid approaches have evolved for pattern classification. A major thrust has always been there to apply hybrid approaches involving artificial neural network as the main tool for pattern classification. Here, one such hybrid approach is presented with application of Rough set philosophy to unsupervised artificial neural network (UANN) based pattern classifier. This enhances the performance of the classifier and makes it more suitable for real time classification applications dealing with large and unlabeled data. The idea presented here discusses with possibility and application of various Rough set based approaches at different levels of implementation of such classifier. The concluding section presents the results achieved for data of two case studies related to face recognition and mobile handoff prediction.

Associating features with weights is a common approach in clustering algorithms and determining the weight values is crucial in generating valid partitions. In this paper, we introduce a novel method in the framework of granular computing that incorporates fuzzy sets, rough sets and shadowed sets, and calculates feature weights automatically. Experiments on synthetic and real data patterns show that our algorithms always converge and are more effective in handling overlapping among clusters and more robust in the presence of noisy data and outliers.

Estimation by analogy (EBA) predicts effort for a new project by learning from the performance of former projects. This is done by aggregating effort information of similar projects from a given historical data set that contains projects, or objects in general, and attributes describing the objects. While this has been successful in general, existing research results have shown that a carefully selected subset, as well as weighting, of the attributes may improve the performance of the estimation methods.

In order to improve the estimation accuracy of our former proposed EBA method AQUA, which supports data sets that have non-quantitative and missing values, an attribute weighting method using rough set analysis is proposed in this paper. AQUA is thus extended to AQUA⁺ by incorporating the proposed attribute weighting and selection method. Better prediction accuracy was obtained by AQUA⁺ compared to AQUA for five data sets. The proposed method for attribute weighting and selection is effective in that (1) it supports data sets that have non-quantitative and missing values; (2) it supports attribute selection as well as weighting, which are not supported simultaneously by other attribute selection methods; and (3) it helps AQUA⁺ to produce better performance.

In this study, we highlight some fundamental issues of knowledge management and cast them in the setting of Granular Computing (GrC). We show how its formal constructs — information granules are instrumental in knowledge representation and specification of its level of abstraction.

Extensive amounts of knowledge and data stored in medical databases require the development of specialized tools for storing, accessing, analysis, and effectiveness usage of stored knowledge and data. Intelligent methods such as neural networks, fuzzy sets, decision trees, and expert systems are, slowly but steadily, applied in the medical fields. Recently, rough set theory is a new intelligent technique was used for the discovery of data dependencies, data reduction, approximate set classification, and rule induction from databases.

In this paper, we present a rough set method for generating classification rules from a set of observed 360 samples of the breast cancer data. The attributes are selected, normalized and then the rough set dependency rules are generated directly from the real value attribute vector. Then the rough set reduction technique is applied to find all reducts of the data which contains the minimal subset of attributes that are associated with a class label for classification. Experimental results from applying the rough set analysis to the set of data samples are given and evaluated. In addition, the generated rules are also compared to the well-known ID3 classifier algorithm. The study showed that the theory of rough sets seems to be a useful tool for inductive learning and a valuable aid for building expert systems.

In this paper a mereological theory of frames of reference is presented. It shows that mereology extended by the notion of granularity and approximation is sufficient to provide a theory for location based features of frames of reference. More complex theories, taking also into account orientation and metric properties can be built as extensions of the presented theory. In order to take the hierarchical organization of frames of reference into account we introduce the notion of stratified approximation to facilitate transformations between different levels of granularity. This paper shows that the ontological grounding of the theory of frames of reference into mereology allows us to give a clear semantics to the notion 'degree of parthood' which is central to the notion of approximation. It also shows how epistemic aspects which affect the use of frames of reference help us to understand the feature of epistemic vagueness and the way it affects the notions of approximation and of degree of parthood.

We present the three-step GRG approach for learning decision rules from large relational databases. In the first step, an attribute-oriented concept tree ascen sion technique is applied to generalize an information system. This step loses some information but substantially improves the efficiency of the following steps. In the second step, a reduction technique is applied to generate a minimalized information system called a reduct which contains a minimal subset of the generalized attributes and the smallest number of distinct tuples for those attributes. Finally, a set of maximally general rules are derived directly from the reduct. These rules can be used to interpret and understand the active mechanisms underlying the database.

Rough set theory is emerging as a powerful tool for reasoning about data, knowledge reduction is one of the important topics in the research on rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem of attributes. In this paper, knowledge reduction is defined from the view of information, a heuristic algorithm based on rough entropy for knowledge reduction is proposed in incomplete information systems, the time complexity of this algorithm is O(|A|²|U|). An illustrative example is provided that shows the application potential of the algorithm.

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets.

In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.

This paper considers the introduced relations between fuzzy property-oriented concept lattices and fuzzy relation equations, on the one hand, and mathematical morphology, on the other hand, in the retrieval processing of images and signals. In the first part, it studies how the original images and signals can be retrieved using fuzzy property-oriented concept lattices and fuzzy relation equations. In the second one we analyze two of the most important tools in fuzzy mathematical morphology from the point of view of the fuzzy property-oriented concepts and the aforementioned study. Both parts are illustrated with practical examples.

In this paper we present a new approach to rough set approximations that permits to distinguish between two kinds of “imperfect” knowledge in a joint framework: on one hand, vagueness, due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity, due to granularity of knowledge originating from the coarseness typical of rough sets. The basic idea of our approach is that each concept is represented by an orthopair, that is, a pair of disjoint sets in the universe of knowledge. The first set in the pair contains all the objects that are considered as surely belonging to the concept, while the second set contains all the objects that surely do not belong to the concept. In this context, following some previous research conducted by us on the algebra of rough sets, we propose to define as rough approximation of the orthopair representing the considered concept another orthopair composed of lower approximations of the two sets in the first orthopair. We shall apply this idea to the classical rough set approach based on indiscernibility, as well as to the dominance-based rough set approach. We discuss also a variable precision rough approximation, and a fuzzy rough approximation of the orthopairs. Some didactic examples illustrate the proposed methodology.

Attribute reduction plays an important role in knowledge discovery and data mining. Confronted with data characterized by the interval and missing values in many data analysis tasks, it is interesting to research the attribute reduction for interval-valued data with missing values. Uncertainty measures can supply efficient viewpoints, which help us to disclose the substantive characteristics of such data. Therefore, this paper addresses the attribute reduction problem based on uncertainty measure for interval-valued data with missing values. At first, an uncertainty measure is provided for measuring candidate attributes, and then an efficient attribute reduction algorithm is developed for the interval-valued data with missing values. To improve the efficiency of attribute reduction, the objects that fall within the positive region are deleted from the whole object set in the process of selecting attributes. Finally, experimental results demonstrate that the proposed algorithm can find a subset of attributes in much shorter time than existing attribute reduction algorithms without losing the classification performance.

In this paper, we provide a definition of α-fuzzified lower and upper approximations for fuzzy sets based on the α-cut of fuzzy binary relations. We show that the definition is a proper generalization of the previous one for approximations of crisp sets and compare it with an existing definition in the context of fuzzy tolerance relation.

Effective feature selection is essential to the development of any intelligent classifier which is intended for use in high-dimension domains. This paper presents an approach that incorporates a rough set-assisted feature reduction method and a neural network-based classifier for image classification. The approach minimises the need for feature extraction without altering the underlying semantics of the features chosen. Through the proposed integration the size of the neural network classifier, which is sensitive to the dimensionality of the dataset, becomes manageable and the network is able to classify images that would otherwise require many more features to represent. Comparative study results from realistic applications demonstrate the success of this work.