Knowledge Granularity Research Articles

A Group Incremental Reduction Algorithm with Varying Data Values

Attribute reduction based on rough set theory has attracted much attention recently. In real-life applications, many decision tables may vary dynamically with time, e.g., the variation of attributes, objects, and attribute values. The reduction of decision tables may change on the alteration of attribute values. The paper focuses on dynamic maintenance of attribute reduction when varying data values of multiple objects. Incremental mechanisms for knowledge granularity are proposed first, which aims to update attribute reduction effectively. Then, a group incremental reduction algorithm with varying data values is developed. When attribute values of multiple objects have been replaced by new ones in decision table, the proposed incremental algorithm can find the new reduct in a much shorter time. The time complexity analysis and experiments on different data sets from UCI have validated that the proposed incremental algorithms are efficient and effective to update the reduction with the variation of attribute values.

Prevalence and Measurement of Anxiety in Samples of Patients With Heart Failure: Meta-analysis.

Objectives:Rates of anxiety in patients with heart failure (HF) vary widely, and not all assessment instruments used in this patient population are appropriate. It is timely to consolidate the evidence base and establish the prevalence and variance of anxiety in HF samples.Methods:A systematic review, meta-analysis, and meta-regression were conducted to identify the prevalence, variance, and measurement of anxiety in patients with HF.Results:A total of 14,367 citations were identified, with 73 studies meeting inclusion criteria. A random effects pooled prevalence of 13.1% (95% confidence interval [CI], 9.25%–16.86%) for anxiety disorders, 28.79% (95% CI, 23.30%–34.29) for probable clinically significant anxiety, and 55.5% (95% CI, 48.08%–62.83%) for elevated symptoms of anxiety was identified. Rates of anxiety were highest when measured using the Brief Symptom Scale-Anxiety scale (72.3%) and lowest when measured using the Generalised Anxiety Disorder-7 (6.3%).Conclusion:Many patients with HF would benefit if screened for anxiety and treated. The conceptualization and measurement of anxiety accounted for most variance in prevalence rates. The Generalised Anxiety Disorder-7 or the Hospital Anxiety and Depression Scale appear to be the most appropriate instruments for this clinical population, with evidence to suggest they can discriminate between depression and anxiety, omit somatic items that may contaminate identification of anxiety in a population with physical comorbidities, and provide thresholds with which to differentiate patients and target treatments. Although there are limitations with the collation of diverse measurement methods, the current review provides researchers and clinicians with a more granular knowledge of prevalence estimates of anxiety in a population of HF patients.

An incremental attribute reduction approach based on knowledge granularity under the attribute generalization

Attribute reduction is a key step to discover interesting patterns in the decision system with numbers of attributes available. In recent years, with the fast development of data processing tools, the information system may increase quickly in attributes over time. How to update attribute reducts efficiently under the attribute generalization becomes an important task in knowledge discovery related tasks since the result of attribute reduction may alter with the increase of attributes. This paper aims for investigation of incremental attribute reduction algorithm based on knowledge granularity in the decision system under the variation of attributes. Incremental mechanisms to calculate the new knowledge granularity are first introduced. Then, the corresponding incremental algorithms are presented for attribute reduction based on the calculated knowledge granularity when multiple attributes are added to the decision system. Finally, experiments performed on UCI data sets and the complexity analysis show that the proposed incremental methods are effective and efficient to update attribute reducts with the increase of attributes.

An incremental approach for attribute reduction based on knowledge granularity

Rough set provides a theoretical framework for classification learning in data mining and knowledge discovery. As an important application of rough set, attribute reduction, also called feature selection, aims to reduce the redundant attributes in a given decision system while preserving a particular classification property, e.g., information entropy and knowledge granularity. In view of the dynamic changes of the object set in a decision system, in this paper, we focus on knowledge granularity-based attribute reduction approach when some objects vary dynamically. We first introduce incremental mechanisms to compute new knowledge granularity. Then, the corresponding incremental algorithms for attribute reduction are developed when some objects are added into and deleted from the decision system. Experiments conducted on different data sets from UCI show that the proposed incremental algorithm can achieve better performance than the non-incremental counterpart and incremental algorithm based on entropy.

A roughness measure of fuzzy sets from the perspective of distance

Covering generalized rough set theory is an important extension of classical rough set theory. To characterize a fuzzy set in a given covering approximation space, a pair of fuzzy sets, called covering rough fuzzy lower and upper approximations, were introduced, but they do not describe well how much uncertainty is induced by the granularity of knowledge. In this paper, we first discuss the relationship between uncertainty and granularity of knowledge. Then we examine several commonly used distance measures, and indicate that some of them exhibit some limitations. Next we propose a roughness measure based on Minkowski distance, and examine some important properties of this measure. Finally, an illustrative example is provided to demonstrate the application of the roughness measure to incomplete information systems with fuzzy decision.

Fuzzy equivalence relation and its multigranulation spaces

Multigranulation rough sets focus on describing uncertain sets in different granularity spaces. Different approximation accuracy of an uncertain set can be obtained through changing knowledge granularities according to user’s need. However, it is a bottleneck for establishing a multigranulation space to better describe an uncertain set in a proper granulation space. And the typical way of a multigranulation space is a hierarchical quotient space determined by a fuzzy equivalence relation. In this paper, a new concept, granularity of binary relation (GB) is put forward firstly. And knowledge granulation (GK) is proved to be a special case of GB. The changing rules of granularity series for describing a hierarchical quotient space structure are proposed, and approximation accuracy series of an uncertain set is presented. For automatically searching optimal knowledge space according to user’s requirement, a utility function with both knowledge space granularity and approximation accuracy is proposed. Then classification isomorphism and granularity isomorphism between two hierarchical quotient space structures are defined and discussed. Through the hierarchical quotient space structure of a fuzzy equivalence relation, the essence of classification ability of a fuzzy equivalence relation is also revealed. Finally, a new algorithm for establishing isomorphic fuzzy equivalence relations based on a hierarchical quotient space structure is presented, and this algorithm can further explain the nature of those isomorphic fuzzy equivalence relations from a new perspective.

Ontology Knowledge Mining for Ontology Alignment

AbstractAs the ontology alignment facilitates the knowledge exchange among the heterogeneous data sources, several methods have been introduced in literature. Nevertheless, few of them have been interested in decreasing the problem complexity and reducing the research space of correspondences between the input ontologies.This paper presents a new approach for ontology alignment based on the ontology knowledge mining. The latter consists on producing for each ontology a hierarchical structure of fuzzy conceptual clusters, where a concept can belong to several clusters simultaneously. Each level of the hierarchy reflects the knowledge granularity degree of the knowledge base in order to improve the effectiveness and speediness of the information retrieval. Actually, such method allows the knowledge granularity analyze between the ontologies and facilitates several ontology engineering techniques. The ontology alignment process is performed iteratively over the produced hierarchical structure of the fuzzy cl...

Interpretive Strategies for Screen-Based Creative Technologies

This paper brings together the disciplines of media and creative technologies studies and software systems engineering; it focuses on the challenge of finding methodologies to measure, test and decode meaning in digital cultural objects. Just as rough set theory is a mathematical tool to deal with vagueness and uncertainty in artificial intelligence, and approximation accuracy and knowledge granularity are approaches to uncertainty research, the authors argue that découpage analytique is a possible method for decoding screen-based information. They draw on a variety of examples: interactive online digital art projects; an interactive, immersive screen-based art installation; re-mediated digital art installation; expanded cinema; a videogame; and a medical interface example, in order to determine if it is possible to map interpretive strategies that include a blending of old and new criteria, but ultimately promoting an equal partnership between artist and audience, and thus, a community of co-creators. Additionally, the authors present experimental evidence on the difference introduced by the screen size to further qualify the effectiveness of découpage analytique in relation to the amount of screen real estate afforded.

Application of TRIZ in Creative Design Based on Knowledge Granularity

Application of TRIZ in Creative Design Based on Knowledge Granularity

Special Issue on Granular Knowledge Discovery

Special Issue on Granular Knowledge Discovery

Granular knowledge discovery framework for fire and rescue reporting system

Granular knowledge discovery framework for fire and rescue reporting system

Relationships between generalized rough sets based on covering and reflexive neighborhood system

Rough set theory is an important tool to deal with uncertainty, granularity and incompleteness of knowledge. The covering-based rough sets is one of the most important extensions of the classical Pawlak rough sets. In covering-based rough set theory, many types of rough sets were already defined in the literature. To find out the relationships among different types of covering-based rough sets and give an axiomatic definition is a very important issue. The generalized rough sets in neighborhood system is another important extension of the classical Pawlak rough sets. In this paper, we investigate relationships between covering-based rough sets and generalized rough sets in neighborhood system. Then, twenty-three types of the element based, the granule based and the subsystem based definitions of covering approximation operators are unified under the framework of generalized approximation operators in neighborhood systems. Moreover, properties of the generalized approximation operators in neighborhood systems are presented.

The approximation set of a vague set in rough approximation space

Vague set is a further generalization of fuzzy set. In rough set theory, a target concept may be a defined set, fuzzy set or vague set. That the target concept is a defined set or fuzzy set was analyzed in detail in our other papers respectively. In general, we can only get two boundaries of an uncertain concept when we use rough set to deal with the uncertain problems and can not get a useable approximation defined set which is a union set with many granules in Pawlak’s approximation space. In order to overcome above shortcoming, we mainly discuss the approximation set of a vague set in Pawlak’s approximation space in the paper. Firstly, many preliminary concepts or definitions related to the vague set and the rough set are reviewed briefly. And then, many new definitions, such as 0.5-crisp set, step-vague set and average-step-vague set, are defined one by one. The Euclidean similarity degrees between a vague set and its 0.5-crisp set, step-vague set and average-step-vague set are analyzed in detail respectively. And then, the conclusion that the Euclidean similarity degree between a vague set and its 0.5-crisp set is better than the Euclidean similarity degree between the vague set and the other defined set in the approximation space (U,R) is drawn. Afterward, it is proved that average-step-vague set is an optimal step-vague set because the Euclidean similarity degree between a vague set and its average-step-vague set in the approximation space (U,R) can reach the maximum value. Finally, the change rules of the Euclidean similarity degree with the different knowledge granularities are discussed, and these rules are in accord with human cognitive mechanism in a multi-granularity knowledge space.

Covering-based rough fuzzy sets and binary relation

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. In this paper we study covering-based rough fuzzy sets in which a fuzzy set can be approximated by the intersection of some elements in a covering of the universe of discourse. Some properties of the covering-based fuzzy lower and upper approximation operators are examined. We present the conditions under which two coverings generate the same covering-based fuzzy lower and upper approximation. We approximate fuzzy sets based on a binary relation and its properties are introduced. Finally, we establish the equivalency between rough fuzzy sets generated by a covering and rough fuzzy sets generated by a binary relation.

On Links between Rough Sets and Digital Topology

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. In addition, digital topology deals with properties and features of two-dimensional or three-dimensional digital images that correspond to topological properties of objects. So, we try to describe the relationship between rough sets and digital topology. Firstly, we will study the classifications of topologies in rough sets. Secondly, we will use the upper approximation operator to span the digital line, which is the basic building block of the digital spaces.

Matroidal structure of generalized rough sets based on tolerance relations.

Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets. In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relation. First, a family of sets are constructed through the lower approximation of a tolerance relation and they are proved to satisfy the circuit axioms of matroids. Thus we establish a matroid with the family of sets as its circuits. Second, we study the properties of the matroid including the base and the rank function. Moreover, we investigate the relationship between the upper approximation operator based on a tolerance relation and the closure operator of the matroid induced by the tolerance relation. Finally, from a tolerance relation, we can get a matroid of the generalized rough set based on the tolerance relation. The matroid can also induce a new relation. We investigate the connection between the original tolerance relation and the induced relation.

Pattern analysis by active learning method classifier

Active Learning Method ALM is a powerful fuzzy soft computing tool, developed originally in order to promote an engineering realization of human brain. This algorithm, as a macro-level brain imitation, has been inspired by some behavioral specifications of human brain and active learning ability. ALM is an adaptive recursive fuzzy learning algorithm, in which a complex Multi Input, Multi Output system can be represented as a fuzzy combination of several Single-Input, Single-Output systems. SISO systems as associative layer of algorithm capture partial spatial knowledge of sample data space, and enable a granular knowledge resolution tuning mechanism through the learning process. The knowledge in each sub-system and its effectiveness in the whole system would be extracted by Ink Drop Spread in brief IDS operator and consolidated using a Fuzzy Rule Base FRB, in order to acquire expert knowledge. In this paper we investigate ALM as a conspicuous classifier in different types of classification problems. Also, a new ALM architecture to actively analyze ill-balanced image patterns is proposed. Different types of data sets are used as a benchmark, including a remote sensing image classification problem, to evaluate the ALM Classifier ALMC. With active pattern generation ability and knowledge resolution tuning, ALMC has been distinguished from many conventional classification tools especially for complex structures and image patterns analysis. This work demonstrates that ALMC is a good noise robust and active classifier, which is adaptively adjusted through structural evolution and pattern evaluation mechanism. These remarkable capabilities, along with its straightforward learning process, make ALMC as a convenient soft computing tool to use in different types of low dimensional pattern recognition problems.

Research on Theory of Set Knowledge Granularity Logic Based on the Decision Logic

Combined set pair analysis and knowledge granularity theory, the author puts forward set pair granularity space, and extended rough logic of Pawlak and the decision logic to set pair granularity space, Studied the formula and some special properties of set pair granularity space, thereby expand the application scope of the logic theory.

Entropy measures and granularity measures for set-valued information systems

Set-valued information systems are generalized models of single-valued information systems. In this paper, we propose two new relations for set-valued information systems. Based on these two relations, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation and knowledge granularity measure are defined in set-valued information systems, and some properties are investigated. Moreover, relationship between knowledge information entropy and knowledge granulation, knowledge rough entropy and knowledge granularity measure are studied. It is also shown that knowledge information entropy and knowledge granularity measure can be used to evaluate the certainty degree of knowledge in set-valued information systems, and knowledge rough entropy and knowledge granulation can be used to evaluate the uncertainty degree of knowledge in set-valued information systems. These results may supply a further understanding the essence of uncertainty and granularity in set-valued information systems.

Information interpretation of knowledge granularity

The quantitative analysis of the degree of knowledge granularity poses theoretical challenges for the development of granular computing. Information-theoretic measures have been proposed to address this problem, which exhibit usefulness in complete information systems. However, mathematical analysis of relationships between these information-theoretic measures and knowledge granularity has not been done. In this paper, after introducing Shannon's entropy and mutual information into complete information systems, we prove, for the first time, that these information-theoretic measures decrease monotonously as partition becomes coarser under complete information systems. Moreover, we illustrate that their inverse relationships do not hold generally and present an additional condition under which the inverse relationships are valid. By generalizing Shannon's entropy to incomplete information systems, we further discuss the relationship between the generalized Shannon's entropy termed as rough information entropy and knowledge granularity based on covering generalized rough sets. We find that in incomplete information systems, the rough information entropy varies nonmonotonously as covering becomes coarser. An illustrative example is given to verify the above observation result.