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The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set,...
The goal of the paper is to present the modification of classical indiscernibility relation, dedicated for rough set theory in a real-valued attributes space. Contrary to some other known generalizations, indiscernibility relation modified here, remains an equivalence relation and it is obtained by introducing a structure into collection of attributes. It defines real-valued subspaces, used in a multidimensional...
In this article we further explore the idea which led to the standard rough inclusion function. As a result, two more rough inclusion functions (RIFs in short) are obtained, different from the standard one and from each other. With every RIF we associate a mapping which is in some sense complementary to it. Next, these complementary mappings (co-RIFs) are used to define certain metrics. As it turns...
This paper presents a comparison of the effectiveness of two computational intelligence approaches applied to the task of retrieving rhythmic structure from musical files. The method proposed by the authors of this paper generates rhythmic levels first, and then uses these levels to compose rhythmic hypotheses. Three phases: creating periods, creating simplified hypotheses and creating full hypotheses...
In this paper, we present our Fun algorithm for discovering minimal sets of conditional attributes functionally determining a given dependent attribute. In particular, the algorithm is capable of discovering Rough Sets certain, generalized decision, and membership distribution reducts. Fun can operate either on partitions of objects or alternatively on stripped partitions, which do not store singleton...
Granular computing is a multidisciplinary theory rapidly developed in recent years. It provides a conceptual framework for many research fields, among others data mining. Data mining techniques and algorithms focus on knowledge discovery from data. When data labels are unknown one can use methods of exploratory data analysis called clustering algorithms. Clustering algorithms are also useful to find...
Image segmentation is an indispensable process in the visualization of human tissues, particularly during clinical analysis of magnetic resonance (MR) images. In this paper, the rough-fuzzy c-means (RFCM) algorithm is presented for segmentation of brain MR images. The RFCM algorithm comprises a judicious integration of the rough sets, fuzzy sets, and c-means algorithm. While the concept of lower and...
Approximate reasoning is used in a variety of reasoning tasks in logic-based artificial intelligence. In this paper we present several such reasoning schemes and show how they relate and differ from the approach of Pawlak’s Rough Sets.
The NetTRS system is a web service that makes induction, evaluation and postprocessing of decision rules possible. The TRS library is the kernel of the system. It allows to induce rules by means of the tolerance rough sets model. The NetTRS makes user interface of the TRS library available in the Internet. The main emphasis of the NetTRS system is placed on induction and postprocessing of decision...
An inference engine for classification of Electrocardiogram (ECG) signals is developed with the help of a rule based rough set decision system. For this purpose an automated data extraction system from ECG strips is being developed by using a few image processing techniques. A knowledge base is developed after consulting different medical books as well as feedback of reputed cardiologists on interpretation...
In the paper, some generalizations of the notions of reduct, test (superreduct), partial (approximate) reduct and partial test are considered. The accuracy of greedy algorithm for construction of partial test is investigated. A lower bound on the minimal cardinality of partial reducts based on an information about greedy algorithm work is studied. A bound on the precision of greedy algorithm which...
The direct searching for relevant reducts in the set of all reducts of a given data table can be often computationally infeasible, especially for large data tables. Hence, there is a need for developing efficient methods for extracting relevant information about reducts from data tables which could help us to perform efficiently the inducing process of the high quality data models such as rule based...
The data structures dealt with in formal concept analysis are referred to as contexts. In this paper we study contexts within the framework of discrete duality. We show that contexts can be adequately represented by a class of sufficiency algebras called context algebras. On the logical side we define a class of context frames which are the semantic structures for context logic, a lattice-based logic...
Granular Computing as a paradigm in the area of Approximate Reasoning/Soft Computing, goes back to the idea of L. A. Zadeh (1979) of computing with collections of similar entities. Both fuzzy and rough set theories are immanently occupied with granules as atomic units of knowledge are inverse images of fuzzy membership functions in the first and indiscernibility classes in the other set theory. ...
In this work the subject of granular computing is pursued beyond the content of the previous paper [21]. We study here voting on a decision by granules of training objects, granules of decision rules, granules of granular reflections of training data, and granules of decision rules induced from granular reflections of training data. This approach can be perceived as a direct mapping of the training...
A popular view is that the brain works in a similar way to a digital computer or a Universal Turing Machine by processing symbols. Psychophysical experiments and our amazing capability to recognize complex objects (like faces) in different light and context conditions argue against symbolic representation and suggest that concept representation related to similarities may be a more appropriate model...
Stress echocardiography is an important functional diagnostic and prognostic tool that is now routinely applied to evaluate the risk of cardiovascular artery disease (CAD). In patients who are unable to safely undergo a stress based test, dobutamine is administered which provides a similar effect to stress on the cardiovascular system. In this work, a complete dataset containing data on 558 subjects...
This paper presents a framework of rule generation in Non-deterministicInformationSystems (NISs), which follows rough sets based rule generation in DeterministicInformationSystems (DISs). Our previous work about NISs coped with certainrules, minimalcertainrules and possiblerules. These rules are characterized by...
Knowledge of an agent depends on the granulation procedure adopted by the agent. The knowledge granules may form a partition of the universe or a covering. In this paper dependency degrees of two knowledges have been considered in both the cases. A measure of consistency and inconsistency of knowledges are also discussed. This paper is a continuation of our earlier work [3].
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