In this paper approaches to modelling relations between discrete linguistic features are considered. Linguistic equations as a tool for describing complicated logic dependencies between semantic and syntactic features have been investigated. Finite predicate equations have been considered from the viewpoint of quick finding hidden dependencies in data. A way to defining the tightness of links between discrete features has been suggested. For this purpose, different types of substitution operators have been investigated. A class of finite predicates that allows eliminating non-salient features without an increase in the size of the original formula has been considered in relation with some linguistic examples. The results obtained can be used not only in applied linguistic, but also in other fields where deductive inferences in knowledge bases are important.

A complex system is considered as an algebraic structure having specific properties that do not allow expressing precisely the meaning of information objects included in the system. An algebraic definition of complexity has been given. the complexity has been considered from two viewpoints. A system can be considered to be a complex one if (a) boundary regions for system’s objects and processes are broad; (b) possibilities for system’s decompositions are limited. difficulties associated with complex system description and decomposition have been discussed in the framework of rough set methodology. A method for extracting salient features of information objects available in the system has been outlined. some theoretical aspects of rough set based analysis of complex systems have been discussed. All the operations designated to obtaining new knowledge or data patterns in complex systems are algebraically described from the viewpoint of algebraic systems including predicates (in particular, finite ones) and operations on them. thus, a system is considered to be complex if there is a great degree of uncertainty in the data and/or there are some serious problems with system’s decomposition.”

In this paper we discuss some issues related to generating aggregated association rules which implies the fact that features can take on values from finite sets with any number of elements, not only binary ones. We consider changes in the structure of a rule and the influence of these changes on some association rule parameters. We note that considering rules with low values of the main rule parameters can be of a great importance for resolving security problems. These results can be used by specialists in Big Data processing.

One of the problems in modern software development is the problem of introducing changes and fixes to the deployed software products in an automated fashion thus not requiring the end user to download the redundant product modules that had not been changed and performing manually the uninstall/install/check sequence.In this paper a method for building an automated update system has been suggested.The automated update system guarantees that the end user receives the latest changes and fixes to the product thus maintaining smooth experience from the software product.In this paper one of the methods for implementation of an automatic software update system for desktop applications is considered.

One of the classical Data Mining problems is the problem of classifying new objects on the basis of available information when the information associated with these objects does not allow identifying them unambiguously as elements of some set. In such cases using rough sets theory is often an effective solution. This theory operates with such concepts as “indiscernible” elements and relations. A rough set is characterized by lower and upper approximations for finding which the authors earlier suggested an original algebraic method. The given method uses only logic operations, which makes the process of searching logic rules very quick and efficient. The upper and lower approximations of a rough set allow describing elements of this set as completely as it is possible from the viewpoint of available information. In this connection it seems interesting and important to find irreducible sets of features describing a rough set with the same “precision” as with the help of a full set of features (so called reducts). This problem is quite difficult and complicated and at present it does not have good solutions. Our paper continues research carried out by the authors earlier and we suggest a method for finding reducts based on eliminating non-salient features in the reverse order of their importance. The suggested procedure allows us to avoid exhaustive searching by extracting a predefined number of most significant reducts. In this paper we consider arbitrary features taking on their values from finite sets.

Modern Data Mining methods allow discovering non-trivial dependencies in large information arrays. Since these methods are used for processing and analysis of huge information volumes, reducing the number of features necessary for describing a discrete object is one of the most important problems.One of the classical problems in intelligent data analysis is the problem of classifying new objects based on some a-priori information. This information might not allow us to exactly classify an object as one belonging to a certain set. In such cases using rough sets theory may be an effective solution as this theory operates with the concept of "indiscernible" elements and ambiguous information.In this paper we introduce a concept of a local reduct as a reduced set of features allowing us to describe a particular subset of the original set with the same precision as with the help of the full set of features. A method has been suggested which allows finding reduced sets of features adequately describing a rough set without losing necessary information (so-called reducts), and also assessing the importance of each feature. The suggested method is based on the algebraic approach to finding rough set approximations developed by the authors earlier. The main idea of the developed approach is as follows: if the algebraic approximations of a rough set do not change substantially in the process of excluding features the resulting reduced set of features can be used instead of the original full set. Also the greater changes eliminating a particular feature causes in the approximations, the more important this feature is.

The rough set concept is a relatively new mathematical approach to vagueness and uncertainty in data. The rough set theory is a well-understood formal framework for building data mining models in the form of logic rules, on the basis of which it is possible to issue predictions that allow classifying new cases. The indiscernibility relation and approximations based on this relation form the mathematical basis of the rough set theory. The classical topological definitions of rough approximations are based on the indiscernibility relation. Unlike the classical approaches, in this paper we define rough approximations in an algebraic way. We use a set of predicates and predicate operations, which we call the approximation language. We introduce the terms “exact upper approximation” and “exact lower approximation” to stress the fact that there can exist a variety of approximations but it is always possible to select the approximations that cannot be improved in the terms of the approximation language. These new definitions are compared to the classical ones (which use an equivalence relation) and are shown to be more general in the sense that the classical definitions can be deduced from them if we put some restrictions on our model. The process of generating logic rules based on the exact approximations has also been considered. Logic rules are naturally obtained from predicate formulae for the exact approximations. The introduced approach allows generating logic rules quickly and efficiently since only Boolean operations with binary strings are used to produce logic formulae.

Many practical problems of geometric information representation and pattern recognition require specific methods and tools for describing complex functions and geometric objects in a way that allows us to use such descriptions for making effective mathematical transformations and logic inferences. Since in real world situations we rarely encounter ideal objects that can be described with the help of one elementary function it is important to develop methods and models for integrating geometric information. There are some original approaches to describing complicated geometric structures, one of which is a method based on so-called R-functions. These functions allow complicated geometric objects to be described analytically, which gives an opportunity to operate with complex objects with the help of a single real function. The concept of R-functions is quite simple but the range of practical applications of this theory is very broad. In this paper we have suggested a generalization of R-functions, which we call R-p-Junctions. Any R-function can be associated with a Boolean function and it is always possible to construct an R-function corresponding to a given Boolean one. Similarly, any R-p-function can be associated with a finite predicate and it is always possible to construct an R-p-function corresponding to a given predicate. If R-functions allow us to use Boolean logic for describing complex objects, R-p-functions provide a possibility of using predicate logic, which is more rich and general than Boolean one. Like R-functions, R-p-functions allow the use of knowledge on what logic rules have been used for constructing a complex object to build a function which is positive inside the given domain and negative outside it. R-p-functions also seem to be interesting by themselves as they allow discovery of logic properties of quite a large class of real functions.

The concept of patterns representing functional, logical and other dependencies in data lies in the basis of the Data Mining technology. One of the wide spread forms for representing discovered knowledge patterns is association rules. A method for evaluating an association rule from the viewpoint of information theory has been suggested, which allows us to calculate a generalized characteristic of associations (based on mutual information) with the help of the well known association rule parameters: Support, Confidence and Improvement. Using such a characteristic of associations complements the traditional association parameters and allows setting a linear order on the set of associations, which is useful for evaluating and filtering obtained dependencies. Besides we have carried out analysis of the dependence of the association rule self-descriptiveness on the standard parameters.

The existing algorithms for discovering association rules in databases have been developed mainly for binary features (i.e. a feature is either present in a transaction or not). Nevertheless, in real databases it often happens that a feature can take on values from an arbitrary finite set. Such features are considered to be categorical values. In many cases continuous data is binned to obtain a set of discrete values. We suggest an algorithm for discovering generalised association rules in databases containing categorical data. This algorithm is based on building a tree of covers which allows us to generate associations with necessary support, and also to take into account updated records. To discover generalised associations we use a method of merging different branches of the cover tree for given values of a feature. The resulting rules look as follows: if the feature X takes on values from the set {a1,a2,...ai}, then feature Y takes on values from the set {b1,...,bk}. This is beneficial for small discrete feature domains.

The rough set concept is a relatively new mathematical approach to vagueness and uncertainty in data. The rough set theory is a well-understood formal framework for building data mining models in the form of logic rules, on the basis of which it is possible to issue predictions that allow classifying new cases. The indiscernibility relation and approximations based on this relation form the mathematical basis of the rough set theory. The classical topological definitions of rough approximations are based on the indiscernibility relation. Unlike the classical approaches, in this paper we define rough approximations in an algebraic way. We use a set of predicates and predicate operations, which we call the approximation language. We introduce the terms “exact upper approximation” and “exact lower approximation” to stress the fact that there can exist a variety of approximations but it is always possible to select the approximations that cannot be improved in the terms of the approximation language. These new definitions are compared to the classical ones (which use an equivalence relation) and are shown to be more general in the sense that the classical definitions can be deduced from them if we put some restrictions on our model. The process of generating logic rules based on the exact approximations has also been considered. Logic rules are naturally obtained from predicate formulae for the exact approximations. The introduced approach allows generating logic rules quickly and efficiently since only Boolean operations with binary strings are used to produce logic formulae.

Classical topological definitions of rough approximations are based on the indiscernibility relation. Unlike classical approaches in this paper we define rough approximations in an algebraic way. We do not use any binary indiscernibility relation but only unary predicates in terms of which an arbitrary predicate should be described. The terms “exact upper approximation” and “exact lower approximation” have been introduced to stress the fact that there can exist a variety of approximations but it is always possible to select the approximations that cannot be improved in the terms of the approximation language. These new definitions are compared to the classical ones (which use an equivalence relation) and are shown to be more general in the sense that the classical definitions can be deduced from them if we put some restrictions on our model. The process of generating logic rules based on the exact approximations is considered. We also introduce an algebraic definition of a local reduct (a minimal set of predicates describing a rough set) for any subset of the universe.

Expert SystemsVolume 19, Issue 4 p. 244-247 News feature and call for papers Brendan D’Cruz, Brendan D’Cruz University College Northampton, UK,Search for more papers by this authorDmitry Sitnikov, Dmitry Sitnikov Kharkov Academy of Culture, UkraineSearch for more papers by this author Brendan D’Cruz, Brendan D’Cruz University College Northampton, UK,Search for more papers by this authorDmitry Sitnikov, Dmitry Sitnikov Kharkov Academy of Culture, UkraineSearch for more papers by this author First published: 16 December 2002 https://doi.org/10.1111/1468-0394.00209AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume19, Issue4September 2002Pages 244-247 RelatedInformation