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EN
The article presents a system for testing the independence of solutions to algorithmic problems sent by students as part of the student programming competition. First, the context was discussed, as well as the need to organize programming competitions resulting from this context. Then, an algorithm was proposed to study the mutual similarity of source codes of programs sent as part of a programming competition. Since, after implementation, the algorithm was used in practice, examples of its application for detecting the plagiarism of source codes of solutions in two programming competitions conducted as part ofmclasses on Algorithms and Numerical Methods were also presented. Finally, the effectiveness of the solutions used in the work was discussed.
2
Content available remote Generalized Quantifiers in the Context of Rough Set Semantics
EN
Looking back to Prof. Zadeh’s paradigm of Computing withWords (CWW) [28, 29, 30], one can notice that the initial attempt of such an endeavour was to set up a basic vocabulary of linguistic words, and fix their semantics based on fuzzy sets. Then a grammar was proposed to generate compound linguistic expressions based on the primitive ones, and simultaneously based on the semantic interpretations of those basic linguistic expressions a general scheme for the semantics of the rest of linguistic expressions were proposed. Sentences involving linguistic quantifiers and vague predicates constitute a fragment of natural language. In this paper, we choose this fragment of the natural language, and explore the semantics from the perspective of rough sets [13, 14, 16, 17, 18, 21]. We fix a set of basic crisp quantifiers, mainly of proportional kind. A set of vague quantifiers are proposed to lie in a close vicinity of those crisp quantifiers in the sense that a particular vague quantifier can be visualized as a blurred, may be called rough, image of a set of crisp quantifiers. Semantics of the rest of the vague quantifiers can be obtained based on the subjective perception of the interrelations among the (vague) quantifiers.
EN
The article presents the concept of using the theory of similarity in the recognition of medical patterns. The aim of the work is to construct a graphical model of disease entity pattern and the state of the patient's health in such a way as to use natural human ability of perception to identify similarities between them. With this approach, the representation of medical patterns can be used to support the diagnosis process of disease entities.
PL
W artykule przedstawiono koncepcję wykorzystania teorii podobieństwa w rozpoznawaniu wzorców medycznych. Celem prowadzonych prac jest skonstruowanie postaci graficznej wzorca jednostki chorobowej oraz stanu zdrowia pacjenta, w taki sposób, aby wykorzystać naturalne zdolności percepcyjne człowieka do identyfikacji podobieństwa między nimi. Dzięki takiemu podejściu, reprezentacja wzorców medycznych może zostać zastosowana do wsparcia procesu diagnozowania jednostek chorobowych.
PL
W pracy przedstawiona została metoda warunkowego uzupełniania niekompletnych danych dopełnieniami klas podobieństwa.
EN
The problem of the incomplete data is quite common especially in the case of the actual measurement samples. In this connection, it has been vastly commented in the literaturt, especially in the rough set theory. The rough set theory was meant as a tool for imprecise and inconsistent information systems. The aim of this work is to supplement the incomplete data relying on the relations designed to this problem, (similarity and tolerance relation). Basing on the opposite information to the incomplete object we know the area of permitted values for this object. The method proposed in the article works on the assumption that we possess with the opposite information to the supplemented sample in our information system.
5
Content available remote Approximation Spaces Based on Relations of Similarity and Dissimilarity of Objects
EN
In this article, we aim at extension of similarity-based approximation spaces to the case, where both similarity and dissimilarity of objects are taken into account. Apart from the well-known notions of lower rough approximation, upper rough approximation, and variable-precision positive regions of concepts, adapted to our case, the notions of exterior, possibly negative region, and ignorance region of concepts are introduced and investigated.
EN
This paper focuses on approximate reasoning based on the use of similarity spaces. Similarity spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak [17, 18]. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logic which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between approximate relations, similarity spaces and three-valued logics. Using ideas from correspondence theory for modal logics and constraints on an accessibility relation, we develop an analogous framework for three-valued logics and constraints on similarity relations. In this manner, we can provide a tool which helps in determining the proper three-valued logical reasoning engine to use for different classes of approximate relations generated via specific types of similarity spaces. Additionally, by choosing a three-valued logic first, the framework determines what constraints would be required on a similarity relation and the approximate relations induced by it. Such information would guide the generation of approximate relations for specific applications.
7
Content available remote On Rough Set Logics Based on Similarity Relations
EN
In this paper, dedicated to Professor Solomon Marcus on the occasion of His 80th birthday, we discuss the idea of intensional many-valued logic reflecting the logical content of rough set approach to analysis and treatment of uncertainty. In constructing the variety of logics presented in the paper, we make use of a certain kind of tolerance (similarity) relations called rough mereological tolerances. A study of tolerance relations that arise in rough set environments was initiated in 1994, with the paper [23], in which basic ideas pertaining to tolerance relations in the rough set framework were pointed to. The analysis of the role tolerance relations may play in machine learning based on rough set-theoretic ideas was carried out by Professor Solomon Marcus in His seminal paper, written during His stay in Warsaw in December of the year 1994. At the same time the first author had first ideas related to the applicability of ideas of mereology in the rough set analysis of uncertainty. In a later analysis it has turned out that mereological approach has led to a development of a new paradigm in reasoning under uncertainty, called rough mereology, proposed by Lech Polkowski and Andrzej Skowron. Within this paradigm, one is able to construct a variety of tolerance relations. Those tolerance relations, induced by rough mereological constructs called rough inclusions, serve as a basis for constructing a variety of logics, called rough mereological logics, that are related to the inherent structure of any rough set universe. In this paper, we introduce gradually all essential and necessary notions from the area of rough set theory, mereology and rough mereology, and then we discuss tolerance relations induced by rough inclusions along with some methods for inducing rough inclusions with desired properties. The paper culminates with a discussion of intensional logics based on rough mereological tolerance relations. In this way, we explore one of so many paths in scientific research, that have been either pointed to or threaded by Professor Solomon Marcus.
8
Content available remote Reducts and Constructs in Attribute Reduction
EN
One of the main notions in the Rough Sets Theory (RST) is that of a reduct. According to its classic definition, the reduct is a minimal subset of the attributes that retains some important properties of the whole set of attributes. The idea of the reduct proved to be interesting enough to inspire a great deal of research and resulted in introducing various reduct-related ideas and notions. First of all, depending on the character of the attributes involved in the analysis, so called absolute and relative reducts can be defined. The more interesting of these, relative reducts, are minimal subsets of attributes that retain discernibility between objects belonging to different classes. This paper focuses on the topological aspects of such reducts, identifying some of their limitations and introducing alternative definitions that do not suffer from these limitations. The modified subsets of attributes, referred to as constructs, are intended to assist the subsequent inductive process of data generalisation and knowledge acquisition, which, in the context of RST, usually takes the form of decision rule generation. Usefulness of both reducts and constructs in this role is examined and evaluated in a massive computational experiment, which was carried out for a collection of real-life data sets.
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