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1

Positive regions of computable binary relations

Wu Huishan

Reports on Mathematical Logic

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2025

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Vol. 60

47--65

EN

Positive region plays a fundamental role in rough set-based attribute reduction. We study positive regions of decision systems and of binary relations in rough set theory within the framework of reverse mathematics and computability theory. First, we propose the notion of infinite decision systems and prove that the existence of positive regions of decision systems is equivalent to arithmetic comprehension over the weak base theory RCA0. We also show that the complexity of positive regions of computable decision systems lies exactly in Π02 of the arithmetic hierarchy. Next, we study positive regions of equivalence relations and binary relations. We show that the existence of each of the two positive regions is equivalent to arithmetic comprehension over RCA0; however, the exact complexity of positive regions of computable equivalence relations lies in Π01 and the exact complexity of positive regions of computable binary relations lies in Σ02 of the arithmetic hierarchy.

2

Analiza zbioru danych dotyczących oceny akceptowalności samochodów za pomocą teorii zbiorów przybliżonych i programu RSES

Gorączka Mateusz

Studia i Materiały Informatyki Stosowanej

|

2024

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T. 16, nr 1

24--32

PL

Artykuł skupia się na analizie danych z wykorzystaniem teorii zbiorów przybliżonych oraz różnych metod, takich jak algorytm genetyczny, klasyfikacja za pomocą zestawu reguł i metoda walidacji krzyżowej. Przedstawiono także kompletny proces analizy danych przy użyciu programu RSES. Wykorzystany zbiór danych oraz wyniki analizy zostałyomówione w kontekście teorii zbiorów przybliżonych. Artykuł kończy się podsumowaniem i wnioskamiskupiającymi się na aspekcie skuteczności wspomnianych metod w analizie zbioru danych oraz efektywności programu w kwestii przeprowadzania w nim analiz.

EN

The article focuses on data analysis using rough set theory and various methods such as the genetic algorithm, rule set classification and the cross-validation method. The complete data analysis process using RSES is also presented. The data set used and the results of the analysis are discussed in the context of rough set theory. The article concludes with a summary and conclusions focusing on the aspect of the effectiveness of aforementioned methods in analysing the dataset and the efficiency of the programin terms of performing analysis in it.

3

Two-dimensional hydrodynamic modeling for prediction of bank erosion and bed incision in the Indus River

Boota Muhammad Waseem, Yan Chaode, Soomro Shan-e-hyder, Zafar Muhammad Awais, Li Ziwei, Xu Jikun, Yousaf Ayesha

Acta Geophysica

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2024

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Vol. 72, no. 3

2041--2058

EN

The Lower Indus River (LIR) in the Southern Sindh has experienced by multiple measurable changes in its planform and longitudinal profiles over the last 100 years. This research deals with a hydrodynamic model coupled with rough set theory (RST) model findings that accounts for the prediction of lateral and vertical morphodynamic evolution observed over the 32 km reach during the flood episode of 2020. Human interferences and hydrodynamic aspects during high flood periods were assessed in the context of channel morphology. Surveyed cross-sections were used to construct the geometry using two-dimensional (2D) Hydrologic Engineering Center's River Analysis System (HEC-RAS) model, and simulation was completed under the unsteady flow values among the highest runoff and bankfull values. The island and natural bend of the river have higher values of velocities and shear stresses, and consequently higher erosion and incision rate was observed. The bank erosion was computed with high precision (R2 = 0.83) based on improved connection of erodibility coefficient and excess shear stress technique. The present study findings will be helpful to assist in the implementation of river protection works at the given locations of Indus River and will serve as a framework for similar river reaches.

4

Metody szacowania wskaźnika nagromadzenia odpadów służącego do określenia lokalnego potencjału energetycznego z odpadów komunalnych na terenie gmin w Polsce

Nęcka Krzysztof, Szul Tomasz

Przegląd Elektrotechniczny

|

2022

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R. 98, nr 12

258--261

PL

W pracy sprawdzono przydatność wybranych metod prognostycznych do szacowania lokalnego wskaźnika ilości generowanych odpadów komunalnych a tym samym potencjału energetycznego odpadów, które będą mogły być wykorzystane w instalacjach termicznego przetwarzania odpadów. Prognozy stawiano w oparciu o metody: sztucznych sieci neuronowych (ANN), drzewa regresyjne (CART), wielozmienną regresję adaptacyjną z użyciem funkcji sklejanych (MARS), losowy las dla regresji (RFR), teorii zbiorów przybliżonych (RST), wzmacniane drzewa regresyjne (SRT) a także metody kombinowane będące połączeniem kilku metod prognostycznych.

EN

In this paper, the usefulness of selected forecasting methods was tested to estimate the local rate of municipal waste generation, and thus the energy potential of waste, which can be utilised in thermal waste treatment plants. Forecasts were made on the basis of the following methods: artificial neural networks (ANN), regression trees (CART), multivariate adaptive regression with glued functions (MARS), random forest for regression (RFR), rough set theory (RST), boosted regression trees (SRT), and combined methods which are a combination of several forecasting methods.

5

Rule modeling of ADI cast iron structure for contradictory data

Soroczyński Artur, Biernacki Robert, Kochański Andrzej

Computer Methods in Materials Science

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2022

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Vol. 22, No. 4

211--228

EN

Ductile iron is a material that is very sensitive to the conditions of crystallization. Due to this fact, the data on the cast iron properties obtained in tests are significantly different and thus sets containing data from samples are contradictory, i.e. they contain inconsistent observations in which, for the same set of input data, the output values are significantly different. The aim of this work is to try to determine the possibility of building rule models in conditions of significant data uncertainty. The paper attempts to determine the impact of the presence of contradictory data in a data set on the results of process modeling with the use of rule-based methods. The study used the well-known dataset (Materials Algorithms Project Data Library, n.d.) pertaining to retained austenite volume fraction in austempered ductile cast iron. Two methods of rulebased modeling were used to model the volume of the retained austenite: the decision trees algorithm (DT) and the rough sets algorithm (RST). The paper demonstrates that the number of inconsistent observations depends on the adopted data discretization criteria. The influence of contradictory data on the generation of rules in both algorithms is considered, and the problems that can be generated by contradictory data used in rule modeling are indicated.

6

A Detailed Study of the Distributed Rough Set Based Locality Sensitive Hashing Feature Selection Technique.

Chelly Dagdia Zaineb, Zarges Christine

Fundamenta Informaticae

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2021

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Vol. 182, nr 2

111--179

EN

In the context of big data, granular computing has recently been implemented by some mathematical tools, especially Rough Set Theory (RST). As a key topic of rough set theory, feature selection has been investigated to adapt the related granular concepts of RST to deal with large amounts of data, leading to the development of the distributed RST version. However, despite of its scalability, the distributed RST version faces a key challenge tied to the partitioning of the feature search space in the distributed environment while guaranteeing data dependency. Therefore, in this manuscript, we propose a new distributed RST version based on Locality Sensitive Hashing (LSH), named LSH-dRST, for big data feature selection. LSH-dRST uses LSH to match similar features into the same bucket and maps the generated buckets into partitions to enable the splitting of the universe in a more efficient way. More precisely, in this paper, we perform a detailed analysis of the performance of LSH-dRST by comparing it to the standard distributed RST version, which is based on a random partitioning of the universe. We demonstrate that our LSH-dRST is scalable when dealing with large amounts of data. We also demonstrate that LSH-dRST ensures the partitioning of the high dimensional feature search space in a more reliable way; hence better preserving data dependency in the distributed environment and ensuring a lower computational cost.

7

Application of machine learning and rough set theory in lean maintenance decision support system development

Antosz Katarzyna, Jasiulewicz-Kaczmarek Małgorzata, Paśko Łukasz, Zhang Chao, Wang Shaoping

Eksploatacja i Niezawodność

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2021

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Vol. 23, no. 4

695--708

EN

Lean maintenance concept is crucial to increase the reliability and availability of maintenance equipment in the manufacturing companies. Due the elimination of losses in maintenance processes this concept reduce the number of unplanned downtime and unexpected failures, simultaneously influence a company’s operational and economic performance. Despite the widespread use of lean maintenance, there is no structured approach to support the choice of methods and tools used for the maintenance function improvement. Therefore, in this paper by using machine learning methods and rough set theory a new approach was proposed. This approach supports the decision makers in the selection of methods and tools for the effective implementation of Lean Maintenance.

8

Benefit evaluation of energy-saving and emission reduction in construction industry based on rough set theory

Zhong Zhengjun, Zhang Xin, Yang Xudong

Ecological Chemistry and Engineering. S

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2021

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Vol. 28, nr 1

61--73

EN

Achieving energy conservation and emission reduction in the industry is an inevitable way to promote harmony between society and nature and achieve sustainable human development. China’s infrastructure construction industry is developing rapidly. Still, there is a lack of a well-established industry standard for evaluating the potential and level of energy reduction in infrastructure construction. A severe lack of quantitative research on energy-saving and CO2 outflow decreases the benefits of green development advances. This study takes the energy conservation and outflow decrease of construction waste slurry treatment in Guangdong Province, China, as the background, establishes an evaluation system with three rule levels: social, economic, and environmental, and adopts rough set theory to determine the weights of each index to ensure the objectivity of each index. According to the recommendations of the carbon emission calculation guidelines, select the relevant data to evaluate the energy-saving and emission reduction benefits of the new green construction technology of grouted piles in a road project in Guangdong Province. The results show that the development level and potential of energy saving and emission reduction technology in the construction sector in Guangdong Province are increasing year by year. It’s potential changes with the increase or decrease of highway mileage, and it is an urgent need to increase investment in pollution control. The research results can evaluate the benefits of energy-saving and carbon dioxide emission reduction in the construction industry，also be used as a reference to assess energy-saving and emission reduction in the construction industry in other countries.

9

The use of rough rules in the selection of topographic objects for generalizing geographical information

Fiedukowicz Anna

Polish Cartographical Review

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2020

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Vol. 52, No. 1

1--15

EN

Selection is a key element of the cartographic generalisation process, often being its first stage. On the other hand it is a component of other generalisation operators, such as simplification. One of the approaches used in generalization is the condition-action approach. The author uses a condition-action approach based on three types of rough logics (Rough Set Theory (RST), Dominance-Based Rough Set Theory (DRST) and Fuzzy-Rough Set Theory (FRST)), checking the possibility of their use in the process of selecting topographic objects (buildings, roads, rivers) and comparing the obtained results. The complexity of the decision system (the number of rules and their conditions) and its effectiveness are assessed, both in terms of quantity and quality – through visual assessment. The conducted research indicates the advantage of the DRST and RST approaches (with the CN2 algorithm) due to the quality of the obtained selection, the greater simplicity of the decision system, and better refined IT tools enabling the use of these systems. At this stage, the FRST approach, which is characterised by the highest complexity of created rules and the worst selection results, is not recommended. Particular approaches have limitations resulting from the need to select appropriate measurement scales for the attributes used in them. Special attention should be paid to the selection of network objects, in which the use of only a condition-action approach, without maintaining consistency of the network, may not produce the desired results. Unlike approaches based on classical logic, rough approaches allow the use of incomplete or contradictory information. The proposed tools can (in their current form) find an auxiliary use in the selection of topographic objects, and potentially also in other generalisation operators.

10

From Data to Pattern Structures : Near Set Approach

Wolski Marcin, Gomolińska Anna

Fundamenta Informaticae

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2019

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Vol. 165, nr 3-4

363--380

EN

Pattern structures were introduced by Ganter and Kuznetsov in the framework of formal concept analysis (FCA) as a mean to direct analysis of objects having complex descriptions, e.g., descriptions presented in the form of graphs instead of a set of properties. Pattern structures actually generalise/replace the original FCA representation of the initial information about objects, that is, formal contexts (which form a special type of data tables); as a consequence, pattern structures are regarded in FCA as given (in some sense a priori to the analysis) rather than built (a posteriori) from data. The main goal of this paper is twofold: firstly, we would like to export the idea of pattern structures to and consistently with the framework/methodology of rough set theory (RST); secondly, we want to derive pattern structures from simple data tables rather than to regard them as the initial information about objects. To this end we present and discuss two methods of generating non-trivial pattern structures from simple information systems/tables. Both methods are inspired by near set theory, which is a methodology theoretically close to rough set theory, but developed in the topological settings of (descriptive) nearness of sets. Interestingly, these methods bear formal connections to other ideas from RST such as generalised decisions or symbolic value grouping.

11

Algebras of Definable Sets vs. Concept Lattices

Wasilewski Piotr

Fundamenta Informaticae

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2019

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Vol. 167, nr 3

235--256

EN

The paper is aimed at comparing Rough Set Theory (RST) and Formal Concept Analysis (FCA) with respect to algebraic structures of concepts appearing in both theories, namely algebras of definable sets and concept lattices. The paper presents also basic ideas and concepts of RST and FCA together with some set theoretical concepts connected with set spaces which can serve as a convenient platform for a comparison of RST and FCA. In the last section there are shown necessary and sufficient conditions for the fact, that families of definable sets and concept extents determined by the same formal contexts are equal. This in finite cases is equivalent to an isomorphism of respective structures and generally reflects a very specific situation when both theories give the same conceptual hierarchies.

12

Information granule system induced by a perceptual system

Bryniarska Anna

Annals of Computer Science and Information Systems

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2019

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Vol. 18

19--27

EN

Knowledge represented in the semantic network, especially in the Semantic Web, can be expressed in attributive language AL. Expressions of this language are interpreted in different theories of information granules: set theory, probability theory, possible data sets in the evidence systems, shadowed sets, fuzzy sets or rough sets. In order to unify the interpretations of expressions for different theories, it is assumed that expressions of the AL language can be interpreted in a chosen relational system called a granule system. In this paper, it is proposed to use information granule database and it is also demonstrated that this database can be induced by the measurement system of the adequacy of information retrieval, called a perceptual system. It can simplify previous formal description of the information granule system significantly. This paper also shows some examples of inducing rough and fuzzy granule databases by some perceptual systems.

13

Slime mould games based on rough set theory

Pancerz K., Schumann A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

531--544

EN

We define games on the medium of plasmodia of slime mould, unicellular organisms that look like giant amoebae. The plasmodia try to occupy all the food pieces they can detect. Thus, two different plasmodia can compete with each other. In particular, we consider game-theoretically how plasmodia of Physarum polycephalum and Badhamia utricularis fight for food. Placing food pieces at different locations determines the behavior of plasmodia. In this way, we can program the plasmodia of Physarum polycephalum and Badhamia utricularis by placing food, and we can examine their motion as a Physarum machine—an abstract machine where states are represented as food pieces and transitions among states are represented as movements of plasmodia from one piece to another. Hence, this machine is treated as a natural transition system. The behavior of the Physarum machine in the form of a transition system can be interpreted in terms of rough set theory that enables modeling some ambiguities in motions of plasmodia. The problem is that there is always an ambiguity which direction of plasmodium propagation is currently chosen: one or several concurrent ones, i.e., whether we deal with a sequential, concurrent or massively parallel motion. We propose to manage this ambiguity using rough set theory. Firstly, we define the region of plasmodium interest as a rough set; secondly, we consider concurrent transitions determined by these regions as a context-based game; thirdly, we define strategies in this game as a rough set; fourthly, we show how these results can be interpreted as a Go game.

14

Implementation of the attribute significance analysis with the use of soft reduction of attributes in the rough set theory on the basis of the SQL mechanisms

Nozdrzykowski Ł., Nozdrzykowska M.

Measurement Automation Monitoring

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2017

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Vol. 63, No. 1

10--14

EN

This article presents a way to use databases supporting the SQL and PL/SQL in the implementation of a method of attribute significance analysis with the use of soft reduction of attributes in the rough set theory. A number of SQL queries are presented, which facilitate the implementation. The original mechanisms presented previously [1] are supplemented with queries which facilitate the execution of attribute coding. The authors present a complete implementation of the method, from the coding of attributes to the determination of the significance of conditional attributes. Application of queries to the database eliminates the necessity to build data grouping and data mining mechanisms and calculation of repetitions of identical rules in the reduced decision rule space. Without the support of a database, the creation of universal data grouping and data mining mechanisms which could be used with any number of attributes is a challenging task.

15

Rough Set Theory and Digraphs

Chiaselotti G., Ciucci D., Gentile T., Infusino F.

Fundamenta Informaticae

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2017

|

Vol. 153, nr 4

291--325

EN

In this paper we apply rough set theory to information tables induced from finite directed graphs without loops and multiples arcs (digraphs). Specifically, we use the adjacency matrix of a digraph as a particular type of information table. In this way, we are able to explore on digraphs the notions of indiscernibility partitions, lower and upper approximations, generalized core, reducts and discernibility matrix. All these ideas will be exemplified on standard digraph families as well on examples from social networks and patterns of flight routes between airports.

16

Application of rough set theory to establish the amount of waste in households in rural areas

Szul T., Knaga J., Nęcka K.

Ecological Chemistry and Engineering. S

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2017

|

Vol. 24, nr 2

311--325

EN

The method based on rough set theory (RST) was used in the study to establish the rate of mass accumulation of waste in households in rural areas, which are characterised by different economic types, in case of which traditional statistical analyses are usually hardy reliable. The following indicators available in the General Statistical Office’s statistics were used in the analysis: population density, income level, main source of income, economic type of the municipality, area of agricultural land, age of the buildings and participation of gaseous fuels in meeting heat demands. The method shown should not be considered as a competition for statistical methods, but it could complement them, especially in cases when there are few objects to analyse, the more so as it proves useful in cases where input data are general, imprecise and uncertain. As has been shown in the study, with such data and a small number of objects, the relative error of estimation was 13% on average.

17

The use of SQL as a tool supporting the implementation of a method of attribute significance analysis based on soft reduction of attributes in the rough set theory

Nozdrzykowski Ł., Wróbel M.

TTS Technika Transportu Szynowego

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2016

|

R. 23, nr 12

172--176

EN

The article presents a way to quickly implement a method of analyzing the significance of attributes by using soft reduction of conditional attributes in the rough set theory. The analysis is a universal instrument for testing the significance of attributes and may be successfully used in many fields, including transport. It uses the rules that can be considered useful and allows reducing those attributes that do not cause a significant decrease in the number of rules generating entirely certain rules. At the same time it is a rapid mechanism of analyzing large data sets such as encoded attributes of rules. For implementation purposes we propose to use the mechanisms of modern relational databases and the capabilities presently offered by the SQL language, including its expansion with conditional CASE queries.

PL

W artykule przedstawiono sposób na szybką implementację metody analizy istotności atrybutów poprzez wykorzystanie miękkiej redukcji atrybutów warunkowy w teorii zbiorów przybliżonych. Analiza ta wykorzystuje reguły, które można uznać za użyteczne i pozwala na redukcję atrybutów, które nie powodują znacznego spadku liczby reguł generujących całkowicie pewne reguły. Jest przy tym szybkim mechanizmem analizy dużych zbiorów danych jakim są zakodowane atrybuty reguł. Do celów implementacyjnych zaproponowano wykorzystanie mechanizmów współczesnych relacyjnych baz danych oraz możliwości jakie obecnie daje język SQL, w tym rozbudowanie go o zapytania warunkowe typu CASE.

18

Mining Rule-based Knowledge Bases Inspired by Rough Set Theory

Nowak-Brzezińska A.

Fundamenta Informaticae

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2016

|

Vol. 148, nr 1/2

35--50

EN

Rule-based knowledge bases are constantly increasing in volume, thus the knowledge stored as a set of rules is getting progressively more complex and when rules are not organized into any structure, the system is inefficient. The aim of this paper is to improve the performance of mining knowledge bases by modification of both their structure and inference algorithms, which in author’s opinion, lead to improve the efficiency of the inference process. The good performance of this approach is shown through an extensive experimental study carried out on a collection of real knowledge bases. Experiments prove that rules partition enables reducing significantly the percentage of the knowledge base analysed during the inference process. It was also proved that the form of the group’s representative plays an important role in the efficiency of the inference process.

19

Zastosowanie teorii zbiorów przybliżonych do analizy wyników badań emisji jonów metali w endoprotezach stawu biodrowego

Wiśniewski T., Libera M.

Tribologia

|

2015

|

nr 4

207--219

PL

Celem pracy była ocena przydatności teorii zbiorów przybliżonych w analizie zużycia endoprotez. W pracy wyodrębnić można dwie zasadnicze części: w pierwszej opisano badania tribologiczne endoprotez stawu biodrowego, natomiast w drugiej dokonano analizy wyników tych badań, wykorzystując metodę generowania reguł decyzyjnych w oparciu o teorię zbiorów przybliżonych. W efekcie stwierdzono, że wygenerowane reguły decyzyjne nie są sprzeczne z aktualnym stanem wiedzy, a zaproponowana metoda analizy może być przydatna w analizie tego rodzaju zagadnień.

EN

The aim of the study was to evaluate the usefulness of rough set theory in the analysis of endoprosthesis wear. In the article, two main parts can be distinguished: the first describes the tribological study of hip endoprosthesis, while the second analyses the results of these tests using the method of generating decision rules based on rough set theory. There were generated two sets of decision rules describing the impact of roughness, friction, wear and the angle of the prosthesis head on the chromium, and cobalt ions emission. As a result, it was found that the generated decision rules are consistent with the current state of knowledge, and the proposed method of analysis may be useful in the analysis of such issues.

20

Analysis of the significance of model parameters for program loop execution time estimation

Nozdrzykowski Ł., Wróbel M.

Przegląd Elektrotechniczny

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2015

|

R. 91, nr 12

237-239

EN

Models for estimating execution times of parallel program loops are discussed. The significance of parameters used for such estimation is analyzed. The significance analysis permits to determine the validity of parameters selected for estimation and to identify low significance parameters that may be eliminated.

PL

W artykule przedstawiono modele szacowania czasów wykonywania się pętli programowych w formie zrównoleglonej oraz przedstawiono analizę istotności parametrów stosowanych do tego szacowania. Analiza istotności pozwala określić trafność doboru poszczególnych parametrów oraz wskazać parametry o niskiej istotności, które można byłoby zredukować.