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1

Rough Sets: Introduction, History and Selected Applications (Tutorial Lecture — Extended Abstract)

Dutta Soma, Ciucci Davide

Annals of Computer Science and Information Systems

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2023

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Vol. 35

69--70

EN

The aim of this tutorial is to present a brief overview of the theory of rough sets from the perspective of its mathematical foundations, history of development, as well as connections with other branches of mathematics and informatics. The content concerns both the theoretical and practical aspects of applications. The above mentioned target of the tutorial will be covered in two parts. In the first part we would aim to present the introduction to rough sets and the second part will focus on the connections with other branches of mathematics and informatics. In particular, in the second part, we will discuss the connections of rough sets with logics, topology and algebra, and graph theory (when it comes to mathematics), as well as knowledge representation, machine learning and data mining, and theoretical computer science (when it comes to informatics).

2

Reducts in Rough Sets: Algorithmic Insights, Open Source Libraries and Applications (Tutorial – Extended Abstract)

Janusz Andrzej, Stawicki Sebastian

Annals of Computer Science and Information Systems

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2023

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Vol. 35

71--71

EN

The theory of rough sets is a powerful mathematical framework for handling imprecise or uncertain information in data analysis and decision-making. At its core, rough set theory introduces the concept of decision reducts, which are subsets of attributes or features that preserve the essential information needed to make accurate decisions while eliminating redundant or irrelevant information. By identifying ensembles of decision reducts, analysts can simplify complex datasets, improve classification accuracy, and gain valuable insights from noisy or incomplete data. These appealing characteristics make rough sets a valuable tool in various fields, including machine learning, data mining, and expert systems. There have been proposed many extensions to the notion of decision reducts, such as approximate decision reducts, dynamic decision reducts, DAARs, decision bireducts, and many others. The key objective of most of them was to prevent the inclusion of illusionary dependencies between attributes and decision values to the reducts. A lot of research was also committed to the problem of algorithms for the efficient computation of diverse reduct sets. This topic is particularly important from the perspective of practical applications of the rough set theory. In this tutorial, we focus on the latter aspect of the decision reduct-related research. We discuss various, both, well-known and relatively new algorithms, and consider their specific advantages. We explain in detail selected implementation aspects that are crucial for the efficient computation of many types of decision reducts. We also overview and demonstrate libraries in popular programming languages that allow easy computation of reducts on real-world datasets, including RoughSets library for R and a novel Python language library scikit-rough. Finally, we share the results of a study aiming at the comparison of the computational efficiency of various reduct algorithms.

3

Combination of Fuzzy Sets and Rough Sets for Machine Learning Purposes (Tutorial Lecture — Extended Abstract)

Cornelis Chris, Bollaert Henri

Annals of Computer Science and Information Systems

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2023

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Vol. 35

67--67

EN

Fuzzy set theory is a popular AI tool designed to model and process vague information. Specifically, it is based on the idea that membership to a given concept, or logical truthhood of a given proposition, can be a matter of degree. On the other hand, rough set theory was proposed as a way to handle potentially inconsistent data inside information systems. In Pawlak's original proposal, this is achieved by providing a lower and upper approximation of a concept, using the equivalence classes of an indiscernibility relation as building blocks. Noting the highly complementary characteristics of fuzzy sets and rough sets, Dubois and Prade proposed the first working definition of a fuzzy rough set, and thus paved the way for a flourishing hybrid theory with numerous theoretical and practical advances. In this tutorial, we will explain how fuzzy rough sets may be successfully applied to a variety of machine learning problems. After a brief discussion of how the hybridization between fuzzy sets and rough sets may be achieved, including an extension based on ordered weighted average operators, we will focus on the following practical applications: 1. Fuzzy-rough nearest neighbor (FRNN) classification, along with its adaptations for imbalanced datasets and multi-label datasets 2. Fuzzy-rough feature selection (FRFS) 3. Fuzzy-rough instance selection (FRIS) and Fuzzy-rough prototype selection (FRPS) We will also demonstrate software implementations of all of these algorithms in the Python library fuzzy-rough-learn.

4

Performance analysis of rough set–based hybrid classification systems in the case of missing values

Nowicki Robert K., Seliga Robert, Żelasko Dariusz, Hayashi Yoichi

Journal of Artificial Intelligence and Soft Computing Research

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2021

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Vol. 11, No. 4

307--318

EN

The paper presents a performance analysis of a selected few rough set–based classification systems. They are hybrid solutions designed to process information with missing values. Rough set-–based classification systems combine various classification methods, such as support vector machines, k–nearest neighbour, fuzzy systems, and neural networks with the rough set theory. When all input values take the form of real numbers, and they are available, the structure of the classifier returns to a non–rough set version. The performance of the four systems has been analysed based on the classification results obtained for benchmark databases downloaded from the machine learning repository of the University of California at Irvine.

5

Hardware rough set processor parallel architecture in FPGA for finding core in big datasets

Kopczyński Maciej, Grześ Tomasz

Journal of Artificial Intelligence and Soft Computing Research

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2021

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Vol. 11, No. 2

99--110

EN

This paper presents FPGA and softcore CPU based solution for large datasets parallel core calculation using rough set methods. Architectures shown in this paper have been tested on two real datasets running presented solutions inside FPGA unit. Tested datasets had 1 000 to 10 000 000 objects. The same operations were performed in software implementation. Obtained results show the big acceleration in computation time using hardware supporting core generation in comparison to pure software implementation.

6

On Variable Precision Generalized Rough Sets and Incomplete Decision Tables

Syau Yu-Ru, Liau Churn-Jung, Lin En-Bing

Fundamenta Informaticae

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2021

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Vol. 179, nr 1

75--92

EN

We present variable precision generalized rough set approach to characterize incomplete decision tables. We show how to determine the discernibility threshold for a reflexive relational decision system in the variable precision generalized rough set model. We also point out some properties of positive regions and prove a statement of the necessary condition for weak consistency of an incomplete decision table. We present two examples to illustrate the results obtained in this paper.

7

A Novel Ensemble Model - The Random Granular Reflections

Artiemjew Piotr, Ropiak Krzysztof

Fundamenta Informaticae

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2021

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Vol. 179, nr 2

183--203

EN

One of the most popular families of techniques to boost classification are Ensemble methods. Random Forests, Bagging and Boosting are the most popular and widely used ones. This article presents a novel Ensemble Model, named Random Granular Reflections. The algorithm used in this new approach creates an ensemble of homogeneous granular decision systems. The first step of the learning process is to take the training system and cover it with random homogeneous granules (groups of objects from the same decision class that are as little indiscernible from each other as possible). Next, granular reflection is created, which is finally used in the classification process. Results obtained by our initial experiments show that this approach is promising and comparable with other tested methods. The main advantage of our new method is that it is not necessary to search for optimal parameters while looking for granular reflections in the subsequent iterations of our ensemble model.

8

Rough support vector machine for classification with interval and incomplete data

Nowicki Robert K., Grzanek Konrad, Hayashi Yoichi

Journal of Artificial Intelligence and Soft Computing Research

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2020

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Vol. 10, No. 1

47--56

EN

The paper presents the idea of connecting the concepts of the Vapnik’s support vector machine with Pawlak’s rough sets in one classification scheme. The hybrid system will be applied to classifying data in the form of intervals and with missing values [1]. Both situations will be treated as a cause of dividing input space into equivalence classes. Then, the SVM procedure will lead to a classification of input data into rough sets of the desired classes, i.e. to their positive, boundary or negative regions. Such a form of answer is also called a three–way decision. The proposed solution will be tested using several popular benchmarks.

9

Rough sets based on Galois connections

Madrid Nicolás, Medina Jesús, Ramírez-Poussa Eloísa

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 2

299--313

EN

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately, different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.

10

Rough-Fuzzy Circular Clustering for Color Normalization of Histological Images

Maji Pradipta, Mahapatra Suman

Fundamenta Informaticae

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2019

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Vol. 164, nr 1

103--117

EN

Color disagreement among histological images may affect the performance of computer-aided histological image analysis. So, one of the most important and challenging tasks in histological image analysis is to diminish the color variation among the images, maintaining the histological information contained in them. In this regard, the paper proposes a new circular clustering algorithm, termed as rough-fuzzy circular clustering. It integrates judiciously the merits of rough-fuzzy clustering and cosine distance. The rough-fuzzy circular clustering addresses the uncertainty due to vagueness and incompleteness in stain class definition, as well as overlapping nature of multiple contrasting histochemical stains. The proposed circular clustering algorithm incorporates saturation-weighted hue histogram, which considers both saturation and hue information of the given histological image. The efficacy of the proposed method, along with a comparison with other state-of-the-art methods, is demonstrated on publicly available hematoxylin and eosin stained fifty-eight benchmark histological images.

11

Graphical Partitions and Graphical Relations

Shaheen Tanzeela, Stell John G.

Fundamenta Informaticae

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2019

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Vol. 165, nr 1

75--98

EN

We generalize the well-known correspondence between partitions and equivalence relations on a set to the case of graphs and hypergraphs. This is motivated by the role that partitions and equivalence relations play in Rough Set Theory and the results provide some of the foundations needed to develop a theory of rough graphs. We use one notion of a partition of a hypergraph, which we call a graphical partition, and we show how these structures correspond to relations on a hypergraph having additional properties. In the case of a hypergraph with only nodes and no edges these properties are exactly the usual reflexivity, symmetry and transitivity properties required for equivalence relations on a set. We present definitions for upper and lower approximations of a subgraph with respect to a graphical partition. These generalize the well-known approximations in Rough Set Theory. We establish fundamental properties of our generalized approximations and provide examples of these constructions on some graphs.

12

Comparison of Heuristics for Optimization of Association Rules

Alsolami Fawaz, Amin Talha, Moshkov Mikhail, Zielosko Beata, Żabiński Krzysztof

Fundamenta Informaticae

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2019

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Vol. 166, nr 1

1--14

EN

In this paper, seven greedy heuristics for construction of association rules are compared from the point of view of the length and coverage of constructed rules. The obtained rules are compared also with optimal ones constructed by dynamic programming algorithms. The average relative difference between length of rules constructed by the best heuristic and minimum length of rules is at most 4%. The same situation is with coverage.

13

A Classifier Based on a Decision Tree with Temporal Cuts

Bazan Jan G., Szczur Adam, Skowron Andrzej, Rzepko Marian, Król Paweł, Bajorek Wojciech, Czarny Wojciech

Fundamenta Informaticae

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2019

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Vol. 165, nr 3-4

263--281

EN

A new method of decision tree construction from temporal data is proposed in the paper. This method uses the so-called temporal cuts for binary partition of data in tree nodes. The novelty of the proposed approach is that the quality of cuts is calculated not on the basis of the discernibility of objects (related to time points), but on the basis of the discernibility of time windows labeled with different decision classes. The paper includes results of experiments performed on our data sets and collections from machine learning repositories. In order to evaluate the presented method, we compared its performance with the classification results of a local discretization decision tree, and other methods well known from literature. Our new method outperforms these known methods.

14

Operation Properties and Algebraic Application of Covering Rough Sets

Kong Q., Xu W.

Fundamenta Informaticae

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2018

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Vol. 160, nr 4

385--408

EN

Rough set theory is one of the most important tools for data mining. The covering rough set (CRS) model is an excellent generalization of Pawlak rough sets. In this paper, we first investigate a number of basic properties of two types of CRS models. Especially, we study the operation properties of the two types of CRS models with respect to the unary covering. Meanwhile, several corresponding algorithms are constructed for computing the intersection and union of rough sets and some examples are employed to illustrate the effectiveness of these algorithms.Finally, as an application of the operation properties of CRS, some basic algebraic properties of CRS are explored. It is evident that these results will enrich the theory of covering rough sets.

15

Neighborhood Systems : Rough Set Approximations and Definability

Syau Y.-R., Lin E.-B., Liau C.-J.

Fundamenta Informaticae

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2018

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Vol. 159, nr 4

429--450

EN

The notions of approximation and definability in classical rough set theory and their generalizations have received much attention. In this paper, we study such generalizations from the perspective of neighborhood systems. We introduce four different types of definability, called interior definability, closure definability, interior-closure (IC) definability, and weak IC definability respectively. We also point out the relationship between IC definability and other types of definability for some special kinds of neighborhood systems. Several examples are presented to illustrate the concepts introduced in this paper.

16

Selected problems of evaluation and classification of historical buildings using rough sets

Czajkowski K.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2017

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T. 7, nr 4

5--10

EN

The paper presents the problems associated with multicriteria evaluation of historic buildings. The capabilities of modeling the monuments in order to use the Rough Sets approach for their evaluation were presented. The problems of selection criteria for the evaluation and taking into account the structure of the object, as well as the problem of discretization and its impact on the generating of the rules were discussed.

PL

W artykule zaprezentowano problemy związane z wielokryterialną oceną budowli zabytkowych. Przedstawione zostały możliwości modelowania obiektu zabytkowego w celu wykorzystania podejścia Zbiorów Przybliżonych dla ich wartościowania. Omówiono problemy doboru kryteriów oceny oraz uwzględnienia struktury obiektu, jak również problem dyskretyzacji i jego wpływ na generowanie reguł.

17

Neighborhood Systems and Variable Precision Generalized Rough Sets

Syau Y.-R., Lin E.-B., Liau C.-J.

Fundamenta Informaticae

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2017

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Vol. 153, nr 3

271--290

EN

In this paper, we present the connection between the concepts of Variable Precision Generalized Rough Set model (VPGRS-model) and Neighborhood Systems through binary relations. We provide characterizations of lower and upper approximations for VPGRS-model by introducing minimal neighborhood systems. Furthermore, we explore generalizations by investigating variable parameters which are limited by variable precision. We also prove some properties of lower and upper approximations for VPGRS-model.

18

From Leśniewski, Łukasiewicz, Tarski to Pawlak : Enriching Rough Set Based Data Analysis. A Retrospective Survey

Polkowski L. T.

Fundamenta Informaticae

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2017

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Vol. 154, nr 1/4

343--358

EN

This work is dedicated to Profesor Andrzej Ehrenfeucht, the eleve of the Warsaw School of Logic and Mathematics on the occasion of His 85th Birthday. We propose to exploit certain of the milestone ideas created by this School and to apply them to data analysis in the framework of the rough set theory proposed by Professor Zdzisław Pawlak. To wit, we apply the idea of fractional truth states due to Jan Łukasiewicz, mereology created by Stanisław Leśniewski and the betweenness relation used by Alfred Tarski as one of primitive predicates in His axiomatization of Euclidean geometry. These ideas applied in problems of approximate reasoning permit us to formalize calculus of granules of knowledge and use it in preprocessing of data before applying a classification algorithm. Introduction of a mereological version of betweenness relation to data allows for partitioning of data into the kernel and the residuum, both sub-data sets providing a faithful representation of the whole data set and reducing the size of data without any essential loss of accuracy of classification. In the process of algorithmic construction of the partition of data into the kernel and the residuum, we exploit the Dual Indiscernibility Matrix which further allows us to introduce notions of a pair classifier and, more generally, k-classifier yet to be studied.

19

Characterizing Rough Algebras

Umadevi D.

Fundamenta Informaticae

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2017

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Vol. 152, nr 2

167--183

EN

In this paper, a characterization for the class of all rough algebras from the class of all Q-rough algebras is obtained.

20

Optymalizacja częściowych reguł asocjacyjnych względem liczby pomyłek

Zielosko B., Robaszkiewicz M.

Studia Informatica

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2016

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Vol. 37, nr 1

187--198

PL

Artykuł przedstawia optymalizację częściowych reguł asocjacyjnych generowanych przez algorytm zachłanny względem liczby pomyłek (błędnych zaklasyfikowań). Zaproponowana optymalizacja ma na celu: (i) uzyskanie reguł o stosunkowo dobrej jakości, które w kolejnych etapach badań zostaną wykorzystane do budowy klasyfikatorów, (ii) zmniejszenie liczby konstruowanych reguł, co ma znaczenie z punktu widzenia reprezentacji wiedzy. Praca przedstawia wyniki eksperymentalne dla zbiorów danych umieszczonych w Repozytorium Uczenia Maszynowego.

EN

In the paper, an optimization of partial association rules relative to number of misclassifications is presented. The aims of proposed optimization are: (i) construction of rules with small number of misclassifications, what is important from the point of view of construction of classifiers, (ii) decreasing the number of rules, what is important from the point of view of knowledge representation. The paper contains experimental results for data sets from UCI Machine Learning Repository.