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1

Siting hydropower plant by rough set and combinative distance-based assessment

Agwa Ahmed Mahmoud, Shaaban Shaaban Mohamed

Przegląd Elektrotechniczny

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2021

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R. 97, nr 3

15--20

EN

Each power plant (PP) is solo entity whose construction site is determined by different criteria in accordance with some physical rules. Latterly, great importance is provided to siting PP in inexact surroundings. Multiple-criteria decision-making for the proper location of the PP construction is relevant. The objective of this research is to create a model for decision-makers to rank available sites for installing hydropower plant (HPP) in accordance with multiple-criteria attributes e.g. accessibility to electrical grid, power potential, economical respects, environmental influence, topography, and natural hazards. In this research, a novel application of a hybrid approach that employs rough set theory (RST) and combinative distance-based assessment (CODAS) method is proposed to prioritize available locations for installing HPP. Firstly, the strength of RST is adopted to get minimal attributes reduction set. Secondly, the relative weights of minimal attributes are determined using RST. Finally, CODAS technique is utilized to calculate the rank of alternatives. The comparison between the proposed method-based results and the results without attributes reduct, proves that the proposed method saves the time and energy.

PL

Zaproponowano nowatorskie zastosowanie podejścia hybrydowego, które wykorzystuje teorię zbiorów przybliżonych (RST) i metodę oceny kombinowanej opartej na odległości (CODAS) w celu ustalenia priorytetów dostępnych lokalizacji do zainstalowania elektrowni wodnej (HPP) zgodnie z atrybutami wielokryterialnymi, np. dostępność do sieci elektrycznej, potencjał energetyczny, aspekty ekonomiczne, wpływ środowiska, topografia i zagrożenia naturalne.

2

A New Description of Transversal Matroids Through Rough Set Approach

Wang Zhaohao

Fundamenta Informaticae

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2021

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Vol. 179, nr 4

399-416

EN

Matroid theory is a useful tool for the combinatorial optimization issue in data mining, machine learning and knowledge discovery. Recently, combining matroid theory with rough sets is becoming interesting. In this paper, rough set approaches are used to investigate an important class of matroids, transversal matroids. We first extend the concept of upper approximation number functions in rough set theory and propose the notion of generalized upper approximation number functions on a set system. By means of the new notion, we give some necessary and sufficient conditions for a subset to be a partial transversal of a set system. Furthermore, we obtain a new description of a transversal matroid by the generalized upper approximation number function. We show that a transversal matroid can be induced by the generalized upper approximation number function which can be decomposed into the sum of some elementary generalized upper approximation number functions. Conversely, we also prove that a generalized upper approximation number function can induce a transversal matroid. Finally, we apply the generalized upper approximation number function to study the relationship among transversal matroids.

3

Near Approximations in Modules

Davvaz Bijan, Setyawati Dian Winda, Soleha, Mukhlash Imam, Subiono

Foundations of Computing and Decision Sciences

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2021

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Vol. 46, No. 4

319--337

EN

Rough set theory is a mathematical approach to imperfect knowledge. The near set approach leads to partitions of ensembles of sample objects with measurable information content and an approach to feature selection. In this paper, we apply the previous results of Bagirmaz [Appl. Algebra Engrg. Comm. Comput., 30(4) (2019) 285-29] and [Davvaz et al., Near approximations in rings. AAECC (2020). https://doi.org/10.1007/s00200-020-00421-3] to module theory. We introduce the notion of near approximations in a module over a ring, which is an extended notion of a rough approximations in a module presented in [B. Davvaz and M. Mahdavipour, Roughness in modules, Information Sciences, 176 (2006) 3658-3674]. Then we define the lower and upper near submodules and investigate their properties.

4

Data irregularities in discretisation of test sets used for evaluation of classification systems: A case study on authorship attribution

Stańczyk Urszula, Zielosko Beata

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 4

art. no. e137629

EN

When patterns to be recognised are described by features of continuous type, discretisation becomes either an optional or necessary step in the initial data pre-processing stage. Characteristics of data, distribution of data points in the input space, can significantly influence the process of transformation from real-valued into nominal attributes, and the resulting performance of classification systems employing them. If data include several separate sets, their discretisation becomes more complex, as varying numbers of intervals and different ranges can be constructed for the same variables. The paper presents research on irregularities in data distribution, observed in the context of discretisation processes. Selected discretisation methods were used and their effect on the performance of decision algorithms, induced in classical rough set approach, was investigated. The studied input space was defined by measurable style-markers, which, exploited as characteristic features, facilitate treating a task of stylometric authorship attribution as classification.

5

Ant-based clustering for flow graph mining

Lewicki Arkadiusz, Pancerz Krzysztof

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 3

561--572

EN

The paper is devoted to the problem of mining graph data. The goal of this process is to discover possibly certain sequences appearing in data. Both rough set flow graphs and fuzzy flow graphs are used to represent sequences of items originally arranged in tables representing information systems. Information systems are considered in the Pawlak sense, as knowledge representation systems. In the paper, an approach involving ant based clustering is proposed. We show that ant based clustering can be used not only for building possible large groups of similar objects, but also to build larger structures (in our case, sequences) of objects to obtain or preserve the desired properties.

6

The Structure of Multigranular Rough Sets

Järvinen Jouni, Radeleczki Sándor

Fundamenta Informaticae

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2020

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Vol. 176, nr 1

17--41

EN

We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called “optimistic” and “pessimistic” multigranular approximation systems are given. We also consider the ordered sets of rough sets determined by these approximation pairs.

7

Comparison of Different Data Mining Methods to Determine Disease Progression in Dissimilar Groups of Parkinson’s Patients

Przybyszewski Andrzej W., Chudzik Artur, Szlufik Stanisław, Habela Piotr, Koziorowski Dariusz M.

Fundamenta Informaticae

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2020

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Vol. 176, nr 2

167--181

EN

Parkinson’s disease (PD) is the second after Alzheimer’s most popular neurodegenerative disease (ND). Cures for both NDs are currently unavailable. OBJECTIVE: The purpose of our study was to predict the results of different PD patients’ treatments in order to find an optimal one. METHODS: We have compared rough sets (RS) and others, in short, machine learning (ML) models to describe and predict disease progression expressed as UPDRS values (Unified Parkinson’s Disease Rating Scale) in three groups of Parkinson’s patients: 23 BMT (Best Medical Treatment) patients on medication; 24 DBS patients on medication and on DBS therapy (Deep Brain Stimulation) after surgery performed during our study; and 15 POP (Postoperative) patients who had had surgery earlier (before the beginning of our research). Every PD patient had three visits approximately every six months. The first visit for DBS patients was before surgery. On the basis of the following condition attributes: disease duration, saccadic eye movement parameters, and neuropsychological tests: PDQ39 (Parkinson’s Disease Questionnaire - disease-specific health-related quality-of-life questionnaire), and Epworth Sleepiness Scale tests we have estimated UPDRS changes (as the decision attribute). RESULTS: By means of RS rules obtained for the first visit of BMT/DBS/POP patients, we have predicted UPDRS values in the following year (two visits) with global accuracy of 70% for both BMT visits; 56% for DBS, and 67%, 79% for POP second and third visits. The accuracy obtained by ML models was generally in the same range, but it was calculated separately for different sessions (MedOFF/MedON). We have used RS rules obtained in BMT patients to predict UPDRS of DBS patients; for the first session DBSW1: global accuracy was 64%, for the second DBSW2: 85% and the third DBSW3: 74% but only for DBS patients during stimulation-ON. ML models gave better accuracy for DBSW1/W2 session S1(MedOFF): 88%, but inferior results for session S3 (MedON): 58% and 54%. Both RS and ML could not predict UPDRS in DBS patients during stimulation-OFF visits because of differences in UPDRS. By using RS rules from BMT or DBS patients we could not predict UPDRS of POP group, but with certain limitations (only for MedON), we derived such predictions for the POP group from results of DBS patients by using ML models (60%). SIGNIFICANCE: Thanks to our RS and ML methods, we were able to predict Parkinson’s disease (PD) progression in dissimilar groups of patients with different treatments. It might lead, in the future, to the discovery of universal rules of PD progression and optimise the treatment.

8

Linking Reaction Systems with Rough Sets

Dutta Soma, Rozenberg Grzegorz, Jankowski Andrzej, Skowron Andrzej

Fundamenta Informaticae

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2019

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Vol. 165, nr 3-4

283--302

EN

Reaction system is a model of interactive computations which was motivated by the functioning of the living cell. It is an idealized mathematical model, also because it abstracts from the complex nature of the physical systems where only partial, incomplete information is available (e.g., about their states). The framework of rough sets was developed to deal with such incomplete information. In this paper we establish a connection between reaction systems and rough sets. This is done in a somewhat broader perspective of the relationship between “pure” mathematical models and “realistic models” that take into account the limitation of perceiving physical reality.

9

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.

10

Rough Sets and Sorites Paradox

Jankowski A., Skowron A., Wasilewski P.

Fundamenta Informaticae

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2018

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Vol. 157, nr 4

371--384

EN

We discuss the rough set approach to approximation of vague concepts. There are already published several papers on rough sets and vague concepts staring from the seminal papers by Zdzisław Pawlak. However, only a few of them are discussing the relationships of rough sets with the sorites paradox. This paper contains a continuation of discussion on this issue.

11

Rough Fuzzy Concept Analysis

Bartl E., Konecny J.

Fundamenta Informaticae

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2017

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Vol. 156, nr 2

141--168

EN

We provide a new approach to fusion of Fuzzy Formal Concept Analysis and Rough Set Theory. As a starting point we take into account a couple of fuzzy relations, one of them represents the lower approximation, while the other one the upper approximation of a given data table. By defining appropriate concept-forming operators we transfer the roughness of the input data table to the roughness of corresponding formal fuzzy concepts in the sense that a formal fuzzy concept is considered as a collection of objects accompanied with two fuzzy sets of attributes— those which are shared by all the objects and those which at least one object has. In the paper we study the properties of such formal concepts and show their relationship with concepts formed by well-known isotone and antitone operators.

12

Interactive Logical Structures

Dutta S., Jankowski A., Skowron A.

Fundamenta Informaticae

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2017

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Vol. 154, nr 1/4

95--108

EN

We present an extension of logical structures, called interactive logical structures, for reasoning about interactive computations performed by Intelligent Systems or Complex Adaptive Systems. Reasoning based on such structures is called adaptive judgment and it goes beyond deduction, induction, and abduction. An extension of logical structures, based on complex granules, couples the abstract world and the physical world of an agent’s environment, and transmits the features of interactions of physical objects realized in the physical world to the abstract world. This allows us to consider the problems of perception and action.

13

Rough Sets and Interactive Granular Computing

Skowron A., Jankowski A.

Fundamenta Informaticae

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2016

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Vol. 147, nr 2/3

371--385

EN

In several papers we have discussed a computing model, called the Interactive Granular Computing (IGrC), for interactive computations on complex granules. In this paper, we compare two models of computing, namely the Turing model and the IGrC model.

14

Rough Approximation Operators in Group Mapping and Their Applications to Coding Theory

Xu J., Qiu R., Tao Z.

Fundamenta Informaticae

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2016

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Vol. 145, nr 1

93--109

EN

This paper focuses on rough approximation operators in group mapping. The relationships between rough set theory and group theory are considered from a novel perspective. The necessary and sufficient conditions for the upper approximation and lower approximation of a group to be groups are analyzed. In addition, the homomorphism and isomorphism between two groups which have related upper or lower approximations are investigated. Finally, the applications of rough approximation operators in group mapping to coding theory are developed.

15

On Some Issues in the Foundation of Rough Sets : the Problem of Definition

Chakraborty M. K.

Fundamenta Informaticae

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2016

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Vol. 148, nr 1/2

123--132

EN

This paper is concerned with some issues connected with the foundations of rough set theory. Particularly the problem of definition of a rough set is discussed.

16

On Four Types of Multi-Covering Rough Sets

Zhang X., Kong Q.

Fundamenta Informaticae

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2016

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Vol. 147, nr 4

457--476

EN

The generalization of Pawlak rough sets is one of the most important directions of rough set theory. In this paper, we propose four types of multi-covering rough set (MCRS) models by combining multi-granulation rough sets with covering rough sets. In the first place,We propose two types of optimistic MCRS models and study their corresponding properties, and then propose another two types of the pessimistic MCRS models and study their corresponding properties as well. Finally, the relationships among the four types of MCRS and the interrelationships between the proposed MCRS models and the existing ones listed in [8] are further investigated.

17

Segmentation of brain MR images using rough set based intuitionistic fuzzy clustering

Dubey Y. K., Mushrif M. M., Mitra K.

Biocybernetics and Biomedical Engineering

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2016

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Vol. 36, no. 2

413--426

EN

Intuitionistic fuzzy sets and rough sets are widely used for medical image segmentation, and recently combined together to deal with uncertainty and vagueness in medical images. In this paper, a rough set based intuitionistic fuzzy c-means (RIFCM) clustering algorithm is proposed for segmentation of the magnetic resonance (MR) brain images. Firstly, we proposed a new automated method to determine the initial values of cluster centroid using intuitionistic fuzzy roughness measure, obtained by considering intuitionistic fuzzy histon as upper approximation of rough set and fuzzy histogram as lower approximation of rough set. A new intuitionistic fuzzy complement function is proposed for intuitionistic fuzzy image representation to take into account intensity inhomogeneity and noise in brain MR images. The results of segmentation of proposed algorithm are compared with the existing rough set based fuzzy clustering algorithms, intuitionistic fuzzy clustering and bias corrected fuzzy clustering algorithm. Experimental results demonstrate the superiority of proposed algorithm.

18

The new module for rules discovering and visualization for NovoSpark® Visualizer software

Pilipczuk O., Cariowa G.

Przegląd Elektrotechniczny

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2015

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R. 91, nr 11

197-200

EN

In this paper we present the new rough sets module for NovoSpark® Visualizer (NV) software. We describe the NV system architecture and the place of the new module in it. We also present the procedure of rough sets analysis with NV software. In addition an example of rules discovering and visualization is provided to evaluate the proposed module. The results show that useful rules are discovered efficiently from the data set.

PL

W artykule zaprezentowano projekt nowego modułu do automatyzacji teorii zbiorów przybliżonych dla oprogramowania NovoSpark® Visualizer (NV). Opisano architekturę systemu oraz wskazano miejsce nowego modułu. Ponadto zaprezentowano przebieg procedury analizy i wizualizacji zbiorów przybliżonych w systemie. Przedstawiono przykład odkrywania i wizualizacji reguł za pomocą opracowanej procedury. W wyniku przeprowadzenia eksperymentu udało się otrzymać szereg użytecznych reguł decyzyjnych.

19

Tolerances Induced by Irredundant Coverings

Järvinen J., Radeleczki S.

Fundamenta Informaticae

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2015

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Vol. 137, nr 3

341--353

EN

In this paper, we consider tolerances induced by irredundant coverings. Each tolerance R on U determines a quasiorder .≤R by setting x .≤R y if and only if R(x) ⊆ R(y). We prove that for a tolerance R induced by a covering H of U, the covering H is irredundant if and only if the quasiordered set (U,.≤R ) is bounded by minimal elements and the tolerance R coincides with the product .≤R ◦ .≤R . We also show that in such a case H = {↑m | m is minimal in (U,.≤R )}, and for each minimal m, we have R(m) = ↑m. Additionally, this irredundant covering H inducing R consists of some blocks of the tolerance R. We give necessary and sufficient conditions under which H and the set of R-blocks coincide. These results are established by applying the notion of Helly numbers of quasiordered sets.

20

Structures of Opposition in Fuzzy Rough Sets

Ciucci D., Dubois D., Prade H.

Fundamenta Informaticae

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2015

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Vol. 142, nr 1-4

1--19

EN

The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exemplified on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.