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1

Inverted Fuzzy Implications in Approximate Reasoning

Suraj Z., Lasek A., Lasek P.

Fundamenta Informaticae

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2016

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Vol. 143, nr 1/2

151--171

EN

In 1973 Lotfi Zadeh introduced the theory of fuzzy logic [17]. Fuzzy logic was an extension of Boolean logic so that it allowed using not only Boolean values to express reality. One kind of basic logical operations in fuzzy logic are so-called fuzzy implications. From over eight decades a number of different fuzzy implications have been described [3] - [16]. In the family of all fuzzy implications the partial order induced from [0,1] interval exists. Pairs of incomparable fuzzy implications can generate new fuzzy implications by usingmin(inf) andmax(sup) operations. As a result the structure of lattice is created ([1], page 186). This leads to the following question: how to choose the correct functions among basic fuzzy implications and other generated as described above. In our paper, we propose a new method for choosing implications. Our method allows to compare two fuzzy implications. If the truth value of the antecedent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication consequent. In other words, we can choose the fuzzy implication, which has the greatest or the smallest truth value of the implication consequent or which has greater or smaller truth value than another implication. Primary results regarding this problem are included in the paper [14].

2

About New Version of RSDS System

Suraj Z., Grochowalski P.

Fundamenta Informaticae

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2014

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Vol. 135, nr 4

503--519

EN

The aim of this paper is to present a new version of a bibliographic database system - Rough Set Database System (RSDS). The RSDS system, among others, includes bibliographic descriptions of publications on rough set theory and its applications. This system is also an experimental environment for research related to the processing of bibliographic data using the domain knowledge and the related information retrieval.

3

ROSECON: a Computer Tool for Synthesis and Verification of Concurrent Systems Specified by Information Systems

Suraj Z., Pancerz K.

Fundamenta Informaticae

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2013

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Vol. 126, nr 4

335--351

EN

In the paper, a computer tool called ROSECON, used for modeling and analyzing systems of concurrent processes, is described. A special attention is focused on synthesis and verification of concurrent systems specified by information systems. Two kinds of models, synchronous and asynchronous, are considered. In the first approach, all processes included in the modeled system are synchronized globally whereas in the second one, each process is synchronized individually. The presented tool allows generating automatically an appropriate model of a system of concurrent processes, in the form of colored Petri nets, from the specification given by an information system. Analysis of the model behaviors enables users to verify the correctness and/or optimality of the obtained models and to provide some modification procedures to get correct and/or more optimal solutions. Examples of selected well known problems in concurrency, in the paper, emphasize usefulness of the tool in the designing systems of concurrent processes.

4

A Rough Set Approach to Information Systems Decomposition

Pancerz K., Suraj Z.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

257--272

EN

The aim of this paper is to present the methods and algorithms of information systems decomposition. In the paper, decomposition with respect to reducts and the so-called global decomposition are considered. Moreover, coverings of information systems by components are discussed. An essential difference between two kinds of decomposition can be observed. In general, global decomposition can deliver more components of a given information system. This fact can be treated as some kind of additional knowledge about the system. The proposed approach is based on rough set theory. To demonstrate the usefulness of this approach, we present an illustrative example coming from the economy domain. The discussed decomposition methods can be applied e.g. for design and analysis of concurrent systems specified by information systems, for automatic feature extraction, as well as for control design of systems represented by experimental data tables.

5

A New Class of Fuzzy Petri Nets for Knowledge Representation and Reasoning

Suraj Z.

Fundamenta Informaticae

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2013

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Vol. 128, nr 1-2

193--207

EN

This paper presents a new class of Petri nets called generalised fuzzy Petri nets. The new class extends the existing fuzzy Petri nets by introducing three operators in the form of triangular norms, which are supposed to function as substitute for the min, max and * (algebraic product) operators. To demonstrate the power and the usefulness of this model, an application of the generalised fuzzy Petri nets in the domain of train traffic control is provided. The new model is more flexible than the classical one as in the former class the user has the chance to define the input/output operators. The proposed approach can be used for knowledge representation and reasoning in decision support systems.

6

Toward Intelligent Searching the Rough Set Database System (RSDS): an Ontological Approach

Suraj Z., Grochowalski P.

Fundamenta Informaticae

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2010

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Vol. 101, nr 1/2

115-123

EN

Themain goal of this paper is to give the outline of some approach to intelligent searching the Rough Set Database System (RSDS). RSDS is a bibliographical system containing bibliographical descriptions of publications connected with methodology of rough sets and its applications. The presented approach bases on created ontologies which are models for the considered domain (rough set theory, its applications and related fields) and for information about publications coming from, for example, abstracts.

7

On Minimal Inhibitory Rules for Almost All k-Valued Information Systems

Moshkov M.Ju., Skowron A., Suraj Z.

Fundamenta Informaticae

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2009

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Vol. 93, nr 1-3

261-272

EN

The minimal inhibitory rules for information systems can be used for construction of classifiers. We show that almost all information systems from a certain large class of information systems have relatively short minimal inhibitory rules. However, the number of such rules is not polynomial in the number of attributes and the number of objects. This class consists of all k-valued information systems, k ≥ 2, with the number of objects polynomial in the number of attributes. Hence, for efficient construction of classifiers some filtration techniques in rule generation are necessary. Another way is to work with lazy classification algorithms based on inhibitory rules.

8

Feature Selection Algorithm for Multiple Classifier Systems: A Hybrid Approach

Delimata P., Suraj Z.

Fundamenta Informaticae

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2008

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Vol. 85, nr 1-4

97-110

EN

Many problems in pattern classification and knowledge discovery require a selection of a subset of attributes or features to represent the patterns to be classified. The approach presented in this paper is designed mostly for multiple classifier systems with homogeneous (identical) classifiers. Such systems require many different subsets of the data set. The problem of finding the best subsets of a given feature set is of exponential complexity. The main aim of this paper is to present ways to improve RBFS algorithm which is a feature selection algorithm. RBFS algorithm is computationally quite complex because it uses all decision-relative reducts of a given decision table. In order to increase its speed, we propose a new algorithm called ARS algorithm. The task of this algorithm is to decrease the number of the decision-relative reducts for a decision table. Experiments have shown that ARS has greatly improved the execution time of the RBFS algorithm. A small loss on the classification accuracy of the multiple classifier used on the subset created by this algorithm has also been observed. To improve classification accuracy the simplified version of the bagging algorithm has been applied. Algorithms have been tested on some benchmarks.

9

Towards Efficient Computing Consistent and Partially Consistent Extensions of Information Systems

Suraj Z., Pancerz K.

Fundamenta Informaticae

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2007

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Vol. 79, nr 3-4

553-566

EN

This paper provides new algorithms for computing consistent and partially consistent extensions of information systems. A maximal consistent extension of a given information system includes only objects corresponding to known attribute values which are consistent with all rules extracted from the original information system. A partially consistent extension of a given information system includes objects corresponding to known attribute values which are consistent to a certain degree with the knowledge represented by rules extracted from the original information system. This degree can be between 0 and 1, 0 for the full inconsistency and 1 for the full consistency. The algorithms presented here do not involve computing any rules true in a given information system. This property differentiates them from methods presented in the earlier papers which concerned extensions of information systems.

10

On Minimal Rule Sets for Almost All Binary Information Systems

Moshkov M.Ju., Skowron A., Suraj Z.

Fundamenta Informaticae

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2007

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Vol. 80, nr 1-3

247-258

EN

The minimal rules for information systems are often used for inducing data models by methods in which the optimization of models is based on the minimal length principle. We show that almost all information systems from a certain large class of information systems have relatively short minimal rules. However, the number of such rules is not polynomial in the number of attributes and the number of objects. This class consists of all binary information systems with the number of objects polynomial in the number of attributes. Hence, for efficient inducing data models some filtration techniques in rule generation are necessary. In our further study we would like to extend our results for arbitrary information systems.

11

Analysis of Approximate Petri Nets by Means of Occurrence Graphs

Suraj Z., Fryc B.

Fundamenta Informaticae

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2007

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Vol. 79, nr 3-4

541-551

EN

Approximate Petri nets (AP-nets) can be used for the knowledge representation and approximate reasoning. The AP-net model is defined on the basis of the rough set approach, fuzzy Petri nets and coloured Petri nets. One of the main advantages of AP-net model is a possibility to present the reachability set of a given AP-net by means of an occurrence graph. Such graphs can serve, among others, for analyzing and evaluating an approximate reasoning realized by using AP-net model. The main contribution of the paper is to present the algorithms for construction and analysis of occurrence graphs for the AP-nets, especially in the context of searching for the best decision and finding the shortest distance in order to compute such decision. This approach can be applied to the design and analysis of the formal models for expert systems, control systems, communication systems, etc.

12

Timed Approximate Petri Nets

Suraj Z., Fryc B.

Fundamenta Informaticae

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2006

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Vol. 71, nr 1

83-99

EN

Time is one of the most important considerations in designing practical systems. The notion of time plays a vital role in performance evaluation of real-time systems. A new class of timed approximate Petri nets (TAP-nets) is proposed in the paper. This net model combines high-level Petri nets with time and uncertain information. The approach presented in the paper for modelling of uncertainty, imprecision and vagueness is based on rough set theory and fuzzy Petri nets. The TAP-nets can be used for modelling and evaluating of approximate reasoning used to build expert systems, control systems, communication systems, etc. The main advantage of modelling practical systems using the TAP-nets is that the resulting models are simple, intuitive and allow the system analyst to evaluate the performance of such system models.

13

Reconstruction of Concurrent System Models Described by Decomposed Data Tables

Suraj Z., Pancerz K.

Fundamenta Informaticae

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2006

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Vol. 71, nr 1

121-137

EN

This paper deals with reconstruction of net models of concurrent systems described by information systems changing in time. Constructed net models have the form of coloured Petri nets. Resulting nets are constructed on the basis of decomposed information systems. In many practical cases, a description of modelled systems changes in time. New knowledge about structures and behaviours of systems appears. When new descriptions appear, the net models should be changed taking into consideration the new knowledge. An approach to reconstruction of net models is here presented. One of many possible cases is considered, i.e., when the new global state of the modelled system appears. The ability to compute reducts and components of a new information system, being a new description of a modelled system, in an efficient way is important for reconstruction. Therefore, some propositions and corollaries useful to compute reducts of a new information system on the basis of reducts of an old information system are given. These propositions and corollaries are the basis to formulate algorithms for computing new reducts and components. Moreover, a way to determine the cost of the reconstruction of a net model is given. The cost of the reconstruction is treated as the cost of adding new functional modules, communication lines or their modifications. The discussed approach to model reconstruction extends and refines that proposed by Z. Suraj in 1998. An example is given in this paper to illustrate the presented idea.

14

On k-NN Method with Preprocessing

Suraj Z., Delimata P.

Fundamenta Informaticae

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2006

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Vol. 69, nr 3

343-358

EN

The objective of this study is to introduce a new model of data classification based on preliminary reduction of the training set of examples (preprocessing) in order to facilitate the use of nearest neighbours (NN) techniques in near real-time applications. This study accordingly addresses the issue of minimising the computational resource requirements of NN techniques, memory as well as time. The approach proposed in the paper is a modification of the classical k-Nearest Neighbours (k-NN) method and the k-NN method with local metric induction. Generally, the k-NN method with local metric induction in comparison with the classical k-NN method gives better results in the classification of new examples. Nevertheless, for the large data sets the k-NN method with local metric induction is less time effective than the classical one. The time/space efficiency of classifying algorithms based on these two methods depends not only on a given metric but also on the size of training data. In the paper, we present three methods of preliminary reduction of the training set of examples. All reduction methods decrease the size of a given experimental data preserving the relatively high classification accuracy. Results of experiments conducted on well known data sets, demonstrate the potential benefits of such reduction methods.

15

A Rough Set Approach to Multiple Classifier Systems

Suraj Z., El Gayar N., Delimata P.

Fundamenta Informaticae

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2006

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Vol. 72, nr 1-3

393-406

EN

During the past decade methods of multiple classifier systems have been developed as a practical and effective solution for a variety of challenging applications. A wide number of techniques and methodologies for combining classifiers have been proposed in the past years in literature. In our work we present a new approach to multiple classifier systems using rough sets to construct classifier ensembles. Rough set methods provide us with various useful techniques of data classification. In the paper, we also present a method of reduction of the data set with the use of multiple classifiers. Reduction of the data set is performed on attributes and allows to decrease the number of conditional attributes in the decision table. Our method helps to decrease the number of conditional attributes of the data with a small loss on classification accuracy.

16

A Petri Net System - an Overview

Suraj Z., Fryc B., Matusiewicz Z., Pancerz K.

Fundamenta Informaticae

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2006

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Vol. 71, nr 1

101-120

EN

Petri nets are one of well established tools in both theoretical analysis and practical modelling of concurrent systems as well as approximate reasoning. However, practical usage of Petri nets is limited by the lack of computer tools which would allow to handle large and complex nets in a comfortable way. Three things are essential for modelling and analyzing by means of Petri nets - good editor, simulator and powerful analysis engine. Moreover, a program should have a graphical user interface providing an opportunity to work directly with the graphical representations of Petri nets and should be able to read and write data in formats of other popular simulators of Petri Nets. This paper presents a set of integrated graphical Petri net tools called Petri Net system (PN-system, in short). PN-system is a following version of PN-tools. This system can be used for constructing, editing and analyzing of different classes of Petri nets. PN-system is enhanced on fuzzy and adaptive fuzzy Petri nets' modules which allow to perform fuzzy reasoning automatically. It has got a graphical user interface. Moreover, PN-system can cooperate with the ROSECON system which is an original software tool for discovering concurrent models from data tables. PN-system is run on IBM PC platform under MS Windows operating system.

17

Restriction-Based Concurrent System Design Using the Rough Set Formalism

Suraj Z., Pancerz K.

Fundamenta Informaticae

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2005

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Vol. 67, nr 1-3

233-247

EN

Design of concurrent systems under various constraints is an important problem in real-life applications in many domains (for example, automatics, robotics, software engineering) and has earlier been discussed in the literature using different formalisms. In this paper some approaches to the concurrent system design based on restrictions will be considered. In our approaches, we will use the rough set formalism. The coloured Petri nets (CP-nets) will be used to model designed concurrent systems.

18

A Controller Design for the Khepera Robot : A Rough Set Approach

Suraj Z., Peters J. F., Grochowalski P.

Fundamenta Informaticae

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2005

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Vol. 67, nr 1-3

219-231

EN

The Khepera robot belongs to the family of miniature mobile robots of the K-Team firm. It is used in a number of places for scientific and educational purposes. Considering its advantages (such as small size, precision of movement, ease of control), it is applied to testing different approaches in the domain of artificial intelligence. This paper describes the methodology of a control system design for the Khepera robot based on a rough set approach. The proposed approach entails a study of robot behaviour insofar as its movements are influenced by measurements from its sensors and the choice of actions that make it possible for the robot to achieve its system goals. The constructed controller concerns the realization of some tasks such as avoiding the obstacles, reaching a target, following an obstacle, finding the way out of a labyrinth. The proposed controller has been tested on both a robot simulator and on a real robot. Our experimental results show that the proposed rough set methodology can be applied to the design of a controller for the Khepera robot.

19

On Fuzzy Reasoning Using Matrix Representation of Extended Fuzzy Petri Nets

Fryc B., Pancerz K., Peters J.F., Suraj Z.

Fundamenta Informaticae

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2004

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Vol. 60, nr 1-4

143--157

EN

In 1990 Shyi-Ming Chen et al. presented a new approach to knowledge representation using fuzzy Petri nets (FPN). A fuzzy Petri net model allows a structural representation of knowledge and has a systematic procedure for supporting fuzzy reasoning. In this paper we propose an algebraic (matrix) representation of FPNs. We use this representation in a fuzzy reasoning algorithm which is simple to implement in modern programming languages such as C++, C# or Java. Furthermore, there exists MATLAB - a computer system which makes it possible to solve many computing problems, especially those with matrix and vector formulations. We present also an approach enabling us to carry out a fuzzy reasoning process using the MATLAB environment.

20

Discovery of Asynchronous Concurrent Models from Experimental Tables

Pancerz K., Suraj Z.

Fundamenta Informaticae

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2004

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Vol. 61, nr 2

97--116

EN

The synthesis problem of concurrent systems has earlier been discussed in the literature using different types of formalisms. This paper presents a new method for discovery of asynchronous concurrent models from experimental tables by using a rough set approach. The proposed method can be applied to the automatic data model discovery. The algorithm for constructing asynchronous concurrent models is described in detail. As a model for concurrency the Coloured Petri Nets are used. Constructed asynchronous models can be helpful to solving some problems arising in design of asynchronous digital systems or addressing of nodes in parallel systems. An example illustrates an application of the proposed approach in such problems.