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1

Treasure Trove at Banacha. Set Patterns in Descriptive Proximity Spaces

Peters J.F., Ramanna S.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

357--367

EN

This paper introduces descriptive set patterns that originated from our visits with Zdzisław Pawlak and Andrzej Skowron at Banacha and environs in Warsaw. This paper also celebrates the generosity and caring manner of Andrzej Skowron, who made our visits to Warsaw memorable events. The inspiration for the recent discovery of descriptive set patterns can be traced back to our meetings at Banacha. Descriptive set patterns are collections of near sets that arise rather naturally in the context of an extension of Solomon Leader's uniform topology, which serves as a base topology for compact Hausdorff spaces that are proximity spaces. The particular form of proximity space (called EF-proximity) reported here is an extension of the proximity space introduced by V. Efremovič during the first half of the 1930s. Proximally continuous functions introduced by Yu.V. Smirnov in 1952 lead to pattern generation of comparable set patterns. Set patterns themselves were first considered by T. Pavlidis in 1968 and led to U. Grenander's introduction of pattern generators during the 1990s. This article considers descriptive set patterns in EF-proximity spaces and their application in digital image classification. Images belong to the same class, provided each image in the class contains set patterns that resemble each other. Image classification then reduces to determining if a set pattern in a test image is near a set pattern in a query image.

2

Sufficiently Near Neighbourhoods of Points in Flow Graphs. A Near Set Approach

Peters J.F., Chitcharoen D.

Fundamenta Informaticae

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2013

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Vol. 124, nr 1/2

175--196

EN

This paper introduces sufficiently near visual neighbourhoods of points and neighbourhoods of sets in digital image flow graphs (NDIFGs). An NDIFG is an extension of a Pawlak flow graph. The study of sufficiently near neighbourhoods in NDIFGs stems from recent work on near sets and topological spaces via near and far, especially in terms of visual neighbourhoods of points that are sufficiently near each other. From a topological perspective, non-spatially near sets represent an extension of proximity space theory and the original insight concerning spatially near sets by F. Riesz at the International Congress of Mathematicians (ICM) in 1908. In the context of Herrlich nearness, sufficiently near neighbourhoods of sets in NDIFGs provide a new perspective on topological structures in NDIFGs. The practical implications of this work are significant. With the advent of a study of the nearness of open as well as closed neighbourhods of points and of sets in NDIFGs, it is now possible to do information mining on a more global level and achieve new insights concerning the visual information embodied in the images that provide input to an NDIFG.

3

Nearness of Visual Objects. Application of Rough Sets in Proximity Spaces

Peters J.F., Skowron A., Stepaniuk J.

Fundamenta Informaticae

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2013

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Vol. 128, nr 1-2

156--176

EN

The problem considered in this paper is how to describe and compare visual objects. The solution to this problem stems from a consideration of nearness relations in two different forms of Efremovič proximity spaces. In this paper, the visual objects are picture elements in digital images. In particular, this problem is solved in terms of the application of rough sets in proximity spaces. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EF- and a descriptive EF-relation. This leads to a study of the nearness of objects either spatially or descriptively in the approximation of a set. The nearness approximation space model developed in 2007 is refined and extended in this paper, leading to new forms of nearness approximation spaces. There is a natural transition from the two forms of nearness relations introduced in this article to the study of nearness granules.

4

Nearness of Sets in Local Admissible Covers : Theory and Application in Micropalaeontology

Peters J.F.

Fundamenta Informaticae

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2013

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Vol. 126, nr 4

433--444

EN

This paper considers the nearness of sets in local descriptive admissible covers of nonempty sets and the problem of quantifying the nearness of such sets. A brief review of descriptive Efremovič spaces as well descriptive intersection and union provides a foundation for the study of descriptive admissible covers. Descriptively near sets in admissible covers contain sequences of points with members having similar descriptions. The motivation for this approach stems from the need to consider fine-grained neighbourhoods of points in admissible covers that facilitate highly accurate measures of nearness of tiny parts of sets of objects of interest. A practical application of local admissible covers is given in terms of micropalaeontology and the detection of minute similarities and differences in microfossils, useful in the study of climate change, mineral and fossil fuel exploration.

5

Crisp and Fuzzy Topological Interior and Closure Operators with Inclusion Degree : Theory and Applications

Fashandi H., Peters J.F.

Fundamenta Informaticae

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2013

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Vol. 122, nr 3

207--225

EN

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a means of dealing with imperfections and small errors, especially in cases such as digital images where boundaries of subsets of an image are not crisp. The properties of the new operators are presented. Applications of the proposed operators are given in terms of rough sets and mathematical morphology.

6

Rough C-means and Fuzzy Rough C-means for Colour Quantisation

Schaefer G., Hu Q., Zhou H., Peters J.F., Hassanien A. E.

Fundamenta Informaticae

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2012

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Vol. 119, nr 1

113-120

EN

Colour quantisation algorithms are essential for displaying true colour images using a limited palette of distinct colours. The choice of a good colour palette is crucial as it directly deter- mines the quality of the resulting image. Colour quantisation can also be seen as a clustering problem where the task is to identify those clusters that best represent the colours in an image. In this paper we propose rough c-means and fuzzy rough c-means clustering algorithms for colour quantisation of images. Both approaches utilise the concept of lower and upper approximations of clusters to define palette colours. While in the rough c-means approach cluster centroids are refined iteratively through a linear combination of elements of the lower and upper approximations, the fuzzy rough c-means technique assigns variable membership values to the elements in the boundary region which in turn are incorporated into the calculation of cluster centres. Experimental results on a standard set of images show that these approaches performs significantly better than other, purpose built colour quantisation algorithms.

7

Optimization in Discovery of Compound Granules

Jankowski A., Peters J.F., Skowron A., Stepaniuk J.

Fundamenta Informaticae

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2008

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Vol. 85, nr 1-4

249-265

EN

The problem considered in this paper is the evaluation of perception as a means of optimizing various tasks. The solution to this problem hearkens back to early research on rough set theory and approximation. For example, in 1982, Ewa Orowska observed that approximation spaces serve as a formal counterpart of perception. In this paper, the evaluation of perception is at the level of approximation spaces. The quality of an approximation space relative to a given approximated set of objects is a function of the description length of an approximation of the set of objects and the approximation quality of this set. In granular computing (GC), the focus is on discovering granules satisfying selected criteria. These criteria take inspiration from the minimal description length (MDL) principle proposed by Jorma Rissanen in 1983. In this paper, the role of approximation spaces in modeling compound granules satisfying such criteria is discussed. For example, in terms of approximation itself, this paper introduces an approach to function approximation in the context of a reinterpretation of the rough integral originally proposed by Zdzisaw Pawlak in 1993. We also discuss some other examples of compound granule discovery problems that are related to compound granules representing process models and models of interaction between processes or approximation of trajectories of processes. All such granules should be discovered from data and domain knowledge. The contribution of this article is a proposed solution approach to evaluating perception that provides a basis for optimizing various tasks related to discovery of compound granules representing rough integrals, process models, their interaction, or approximation of trajectories of discovered models of processes.

8

Nearness of Objects: Extension of Approximation Space Model

Peters J.F., Skowron A.

Fundamenta Informaticae

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2007

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Vol. 79, nr 3-4

497-512

EN

The problem considered in this paper is the extension of an approximation space to include a nearness relation. Approximation spaces were introduced by Zdzisaw Pawlak during the early 1980s as frameworks for classifying objects by means of attributes. Pawlak introduced approximations as a means of approximating one set of objects with another set of objects using an indiscernibility relation that is based on a comparison between the feature values of objects. Until now, the focus has been on the overlap between sets. It is possible to introduce a nearness relation that can be used to determine the "nearness" of sets of objects that are possibly disjoint and, yet, qualitatively near to each other. Several members of a family of nearness relations are introduced in this article. The contribution of this article is the introduction of a nearness relation that makes it possible to extend Pawlak's model for an approximation space and to consider the extension of generalized approximations spaces.

9

Near Sets. Special Theory about Nearness of Objects

Peters J.F.

Fundamenta Informaticae

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2007

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Vol. 75, nr 1-4

407-433

EN

The problem considered in this paper is how to approximate sets of objects that are qualitatively but not necessarily spatially near each other. The term qualitatively near is used here to mean closeness of descriptions or distinctive characteristics of objects. The solution to this problem is inspired by the work of Zdzisaw Pawlak during the early 1980s on the classification of objects by means of their attributes. This article introduces a special theory of the nearness of objects that are either static (do not change) or dynamic (change over time). The basic approach is to consider a link relation, which is defined relative to measurements associated with features shared by objects independent of their spatial relations. One of the outcomes of this work is the introduction of new forms of approximations of objects and sets of objects. The nearness of objects can be approximated using rough set methods. The proposed approach to approximation of objects is a straightforward extension of the rough set approach to approximating objects, where approximation can be considered in the context of information granules (neighborhoods). In addition, the usual rough set approach to concept approximation has been enriched by an increase in the number of granules (neighborhoods) associated with the classification of a concept as near to its approximation. A byproduct of the proposed approximation method is what we call a near set. It should also be observed that what is presented in this paper is considered a special (not a general) theory about nearness of objects. The contribution of this article is an approach to nearness as a vague concept which can be approximated from the state of objects and domain knowledge.

10

Approaches to Conflict Dynamics Based on Rough Sets

Ramanna S., Peters J.F., Skowron A.

Fundamenta Informaticae

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2007

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Vol. 75, nr 1-4

453-468

EN

Conflict analysis and conflict resolution play an important role in negotiation during contract-management situations in many organizations. The issue here is how to model a combination of complex situations among agents where there are disagreements leading to a conflict situation, and there is a need for an acceptable set of agreements. Conflict situations also result due to different sets of view points about issues under negotiation. The solution to this problem stems from pioneering work on this subject by Zdzisaw Pawlak, which provides a basis for a complex conflict model encapsulating a decision system with complex decisions. Several approaches to the analysis of conflicts situations are presented in this paper, namely, conflict graphs, approximation spaces and risk patterns. An illustrative example of a requirements scope negotiation for an automated lighting system is presented. The contribution of this paper is a rough set-based requirements scope determination model and assessment mechanisms using a complex conflict model.

11

Reinforcement Learning with Approximation Spaces

Peters J.F., Henry Ch.

Fundamenta Informaticae

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2006

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Vol. 71, nr 2,3

323-349

EN

This paper introduces a rough set approach to reinforcement learning by swarms of cooperating agents. The problem considered in this paper is how to guide reinforcement learning based on knowledge of acceptable behavior patterns. This is made possible by considering behavior patterns of swarms in the context of approximation spaces. Rough set theory introduced by Zdzisaw Pawlak in the early 1980s provides a ground for deriving pattern-based rewards within approximation spaces. Both conventional and approximation space-based forms of reinforcement comparison and the actor-critic method as well as two forms of the off-policy Monte Carlo learning control method are investigated in this article. The study of swarm behavior by collections of biologically-inspired bots is carried out in the context of an artificial ecosystem testbed. This ecosystem has an ethological basis that makes it possible to observe and explain the behavior of biological organisms that carries over into the study of reinforcement learning by interacting robotic devices. The results of ecosystem experiments with six forms of reinforcement learning are given. The contribution of this article is the presentation of several viable alternatives to conventional reinforcement learning methods defined in the context of approximation spaces.

12

Spatio-Temporal Approximate Reasoning over Complex Objects

Synak P., Bazan J.G., Skowron A., Peters J.F.

Fundamenta Informaticae

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2005

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Vol. 67, nr 1-3

249-269

EN

We discuss the problems of spatio-temporal reasoning in the context of hierarchical information maps and approximate reasoning networks (AR networks). Hierarchical information maps are used for representations of domain knowledge about objects, their parts, and their dynamical changes. AR networks are patterns constructed over sensory measurements and they are discovered from hierarchical information maps and experimental data. They make it possible to approximate domain knowledge, i.e., complex spatio-temporal concepts and reasonings represented in hierarchical information maps. Experiments with classifiers based on AR schemes using a road traffic simulator are also briefly presented.

13

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.

14

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.

15

Rough Sets and Infomorphisms: Towards Approximation of Relations in Distributed Environments

Skowron A., Stepaniuk J., Peters J.F.

Fundamenta Informaticae

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2003

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Vol. 54, nr 2,3

263-277

EN

We discuss the relationships between information systems and classifications as well as between infomorphisms and definability of relations (between whole objects and their parts) in information systems. Infomorphisms between information systems (classifications) IS1 and IS2 make it possible to define some formulas over IS2 by means of formulas over IS1. The remaining formulas over IS2 can be approximatively defined by means of formulas over IS1. The approximation operations are defined using the rough set approach. We present definitions and examples of such approximations.

16

Towards an Ontology of Approximate Reason

Peters J.F., Skowron A., Stepaniuk J., Ramanna S.

Fundamenta Informaticae

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2002

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Vol. 51, nr 1,2

157-173

EN

This article introduces structural aspects in an ontology of approximate reason. The basic assumption in this ontology is that approximate reason is a capability of an agent. Agents are designed to classify information granules derived from sensors that respond to stimuli in the environment of an agent or received from other agents. Classification of information granules is carried out in the context of parameterized approximation spaces and a calculus of granules. Judgment in agents is a faculty of thinking about (classifying) the particular relative to decision rules derived from data. Judgment in agents is reflective, but not in the classical philosophical sense (e.g., the notion of judgment in Kant). In an agent, a reflective judgment itself is an assertion that a particular decision rule derived from data is applicable to an object (input). That is, a reflective judgment by an agent is an assertion that a particular vector of attribute (sensor) values matches to some degree the conditions for a particular rule. In effect, this form of judgment is an assertion that a vector of sensor values reflects a known property of data expressed by a decision rule. Since the reasoning underlying a reflective judgment is inductive and surjective (not based on a priori conditions or universals), this form of judgment is reflective, but not in the sense of Kant. Unlike Kant, a reflective judgment is surjective in the sense that it maps experimental attribute values onto the most closely matching descriptors (conditions) in a derived rule. Again, unlike Kant's notion of judgment, a reflective judgment is not the result of searching for a universal that pertains to a particular set of values of descriptors. Rather, a reflective judgment by an agent is a form of recognition that a particular vector of sensor values pertains to a particular rule in some degree. This recognition takes the form of an assertion that a particular descriptor vector is associated with a particular decision rule. These considerations can be repeated for other forms of classifiers besides those defined by decision rules.

17

A Comparision of Different Decision Algorithms Used in Volumetric Storm Cells Classification

Suraj Z., Peters J.F., Rząsa W.

Fundamenta Informaticae

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2002

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Vol. 51, nr 1,2

201-214

EN

Decision algorithms useful in classifying meteorological volumetric radar data are the subject of described in the paper experiments. Such data come from the Radar Decision Support System (RDSS) database of Environment Canada and concern summer storms created in this country. Some research groups used the data completed by RDSS for verifying the utility of chosen methods in volumetric storm cells classification. The paper consists of a review of experiments that were made on the data from RDSS database of Environment Canada and presents the quality of particular classifiers. The classification accuracy coefficient is used to express the quality. For five research groups that led their experiments in a similar way it was possible to compare received outputs. Experiments showed that the Support Vector Machine (SVM) method and rough set algorithms which use object oriented reducts for rule generation to classify volumetric storm data perform better than other classifiers.

18

Sensor, Filter, and Fusion Models with Rough Petri Nets

Peters J.F., Ramanna S., Borkowski M., Skowron A., Suraj Z.

Fundamenta Informaticae

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2001

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Vol. 47, nr 3,4

307-323

EN

This paper considers models of sensors, filters, and sensor fusion with Petri nets defined in the context of rough sets. Sensors and filters are fundamental computational units in the design of systems. The intent of this work is to construct Petri nets to simulate conditional computation in approximate reasoning systems, which are dependent on filtered input from selected sensors considered relevant in problem solving. In this paper, coloured Petri nets provide a computational framework for the definition of a family of Petri nets based on rough set theory. Sensors are modeled with what are known as receptor processes in rough Petri nets. Filters are modeled as ukasiewicz guards on some transitions in rough Petri nets. A ukasiewicz guard is defined in the context of multivalued logic. ukasiewicz guards are useful in culling from a collection of active sensors those sensors with the greatest relevance in a problem-solving effort such as classification of a "perceived" phenomenon in the environment of an agent. The relevance of a sensor is computed using a discrete rough integral. The form of sensor fusion considered in this paper consists in selecting only those sensors considered relevant in solving a problem. The contribution of this paper is the modeling of sensors, filters, and fusion in the context of receptor processes, ukasiewicz guards, and rough integration, respectively.

19

An application of rough set methods in control design

Peters J.F., Skowron A., Suraj Z.

Fundamenta Informaticae

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2000

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Vol. 43, Nr 1-4

269-290

EN

The paper deals with an automatic concurrent control design method derived from the specification of a discrete event control system represented in the form of a decision table. The main stages of our approach are: the control specification by decision tables, generation of rules from the specification of the system behavior, and converting rules set into a concurrent program represented in the form of a Petri net. Our approach is based on rough set theory.