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1

Uncertainty and information granulation in road traffic control

Płaczek B.

Zeszyty Naukowe. Transport / Politechnika Śląska

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2012

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z. 74

85-93

EN

The contribution discusses the impact of information granulation on uncertainty of decisions in traffic control. Road traffic measurements have a predetermined precision, thus it is convenient to express their results in terms of information granules. A formal model of adaptive traffic control procedure is defined using set theory and relational representation of uncertainty. According to the proposed model, the traffic control decisions are based on a performance comparison for candidate control strategies. In this context, an uncertainty determination algorithm is introduced, which can be used for finding an optimal size of the traffic information granules.

PL

W artykule przedstawiono problem granulacji informacji w systemach sterowania ruchem drogowym oraz omówiono wpływ granulacji informacji na niepewność podejmowanych decyzji sterujących. Pomiary ruchu drogowego są realizowane z określoną precyzją, czego skutkiem jest ziarnisty charakter informacji opisującej parametry ruchu. Zdefiniowano formalny model adaptacyjnej procedury sterowania ruchem drogowym, wykorzystując do tego celu podstawowe definicje teorii zbiorów oraz relacyjny opis niepewności. Zgodnie z przyjętym modelem decyzje sterujące są podejmowane na podstawie porównania efektywności dla różnych wariantów sterowania. Zaproponowano algorytm określania niepewności decyzji sterujących, który może zostać wykorzystany do znajdowania optymalnego rozmiaru ziarna informacji opisującej warunki ruchu drogowego.

2

An Improved Axiomatic Definition of Information Granulation

Zhu P.

Fundamenta Informaticae

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2012

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Vol. 120, nr 1

93-109

EN

To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. In this paper, we try to improve these axiomatic definitions and give a universal construction of information granulation by relating information granulations with a class of functions of multiple variables. We show that the improved axiomatic definition has some concrete information granulations in the literature as instances.

3

Obliczenia ziarniste w modelowaniu nieprecyzyjnych obiektów przy użyciu relacyjnych rozmytych map kognitywnych

Jastriebow A., Słoń G.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 12

1449-1452

PL

Pracę poświęcono analizie parametrów przestrzennej ziarnistości informacji przy modelowaniu systemów z użyciem map kognitywnych. Wprowadzono pojęcie ziarnistości rozmytej dla map kognitywnych oraz przedstawiono wpływ parametrów ziarnistości przestrzennej na precyzyjność modelowania. Z badań symulacyjnych, przeprowadzonych na przykładowej mapie kognitywnej wynika, że wprowadzenie ziarnistości przestrzennej poprawia precyzyjność modelu rozmytego dla zadanej liczby wielkości lingwistycznych.

EN

In complex system modeling processes, accessibility of the information on the system structure and characteristic plays a crucial role. At the lack of the complete knowledge in this matter, calculation processes can be supported with different methods. One of them is using information granularity. The work is devoted to the analysis of spatial information granulation parameters in modeling systems with use of cognitive maps. There is introduced an idea of fuzzy granulation for cognitive maps (according to (6) and (7)). There is also presented the influence of spatial granulation parameters on the modeling precision and time of numerical calculations (Figs. 1 and 9). The method for granulation parameter optimisation is described from the modeling precision improvement point of view (1). There is also introduced the encoding and decoding conformity criterion (9). From simulation investigations carried out on the hypothetical cognitive map (Fig. 7, Tabs. 1 and 2, Eqs. (7), (8) and (9)), it follows that introducing spatial granulation on the basis of a suitable closeness criterion (e.g. (11)) improves precision of the fuzzy model for assigned number of the linguistic variables (Fig. 9).

4

Granular representation of biomedical signals using numerical differentiation methods

Momot M., Momot A., Gacek A.

Journal of Medical Informatics & Technologies

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2010

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Vol. 16

43--49

EN

This work presents the general idea of granular description of temporal signal, particularly biomedical signal sampled with constant frequency. The main idea of presented method is based on using triangular fuzzy numbers as information granules in temporal and amplitude spaces. The amplitude space contains values of first few derivatives of underlying signal. The construction of data granules is performed using the optimization method according to some objective function, which balances the high coverage ability and the low support of fuzzy numbers. The granules (descriptors) undergo the clustering process, namely fuzzy c-means. The centroids of created clusters form a granular vocabulary and the quality of description is quantitatively assessed by reconstruction criterion. There are presented results of experiments with the electrocardiographic signal, digitally sampled and stored in MIT-BIH database. The method of numerical differentiation of function based on finite set of its values is employed, which incorporates polynomial interpolation. The paper presents results of numerical experiments which show the impact of method parameters, such as temporal window length, degree of polynomial, fuzzification parameter, on the reconstruction ability of presented method.

5

Satisfiability and Meaning of Formulas and Sets of Formulas in Approximation Spaces

Gomolińska A.

Fundamenta Informaticae

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2005

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Vol. 67, nr 1-3

77--92

EN

In this paper, we study general notions of satisfiability and meaning of formulas and sets of formulas in approximation spaces. Rather than proposing one particular form of rough satisfiability and meaning, we present a number of alternative approaches. Approximate satisfiability and meaning are important, among others, for modelling of complex systems like systems of adaptive social agents. Finally, we also touch upon derivative concepts of meaning and applicability of rules.

6

Reasoning in Information Maps

Skowron A., Synak P.

Fundamenta Informaticae

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2004

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Vol. 59, nr 2,3

241--259

EN

We investigate patterns over information maps. Such patterns can represent information changes (e.g., in time or space) across information maps. Any map is defined by some transition relation on states. Each state is a pair consisting of a label and information related to the label. Introduced concepts are illustrated by examples. We also discuss searching problems for relevant patterns extracted from data stored in information maps. Some patterns can be expressed by temporal formulas. Then, searching is reduced to searching for relevant temporal formulas. We generalise association rules over information systems to association rules over information maps. Approximate reasoning methods based on information changes are important for many applications (e.g., related to spatio-temporal reasoning). We introduce basic concepts for approximate reasoning about information changes across information maps. We measure degree of changes using information granules. Any rule for reasoning about information changes specifies how changes of information granules from the rule premise influence changes of information granules from the rule conclusion. Changes in information granules can be measured, e.g., using expressions analogous to derivatives. Illustrative examples are also presented.

7

Generation of interpretable fuzzy granules by a double-clustering technique

Castellano G., Fanelli A. M., Mencar C.

Archives of Control Sciences

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2002

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Vol. 12, no. 4

397-410

EN

This paper proposes an approach to derive fuzzy granules from numerical data. Granules are first formed by means of a double-clustering technique, and then properly fuzzyfied so as to obtain interpretable granules, in the sense that they can be described by linquistic labels. The double-clustering technique involves two steps. First, information granules are induced in the space of numerical data via the FCM algorithm. In the second step, the prototypes obtained in the first step are further clustered along each dimension via a hierarchical clustering, in order to obtain one-dimensional granules that are afterwards quantified as fuzzy sets. The derived fuzzy sets can be used as building blocks of fuzzy rule-based model. The approach is illustrated with the aid of a benchmark classification example that provides insight into the interpretability of the induced granules and their effect on the results of classification.

8

Data granulation through optimization of similarity measure

Bargiela A., Pedrycz W., Hirota K.

Archives of Control Sciences

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2002

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Vol. 12, no. 4

469-491

EN

We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching and a similarity level between the prototypes. It is shown how the relevance of the prototypes translates into their granularity. The clustering method helps identify and quantify anisotropy of the feature space. We also show how each prototype is equipped with its own weight vector describing the anisotropy property and thus implying some ranking of the features in the data space.

9

An Algorithm of granulation on numeric attributes for association rules mining

Chien B.-C., Lin Z.-L., Chen Y.-X., Hong T.-P.

Archives of Control Sciences

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2002

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Vol. 12, no. 4

379-395

EN

Mining association rules from numeric data is relatively more difficult than categorical data. The main reason is that the domain of real number lacks of the user's abstraction on reality. In this paper, we propose an algorithm to granualte numeric intervals automatically. The proposed method defines two threshold factors, information density-similarity and information closeness, to measure the condition if two granules should be merged and construct an abstraction hierarchy of intervals. For abstracting the best level of interval from the interval hierarchy automatically, we develop a determination function based on the threshold factors. After the intervals are determined, the fuzzy membership functions for each interval can be generated.Then an algorithm for mining fuzzy association rules can be used mine qualified association rules from the fuzzy intervals.

10

Information Granule Decomposition

Skowron A., Stepaniuk J.

Fundamenta Informaticae

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2001

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Vol. 47, nr 3,4

337-350

EN

Information sources provide us with granules of information that must be transformed, analyzed and built into structures that support problem solving. One of the main goals of information granule calculi is to develop algorithmic methods for construction of complex information granules from elementary ones by means of available operations and inclusion (closeness) measures. These constructed complex granules represent a form of information fusion. Such granules should satisfy some constraints like quality criteria or/and degrees of granule inclusion in (closeness to) a given information granule. Information granule decomposition methods are important components of those methods. We discuss some information granule decomposition methods.

11

Neural Networks in the Framework of Granular Computing

Pedrycz W.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 4

723-745

EN

The study is concerned with the fundamentals of granular computing and its application to neural networks. Granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (embracing a number of individual entitites) and their ensuing processing. We elaborate on the rationale behind granular computing. Next, a number of formal frameworks of information granulation are discussed including several alternatives such as fuzzy sets, interval analysis, rough sets, and probability. The notion of granularity itself is defined and quantified. A design agenda of granular computing is formulated and the key design problems are raised. A number of granular architectures are also discussed with an objective of dealineating the fundamental algorithmic and conceptual challenges. It is shown that the use of information granules of different size (granularity) lends itself to general pyramid architectures of information processing. The role of encoding and decoding mechanisms visible in this setting is also discussed in detail along with some particular solutions. Neural networks are primarily involved at the level of numeric optimization. Granularity of information introduces another dimension to the neurocomputing. We discuss the role of granular constructs in the design of neural networks and knowledge representation therein. The intent of this paper is to elaborate on the fundamentals and put the entire area in a certain perspective while not moving into specific algorithmic details.