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1

Development of the deterministic and stochastic Markovian model of a dendritic neuron

Świetlicka A., Gugała K., Pedrycz W., Rybarczyk A.

Biocybernetics and Biomedical Engineering

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2017

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Vol. 37, no. 1

201--216

EN

In this study, we propose a model of the dendritic structure of the neuron (referred to as a neural network – NN), which can be viewed as an extension of the models that are currently used in the description of the potential on the neuron's membrane. The proposed extensions augment the generic model and offer a fuller description of the neuron's nature. The common assumption being used in most of the previous models stating a single channel (forming component of the neuron's membrane) can be positioned in only one of the two states (permissive – open and non-permissive – closed), is now relaxed by allowing the channel to be positioned in more states (five or eight states). The relationship between these states is expressed in terms of Markov kinetic schemes. In the paper, we demonstrate that the new approach is more suitable for a larger number of applications than the conventional Hodgkin–Huxley model. The study, by providing the mathematical background of the new extended model, forms a significant step towards a hardware implementation of the biologically realistic neural network (NN) of this type. To reduce the number of components required in such implementation, we propose a new optimization technique that significantly reduces the computational complexity of a single neuron.

2

From Numeric to Granular Description and Interpretation of Information Granules

Pedrycz W.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

399--412

EN

Fuzzy sets (membership functions) are numeric constructs. In spite of the underlying semantics of fuzzy sets (which is inherently linked with the higher level of abstraction), the membership grades and processing of fuzzy sets themselves emphasize the numeric facets of all pursuits stressing the numeric nature of membership grades and in this way reducing the interpretability and transparency of results. In this study, we advocate an idea of a granular description of membership functions where instead of numeric membership grades, introduced are more interpretable granular descriptors (say, low, high membership, etc.). Granular descriptors are formalized with the aid of various formal schemes available in Granular Computing, especially sets (intervals), fuzzy sets, and shadowed sets. We formulate a problem of a design of granular descriptors as a certain optimization task, elaborate on the solutions and highlight some areas of applications.

3

A Doctrine of Cognitive Informatics (CI)

Wang Y., Kinsner W., Anderson J.A., Zhang D., Yao Y., Sheu P., Tsai J., Pedrycz W., Latombe J-C., Zadeh L.A., Patel D., Cha Ch.

Fundamenta Informaticae

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2009

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Vol. 90, nr 3

203-228

EN

Cognitive informatics (CI) is the transdisciplinary enquiry of cognitive and information sciences that investigates into the internal information processing mechanisms and processes of the brain and natural intelligence, and their engineering applications via an interdisciplinary approach. CI develops a coherent set of fundamental theories and denotational mathematics, which form the foundation for most information and knowledge based science and engineering disciplines such as computer science, cognitive science, neuropsychology, systems science, cybernetics, software engineering, knowledge engineering, and computational intelligence. This paper reviews the central doctrine of CI and its applications. The theoretical framework of CI is described on the architecture of CI and its denotational mathematic means. A set of theories and formal models of CI is presented in order to explore the natural and computational intelligence. A wide range of applications of CI are described in the areas of cognitive computers, cognitive properties of knowledge, simulations of human cognitive behaviors, cognitive complexity of software, autonomous agent systems, and computational intelligence.

4

A Development of Inclusion-degree-based Rough Fuzzy Random Sets

Ha M., Pedrycz W., Zhang A., Fan Y.

Fundamenta Informaticae

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2008

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Vol. 86, nr 4

481-502

EN

Given a widespread interest in rough sets as being applied to various tasks of data analysis, it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. In this study, we investigate an idea of rough fuzzy random sets. This construct provides us with a certain generalization of rough sets by introducing the concept of inclusion degree. The underlying objective behind this development is to address the problems which involve co-existing factors of fuzziness and randomness thus giving rise to a notion of the fuzzy random approximation space based on inclusion degree. Some essential properties of rough approximation operators of such rough fuzzy random sets are discussed. Further theoretical foundations for the formation of rules constructed on a basis of available decision tables are offered as well.

5

Knowledge-based clustering as a conceptual and algorithmic environment of biomedical data analysis

Pedrycz W., Gacek A.

Journal of Medical Informatics & Technologies

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2004

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Vol. 7

KB13--22

EN

While a genuine abundance of biomedical data available nowadays becomes a genuine blessing, it also posses a lot of challenges. The two fundamental and commonly occurring directions in data analysis deal with its supervised or unsupervised pursuits. Our conjecture is that in the area of biomedical data processing and understanding where we encounter a genuine diversity of patterns, problem descriptions and design objectives, this type of dichotomy is neither ideal nor the most productive. In particular, the limitations of such taxonomy become profoundly evident in the context of unsupervised learning. Clustering (being usually regarded as a synonym of unsupervised data analysis) is aimed at determining a structure in a data set by optimizing a given partition criterion. In this sense, a structure emerges (becomes formed) without a direct intervention of the user. While the underlying concept looks appealing, there are numerous sources of domain knowledge that could be effectively incorporated into clustering mechanisms and subsequently help navigate throughout large data spaces. In unsupervised learning, this unified treatment of data and domain knowledge leads to the general concept of what could be coined as knowledge-based clustering. In this study, we discuss the underlying principles of this paradigm and present its various methodological and algorithmic facets. In particular, we elaborate on the main issues of incorporating domain knowledge into the clustering environment such as (a) partial labelling, (b) referential labelling (including proximity and entropy constraints), (c) usage of conditional (navigational) variables, (d) exploitation of external structure. Presented are also concepts of stepwise clustering in which the structure of data is revealed via a series of refinements of existing domain granular information.

6

Models of computational intelligence in bioinformatics

Pedrycz W.

Journal of Medical Informatics & Technologies

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2003

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Vol. 5

IP13--23

EN

Computational Intelligence has emerged as a synergistic environment of Granular Computing (including fuzzy sets, rough sets, interval analysis), neural networks and evolutionary optimisation. This symbiotic framework addresses the needs of system modelling with regard to its transparency, accuracy and user friendliness. This becomes of paramount interest in various modelling in bioinformatics especially when we are concerned with decision-making processes. The objective of this study is to elaborate on the two essential features of CI that is Granular Computing and the resulting aspects of logic-oriented processing and its transparency. As the name stipulates, Granular Computing is concerned with processing carried out at a level of coherent conceptual entities - information granules. Such granules are viewed as inherently conceptual entities formed at some level of abstraction whose processing is rooted in the language of logic (especially, many valued or fuzzy logic). The logic facet of processing is cast in the realm of fuzzy logic and fuzzy sets that construct a consistent processing background necessary for operating on information granules. Several main categories of logic processing units (logic neurons) are discussed that support aggregative (and-like and or-like operators) and referential logic mechanisms (dominance, inclusion, and matching). We show how the logic neurons contribute to high functional transparency of granular processing, help capture prior domain knowledge and give rise to a diversity of the resulting models.

7

Relations of granular worlds

Pedrycz W., Vukovich G.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 3

347-357

EN

In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence we are interested in the granules that not only reflect the data but also contribute to the performance of such a mapping. The optimization of information granules is realized through a collaboration occurring at the level of the data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and to avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes ...

8

Distributed collaborative knowledge elicitation

Pedrycz W.

Computer Assisted Mechanics and Engineering Sciences

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2002

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Vol. 9, No. 1

87-104

EN

In this study, we develop an idea of knowledge elicitation realized over a collection of databases. The essence of such elicitation deals with a determination of common structure in databases. Depending upon a way in which databases are accessible abd can collaborate, we distinguish between a vertical and horizontal collaboration. In the first case, the databases deal with objects defined in the same attribute (feature) space. The horizontal collaboration takes place when dealing with the same objects but being defined in different attribute spaces and therefore forming separate databases. We develop a new clustering architecture supporting the mechanisms of collaboration. It is based on a standard FCM (Fuzzy C-Means) method. When it comes to the horizontal collaboration, the clustering algorithms interact by exchanging information about local partition matrices. In this sense, the required communication links are established at the level of information granules (more specifically, fuzzy sets forming the partition matrices) rather than patterns directly available in the databases. We discuss how this form of collaboration helps meet requirements of data confidentiality. In case of the horizontal collaboration, the method operates at the level of the prototypes formed for each individual database. Numeric examples are used to illustrate the method.

9

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.

10

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.

11

Architectures of Granular Information and Their Robustness Properties: a Shadowed Sets Approach

Pedrycz W.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 2

435-455

EN

This paper addresses an important issue of information of granulation and relationships between the size of information granules and the ensuing robustness aspects. The use of shadowed sets helps identify and quantify absorption properties of set-based information granules. Discussed is also a problem of determining an optimal level of information granulation arising in the presence of noisy data. The study proposes a new architecture of granular computing involving continuous and granulated variables. Numerical examples are also included.