Wyniki wyszukiwania - BazTech

1

Computational gait analysis for post-stroke rehabilitation purposes using fuzzy numbers, fractal dimension and neural networks

Prokopowicz P., Mikołajewski D., Tyburek K., Mikołajewska E.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 2

191--198

EN

Computational gait analysis constitutes a useful tool for quantitative assessment of gait disturbances, improving functional diagnosis, assessment of treatment planning, and monitoring of disease progress. There is little research on use of computational gait analysis in neurorehabilitation of post-stroke survivors, but current evidence on its clinical application supports a favorable cost-benefit ratio. The research was conducted among 50 adult people: 25 of them after ischemic stroke constituted the study group, and 25 healthy volunteers constituted the reference group. Study group members were treated for 2 weeks (10 neurorehabilitation sessions). Spatio-temporal gait parameters were assessed before and after therapy and compared using a novel fuzzy-based assessment tool, fractal dimension measurement and gait classification based on artificial neural networks. Measured results of rehabilitation (changes of gait parameters) were statistically relevant and reflected recovery. There is good evidence to extend its use to patients with various gait diseases undergoing neurorehabilitation. However, methodology for properly conducting and interpreting the proposed assessment and analysis procedures, providing validity and reliability of their results remains a key issue. More objective clinical reasoning, based on proposed novel tools, requires further research.

2

Computational gait analysis using fuzzy logic for everyday clinical purposes - preliminary findings

Mikołajewska E., Prokopowicz P., Mikołajewski D.

Bio-Algorithms and Med-Systems

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2017

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Vol. 13, no. 1

37--42

EN

Background: Proper, early, and exact identification of gait impairments and their causes is regarded as a prerequisite for specific therapy and a useful control tool to assess efficacy of rehabilitation. There is a need for simple tools allowing for quickly detecting general tendencies. Objective: The aim of this paper is to present the outcomes of traditional and fuzzy-based analysis of the outcomes of post-stroke gait reeducation using the NeuroDevelopmental Treatment-Bobath (NDT-Bobath) method. Materials and methods: The research was conducted among 40 adult people: 20 of them after ischemic stroke constituted the study group, and 20 healthy people constituted the reference group. Study group members were treated through 2 weeks (10 therapeutic sessions) using the NDT-Bobath method. Spatio-temporal gait parameters were assessed before and after therapy and compared using novel fuzzy-based assessment tool. Results: Achieved results of rehabilitation, observed as changes of gait parameters, were statistically relevant and reflected recovery. One-number outcomes from the proposed fuzzy-based estimator proved moderate to high consistency with the results of the traditional gait assessment. Conclusions: Observed statistically significant and favorable changes in the health status of patients, described by gait parameters, were reflected also in outcomes of fuzzy-based analysis. Proposed fuzzy-based measure increases possibility of the clinical gait assessment toward more objective clinical reasoning based on common use of the mHealth solutions.

3

Fuzzy-based computational simulations of brain functions - preliminary concept

Prokopowicz P., Mikołajewski D.

Bio-Algorithms and Med-Systems

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2016

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Vol. 12, no. 3

99-104

EN

Research on the computational models of the brain constitutes an important part of the current challenges within computational neuroscience. The current results are not satisfying. Despite the continuous efforts of scientists and clinicians, it is hard to fully explain all the mechanisms of a brain function. Computational models of the brain based on fuzzy logic, including ordered fuzzy numbers, may constitute another breakthrough in the aforementioned area, offering a completing position to the current state of the art. The aim of this paper is to assess the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited both in the area of theoretical and experimental computational neuroscience and in clinical applications, including our own concept. The proposed approach can open a family of novel methods for a more effective and (neuro)biologically reliable brain simulation based on fuzzy logic techniques useful in both basic sciences and applied sciences.

4

Evaluation of Multicast Routing Algorithms with Fuzzy Sets

Piechowiak M., Prokopowicz P.

Advances in Electronics and Telecommunications

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2013

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Vol. 3, no. 5

44--48

EN

The paper presents a proposal of a new methodology that evaluates multicast routing algorithms in packet-switched networks with an application of fuzzy sets. Proposed multicriteria mechanism evaluate representative multicast routing algorithms: KPP, CSPT and MLRA (Multicast Routing Algorithm with Lagrange Relaxation) that minimize cost of paths between source and each destination node using Lagrange relaxation, and finally, minimize the total cost of multicast tree. A wide range of simulation research carried out by the authors, confirmed both the accuracy of new methodology and the effectiveness of the MLRA algorithm proposed by authors in earlier works.

5

Using fuzzy numbers in fatigue reliability estimation

Bednarek T., Prokopowicz P., Sosnowski W.

Computer Methods in Materials Science

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2009

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Vol. 9, No. 1

43-48

EN

Introduction Increasing safety requirements of structures induces necessity of taking into consideration the random nature of variables in the fatigue design. Fatigue analysis of real structures in connection with probabilistic analysis needs a big computational effort. In this paper a new approach and methodology to fatigue analysis of structures using fuzzy numbers are presented. The method has been developed. A new efficient tool of fatigue analysis was created. The calculation of fatigue life using fuzzy numbers set is illustrated with analysis of hydraulic cylinders. Local fatigue approach is used at critical locations on hydraulic cylinders. The purpose of the probabilistic design is to estimate the probability of failure for critical locations on hydraulic cylinder. Fuzzy numbers idea In common real-life problems often both, parameters and data used in mathematical modeling are vague. In mathematical modeling vagueness can be described by a fuzzy sets and numbers (main idea was started in 1965 by L. Zadeh). Fuzzy set theory has its well-known achievements in many branches of science and technology. Fuzzy concept was introduced in order to model such vague terms, as observed values of some physical or economical terms, pressure values or stock market rates, that can be inaccurate, can be noisy or can be difficult to measure with an appropriate precision because of technical reasons. Fuzzy numbers are a special kind of fuzzy sets, with restrictions, which makes them proper in analysis of imprecise data. As the fatigue is a parameter, which is really hard to determine precisely, so using here the idea of fuzzy numbers looks like the direction worth to investigate. However, in classical fuzzy numbers the problem is which usefulness of results after many calculations. Thus a new model of fuzzy numbers ? ordered fuzzy numbers ? were used in this paper in fatigue analysis of structures. New model has a good and flexible concept of calculations, which makes them easier, and have no basics problems from the classical fuzzy numbers. Thanks to the flexibility of the new concept the four algebraic operations: addition, subtraction, multiplication and division of such fuzzy numbers have been constructed in a way that renders their algebra. Operations rising to a power and finding the logarithm are also defined using numerical methods. Fatigue analysis of structures using fuzzy numbers idea The fatigue life calculations were performed using standard FEM program. The idea of the equivalent amplitude stress described in [fatigue] is used, in order to calculate the number of cycles to failure of the analyzed structure loaded by arbitrary non-symmetric load with any stress ratio. Previously presented equivalent amplitude stress idea and analytical form of S-N fatigue curve were modified. Fuzzy numbers idea was applied to define material parameters and value of external load. In consequence a fatigue life of structure is also fuzzy number. Analysis of fuzzy fatigue life could be estimation of reliability.

PL

Ciągle zwiększające się wymogi bezpieczeństwa wywołują konieczność wzięcia pod uwagę stochastyczną charakterystykę zmiennych w analizie zmęczeniowej konstrukcji. Analizę zmęczeniową rzeczywistych konstrukcji w połączeniu z analizą niezawodności w klasycznym probabilistycznym ujęciu cechuje niezwykle duży koszt obliczeniowy. W artykule przedstawiono nową metodę i oceny niezawodności konstrukcji za pomocą zbioru ukierunkowanych liczb rozmytych. Obliczenia niezawodności konstrukcji i narażonych na zmęczenie materiału przedstawiono na przykładzie analizy cylindra hydraulicznego. Zidentyfikowano miejsca narażone na pękanie zmęczeniowe. Obliczono trwałość zmęczeniową cylindra hydraulicznego za pomocą zbioru liczb rozmytych. Celem analizy zmęczeniowej z wykorzystaniem liczb rozmytych jest oszacowanie prawdopodobieństwa zniszczenia zmęczeniowego dla danej trwałości projektowej lub wyznaczenie okresów serwisowych przy zadanym poziomie niezawodności konstrukcji.

6

Comparison of classical methods of processing fuzzy information with methods using idea of ordered fuzzy numbers based on general linguistic Mamdani model

Prokopowicz P.

Image Processing & Communications

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2006

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Vol. 11, no 1

83-90

EN

Model of ordered fuzzy numbers (OFN) was defined and described in [4][5]. For this model simple and effective methods of arithmetical operations were suggested [4] [5] [6] [7]. OFNs representation is quite easy in the implementation as well as operations on them. Thanks to OFNs using we can free ourselves of the situation, in which results of operations on convex fuzzy numbers (classical model) we get "wider- more and more imprecise. In this paper author wants to pay attention on an important ownership of ordered fuzzy numbers - possibility of practical using as convex fuzzy numbers. Results of the simulation of using OFN to steering simplified fuzzy model of moving vehicle were introduced in [9]. Analysis and comparing results of the processing of imprecise information are a main aim of this publication. Were compared here chosen classical methods (aggregation of premises being based on MAX-MIN t-norm and reasoning methods based on Mamdani, Larsen, Łukasiewicz operators) with methods based on OFN. To get possibiy general results analysis were based on the very general linguistic model of Mamdani type fuzzy controller where we are operating on values of the linguistic variable amount so as little", average", "much". Carried analysis this way permits to get scores independent of units. With merit of introducing linguistic value in the form of fuzzy numbers, there is a possibility of straight and free graduating presented notions to the sizes dependent on the context in the any concrete situation.

7

Algebra liczb rozmytych

Kosiński W., Prokopowicz P.

Matematyka Stosowana : matematyka dla społeczeństwa

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2004

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Nr 5

37-63

PL

Określono algebrę skierowanych liczb rozmytych (ordered fuzzy numbers (OFN)), która umożliwia posługiwanie się pojęciami rozmytymi, ilościowo nieostrymi, w sposób podobny do rachunku na liczbach rzeczywistych. Zbiór skierowanych liczb rozmytych, izomorficzny z kwadratem kartezjańskim przestrzeni funkcji ciągłych na odcinku jednostkowym, ma strukturę przestrzeni liniowo-topologicznej oraz algebry Banacha z jedynką. Algebrę tę można wyposażyć w relację pre-porządku i posiada ona dzielniki zera oraz nietrywialne ideały. Podstawowe, w zastosowaniach praktycznych przy budowaniu rozmytych systemów wnioskujących, operacje wyostrzania (defuzzyficatiori) mogą się pojawić w tej przestrzeni Banacha jako liniowe i ciągłe funkcjonały, reprezentowane przez pary miar Radona (tutaj dwie całki w sensie Stieltjesa względem funkcji o wahaniu skończonym). Dalsze uogólnienie prowadzi do pojęcia skierowanych zbiorów rozmytych i odpowiadającej algebry Banacha. Przedstawione podstawy algebry skierowanych liczb (zbiorów) rozmytych dają możliwość budowy odpowiedników znanych pojęć z teorii równań różniczkowych, wzbogacając metody sterowania o nowe modele rozmyte. Z powodzeniem dokonana w środowisku Windows, w kalkulatorze rozmytym zCalc, programowa implementacja wprowadzonych operacji na liczbach rozmytych pozwala mieć nadzieję na szybki rozwój zastosowań przedstawionych tutaj pojęć i modeli.

EN

An algebra of ordered fuzzy numbers (OFN) is defined. It enables handling fuzzy inputs in a quantitative way, exactly in the same way as for real numbers. Additional two structures : algebraic and normad (topological) are introduced , which makes it possible to define a general form of defuzzyfication operators if fuzzy rules are used in a decision process. A useful implementation of a Fuzzy calculator is given which allows counting with OFNs of general type membership relations.

8

Counting with fuzzy numbers

Kosiński W., Prokopowicz P., Ślęzak D.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2003

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z. 20

221-225

EN

Fuzzy counterpart of real numbers is presented by adding to quasi-concave membership functions an extra feature, called the orientation of their graph. It leads to the novel concept of an ordered fuzzy number, represented by ordered pair of real continuous functions. Appropriately defined algebraic operations on ordered fuzzy numbers enable to avoid existing drawbacks of classical approaches.

PL

Rozmyty odpowiednik liczb rzeczywistych jest zaprezentowany poprzez dodanie do quasi-wklęsłych funkcji przynależności dodatkowej cechy: orientacji ich wykresów. To prowadzi do nowej koncepcji skierowanej liczby rozmytej, reprezentowanej przez parę rzeczywistych funkcji ciągłych. Odpowiednio określone algebraiczne operacje na skierowanych liczbach rozmytych umożliwia uniknięcia istniejących niedociągnięć w klasycznych podejściach.

9

Ordered fuzzy numbers

Kosiński W., Prokopowicz P., Ślęzak D.

Bulletin of the Polish Academy of Sciences. Mathematics

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2003

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Vol. 51, no 3

329-341

EN

Fuzzy counterpart of real numbers is presented. Fuzzy membership functions, which satisfy conditions similar to the quasi-convexity are considered. An extra feature, called the orientation of the curve of fuzzy membership function, is introduced. It leads to a novel concept of an ordered fuzzy number, represented by the ordered pair of real continuous functions. Arithmetic operations defined on ordered fuzzy numbers enable to avoid some drawbacks of the classical approach.