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1

An application of the Pythagorean fuzzy sets in the fault diagnosis

Nguyen Hoang

Journal of KONBiN

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2022

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Vol. 52, iss. 4

63--74

EN

In this paper, a comprehensive review and critical analyses of methods based on the ordinary fuzzy set, Atanassov’s intuitionistic fuzzy set, and its extensions have been conducted to show their limitations and defects. Then, a novel similarity measure based on the generalized score function has been introduced that incorporates the significance (importance) of information, making it more intuitive to compare them. The proposed method is employed for the fault diagnosis of steam turbine generator unit under Pythagorean fuzzy environment. Ten fault types of rotating machines are established as failure patterns in nine different vibration frequency ranges, expressed in terms of Pythagorean fuzzy numbers. The superiority of the proposed method in dealing with uncertain and vague information is shown by comparing it with some existing measures in numerical examples.

PL

W artykule dokonano kompleksowego przeglądu i analiz krytycznych metod opartych na klasycznym zbiorze rozmytym lub intuicjonistycznym zbiorze rozmytym Atanassova i ich rozszerzeniach w celu wykazania ich ograniczeń i wad. Następnie wprowadzono na podstawie miary wiedzy, nową miarę podobieństwa, która uwzględnia znaczenie (ważność) informacji, czyniąc je bardziej intuicyjnymi przy ich porównywaniu. Zaproponowaną metodę weryfikuje się w przypadku diagnozowania uszkodzeń zespołu turbogeneratora w rozmytym środowisku. Dziesięć typów uszkodzeń turbogeneratora jest określanych jako wzorce uszkodzeń wyrażonych za pomocą liczb rozmytych Pitagorasa opisujących ich symptomy w dziewięciu różnych zakresach częstotliwości drgań. Poprzez porównanie z niektórymi istniejącymi miarami w kilku przykładach liczbowych pokazano przewagę proponowanej metody w opisaniu niedokładnych i niepewnych informacji.

2

Niewiarowski Artur

Computer Assisted Methods in Engineering and Science

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2019

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vol. 26, no. 3-4

163--175

EN

This paper presents a new algorithm with an objective of analyzing the similarity measure between two text documents. Specifically, the main idea of the implemented method is based on the structure of the so-called “edit distance matrix” (similarity matrix). Elements of this matrix are filled with a formula based on Levenshtein distances between sequences of sentences. The Levenshtein distance algorithm (LDA) is used as a replacement for various implementations of stemming or lemmatization methods. Additionally, the proposed algorithm is fast, precise, and may be implemented for analyzing very large documents (e.g., books, diploma works, newspapers, etc.). Moreover, it seems to be versatile for the most common European languages such as Polish, English, German, French and Russian. The presented tool is intended for all employees and students of the university to detect the level of similarity regarding analyzed documents. Results obtained in the paper were confirmed in the tests shown in the article.

3

Ďuračiová R., Rášová A., Lieskovský T.

Reports on Geodesy and Geoinformatics

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2017

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Vol. 104

115--130

EN

When combining spatial data from various sources, it is often important to determine similarity or identity of spatial objects. Besides the differences in geometry, representations of spatial objects are inevitably more or less uncertain. Fuzzy set theory can be used to address both modelling of the spatial objects uncertainty and determining the identity, similarity, and inclusion of two sets as fuzzy identity, fuzzy similarity, and fuzzy inclusion. In this paper, we propose to use fuzzy measures to determine the similarity or identity of two uncertain spatial object representations in geographic information systems. Labelling the spatial objects by the degree of their similarity or inclusion measure makes the process of their identification more efficient. It reduces the need for a manual control. This leads to a more simple process of spatial datasets update from external data sources. We use this approach to get an accurate and correct representation of historical streams, which is derived from contemporary digital elevation model, i.e. we identify the segments that are similar to the streams depicted on historical maps.

4

Object-parameter approaches to predicting unknown data in an incomplete fuzzy soft set

Liu Y., Qin K., Rao C., Alhaji Mahamadu M.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 1

157--167

EN

The research on incomplete fuzzy soft sets is an integral part of the research on fuzzy soft sets and has been initiated recently. In this work, we first point out that an existing approach to predicting unknown data in an incomplete fuzzy soft set suffers from some limitations and then we propose an improved method. The hidden information between both objects and parameters revealed in our approach is more comprehensive. Furthermore, based on the similarity measures of fuzzy sets, a new adjustable object-parameter approach is proposed to predict unknown data in incomplete fuzzy soft sets. Data predicting converts an incomplete fuzzy soft set into a complete one, which makes the fuzzy soft set applicable not only to decision making but also to other areas. The compared results elaborated through rate exchange data sets illustrate that both our improved approach and the new adjustable object-parameter one outperform the existing method with respect to forecasting accuracy.

5

Content-based image retrieval using a signature graph and a self-organizing map

Van T. T., Le T. M.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 2

423--438

EN

In order to effectively retrieve a large database of images, a method of creating an image retrieval system CBIR (content-based image retrieval) is applied based on a binary index which aims to describe features of an image object of interest. This index is called the binary signature and builds input data for the problem of matching similar images. To extract the object of interest, we propose an image segmentation method on the basis of low-level visual features including the color and texture of the image. These features are extracted at each block of the image by the discrete wavelet frame transform and the appropriate color space. On the basis of a segmented image, we create a binary signature to describe the location, color and shape of the objects of interest. In order to match similar images, we provide a similarity measure between the images based on binary signatures. Then, we present a CBIR model which combines a signature graph and a self-organizing map to cluster and store similar images. To illustrate the proposed method, experiments on image databases are reported, including COREL, Wang and MSRDI.

6

Akinwale A., Niewiadomski A.

Journal of Applied Computer Science

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2012

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Vol. 20, nr 2

7--26

EN

The purpose of this study is to explore the grammatical proper ties and features of generalized n-gram matching technique in electronic test at programming languages. N-gram matching technique has been success fully employed in information handling and decision support system dealing with texts but its side effect is size n which tends to be rather large. Two new methods of odd gram and sumsquare gram have been proposed for the improvement of generalized n-gram matching together with the modification of existing methods. While generalized n-grams matching is easy to generate and manage, they do require quadratic time and space complexity and are therefore ill-suited to the proposed and modified methods which work in quadratic in nature. Experiments have been conducted with the two new methods and modified ones using real life programming code assignments as pattern and text matches and the derived results were compared with the existing methods which are among the best in practice. The results obtained experimentally are very positive and suggested that the proposed methods can be successfully applied in electronic test at programming languages.

7

Zastosowanie modeli dokładnych sieci do detekcji i lokalizacji wycieków

Tomasik P.

Problemy Eksploatacji

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2011

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nr 2

223-230

PL

W referacie opisano metodę wykorzystującą dokładne modele sieci wodociągowej do detekcji i lokalizacji wycieków. Metoda ta bazuje na prostej mierze podobieństwa pomiędzy rzeczywistymi i modelowymi danymi o przepływach w sieci wodociągowej.

EN

The paper describes a method of using accurate models of the water supply system for detecting and locating leaks. This method is based on a simple measure of similarity between real and simulated data on water flows in the water supply.

8

Analysis of Cotton Maturity Degree on Microstructure Level by Fuzzy Set Conception

Sarna E., Rabiej M., Sarna M., Włochowicz A.

Fibres & Textiles in Eastern Europe

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2008

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Vol. 16, no. 1 (66)

13--18

EN

This paper is a continuation and generalisation of an earlier study of cotton maturity degree determination in the earlier paper. Up till now the maturity degree of cotton has been determined by the analysis of longitudinal outside views of cotton fibres. Early, we proposed a method of cotton maturity determination based on SEM images of cotton fractures. Fuzzy set conception was adopted to analyse each image, considering the fracture category. In this paper have emphasized the fuzzy aspects of cotton maturity determination by analysing the longitudinal outside views of cotton in accordance with the “Russian-standard”, and by using a new method for determination, which is based on analysing SEM images of cotton fractures proposed by as.

PL

Przedstawiona praca stanowi kontynuację wcześniejszych badań nad wyznaczaniem stopnia dojrzałości bawełny do tej pory wyznaczanego na podstawie analizy wzdłużnego, zewnętrznego widoku włókna bawełny. W wcześniejszej pracy zaproponowano metodę wyznaczania dojrzałości bawełny na podstawie analizy obrazów SEM przełomów włókien bawełny. Do analizy cech obrazów przełomów włókien została zastosowana koncepcja zbiorów rozmytych. W prezentowanym opracowaniu zastosowano elementy zbiorów rozmytych również do oceny wzdłużnego widoku włókna. Utworzono „wzorzec rozmyty” bazując na tzw. „Standardach Radzieckich”. Miara „zbliżenia” zbioru rozmytego jest użytecznym narzędziem do wyznaczania stopnia dojrzałości bawełny.

9

Problem of loss compression taking into cosideration the structural components of signal distortion and compression technique unversality

Berkman L. N., Valchuk D.

Computing, Multimedia and Intelligent Techniques

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2007

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Vol. 3, nr 1

42-59

EN

In the paper, the outline of novel loss compression technique presents. The technique provides new possibilities: 1) a mechanism of loss compression quality rationalization into the space of quality indices, which are selected with a special purpose, 2) a mechanism of loss compression technique universality in sense of compressed signal heterogeneity and replacement of compression tasks of an end user. Besides those, a significant indication of the technique is its possibility of a signal structural distortion consideration. To realize this indication, we have selected pseudo-information measure JeK and studded its possibilities as a loss compression criterion for non-media signals. The measure exhibits several features that match experimental findings in multimedia perception.

10

Induction of diagnostic support rules through data mapping - on the example of the Hepar system

Bobrowski L., Wasyluk H.

Biocybernetics and Biomedical Engineering

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2007

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Vol. 27, no. 3

3-14

EN

Induction of similarity measures through data transformations is considered in the paper. Particular attention is paid to the separable linear transformation of multidimensional data on a plane and the data visualisation on diagnostic maps. Diagnostic support in the Hepar computer system is based on diagnostic maps. Separable linear transformations in the Hepar system are based on minimization of the convex and piecewise linear (CPL) criterion functions. The CPL criterion functions give a possibility for a flexible and efficient design of the visualising transformations which well separates the disease on the diagnostic maps.

11

Podziałowe i hierarchiczne algorytmy grupowania danych

Stąpor K.

Studia Informatica

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2004

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Vol. 25, nr 1

157-170

PL

W artykule przedstawiono najważniejsze podziałowe oraz hierarchiczne algorytmy grupowania danych. Wśród algorytmów podziałowych omówiono algorytmy oparte na prototypach punktowych oraz liniowych. Przedstawiono algorytmy hierarchiczne dla różnych miar podobieństwa oraz omówiono skrótowo kla-steryzację neuronową wykorzystującą sieć Kohonena.

EN

In this paper the most important partitional and hierarchical data clustering algorithms arę described. Among partitional algorithms those based on point and linear prototypes arę discussed. In hierarchical algorithms different similarity measures arę described. Also, neural network clustering based on Kohonen network is described.

12

Właściwości miar podobieństwa w modelu sieci idiotypowej z binarną reprezentacją wzorców

Trojanowski K., Jankowiak M.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

|

2004

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Nr 977

1-20

PL

W niniejszej pracy analizowany jest model sieci idiotypowej zaproponowany w artykule autorstwa Farmer et al. w 1986 roku i wykorzystujący ciągi binarne do reprezentacji przeciwciał i antygenów. Jak pisali de Castro i Timmis o tej pracy w swojej książce w 2002 roku: "Ich (tj. Farmera i pozostałych autorów) prace mają wyjątkowe znaczenie, ponieważ stanowią pierwsze podejście do połączenia w całość matematycznej immunologii teoretycznej z paradygmatami inteligencji obliczeniowej. Tak jak w pracach Jerne~Ra ich model składał się ze zbioru równań różniczkowych służących obliczaniu dynamiki składników sieci." Jedno z tych równań, miara podobieństwa używana do obliczania dopasowania pomiędzy ciągami binarnymi była przedmiotem badań prezentowanych poniżej. Wykonany został zbiór testów mających na celu zbadanie wrażliwości miary na różne rodzaje binarnych wzorców oraz liczby bitów różniących mierzone wzorce. Ponadto zaproponowany został również nowy operator transformacji ciągów binarnych. Operator ten zmienia własności miary podobieństwa proponowanej przez Farmera, przy czym nowa miara z włączonym w nią operatorem transformacji okazuje się bardziej selektywna na różne ilości niepasujących bitów oraz położenie tych bitów w mierzonych ciągach binarnych niż jej poprzedniczka.

EN

The bitstring model of the immune network model proposed by Farmer et al. in 1986 is studied in this text. As de Castro and Timmis wrote about the paper in their book (2002): "Their works arę of extreme importance, as they constituted the first attempts to bring together mathematical theoretical immunology and computational intelligence paradigms. As in Jerne's work their model consisted of a set of differential eąuations to ąuantify the dynamics of the components of the immune network." One of these eąuations, the affinity measure used to evaluate match between binary strings, was the subject of the study presented below. A set of tests was perform to study the sensitivity of the measure to the different types of binary patterns and numbers of different bits in the strings. A new transformation operator for binary strings is also proposed. The operator modifies properties of the affinity measure proposed by Farmer. The new measure with the transformation operator included proves to be morę selective to the different numbers of non-matching bits and their position in the evaluated bit strings, than the previous one.

13

An adaptive stochastic optimization method for medical registration problem

Król Z.

Journal of Medical Informatics & Technologies

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2004

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Vol. 7

MIP79--88

EN

This paper presents a methodology that addresses important issues concerned with the optimization of the misregistration measures in the volumetric medical data registration problem. Our registration framework uses robust simulated annealing method to handle multiple local minima of the cost function. Our efforts have been centred on obtaining a reliable, efficient and generally applicable method to solve such optimization problems. This has been accomplished through developing an adaptive cooling schedule for the simulated annealing method. The proposed method is very reliable for the estimation of the global minimum in the optimization of objective functions with highly differentiated search space landscapes. We present the detailed description of the method as well as discussion of its advantages and disadvantages.

14

The method of preliminary medical images selection

Porwik P., Wróbel K., Widuch S., Doroz R.

Journal of Medical Informatics & Technologies

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2001

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Vol. 2, Part. 1

MI169--MI176

EN

This work investigates the use of some features computed using the Hough Transform as a criterion for image similarity evaluation based on picture retrieval. The method is based on a modified Hough Transform and used to approximate edges detected in the input image with straight lines. We consider retrieving images from a thematic database, where the semantic contents of images is limited to a specific domain (for example medical images). Proposed analysis of images does not claim that all features will be used, but special selection of features is well suited for evaluating of the visual coherence of images. In the first stage line elements are extracted from the image by using Hough Transform. In the second stage similarity coefficients are computed.