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1

Defuzzification with optimal representation method

Piegat A., Tomaszewska M.

Przegląd Elektrotechniczny

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2017

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R. 93, nr 1

108--111

EN

Though the number of existing defuzzification methods is considerable, scientists further work on the new methods trying to elaborate more perfect ones and eliminate imperfection and weak-points of existing methods. The paper proposes a new defuzzification method, which in the authors opinion, has chances for scientific acknowledgement because it is based on a new approach. In this method there is no aggregation of activated rule conclusions as in many other methods. Instead of aggregation, the method determines the best, optimal fuzzy representation of the activated conclusions and then finds the optimal crisp representation. The main advantage of the proposed method is simplicity of calculations.

PL

Choć liczba istniejących metod defuzyfikacji jest znaczna, naukowcy prowadzą dalsze prace nad nowymi metodami, starając się opracować bardziej doskonałe i wyeliminować niedoskonałości istniejących już metod. W pracy zaproponowano nową metodę defuzyfikacji, która w opinii autorów, ma szanse zdobycia uznania w środowisku naukowym, ponieważ pokazuje zupełnie nowe podejście. W sposobie tym nie ma agregacji zaktywowanych reguł wnioskowych tak jak w wielu innych metodach. Zamiast agregacji, metoda wyznacza najlepszą, optymalną rozmytą reprezentację aktywowanych wniosków, a następnie znajduje optymalną punktową reprezentację. Główną zaletą proponowanej metody jest prostota obliczeń.

2

Is an interval the right result of arithmetic operations on intervals?

Piegat A., Landowski M.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 3

575--590

EN

For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct result but only a simplified representative (indicator) of the result. This hypothesis seems surprising, but investigations prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples illustrate the proposed method of interval computations.

3

Fuzzy number division and the multi-granularity phenomenon

Piegat A., Pluciński M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 4

497--511

EN

The paper presents difficulties connected with fuzzy and interval division. If operations such as fuzzy addition, subtraction and multiplication provide as a result one compact, multidimensional granule, then a result of the fuzzy division can consists of few separated granules. Such results are more difficult to use in next calculations. The paper shows that the number of solution granules can be higher than 2 and that in certain problems division does not occur explicitly. In certain problems, separation of particular solution granules can be considerable. The paper also shows how to realize the fuzzy division when its denominator contains zero. Most types of fuzzy arithmetics forbid such operation. However, the paper shows that it is possible. Multidimensional fuzzy RDM arithmetic and horizontal membership functions which facilitate detecting of solution granules are also described. The considered problems are visualized by examples.

4

Synthesis and characterization of amphiphilic chitosan derivatives as nano/microstructures

Goszczyńska A., Niemczyk A., Piegat A.

Engineering of Biomaterials

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2016

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Vol. 19, no. 138 spec. iss.

38

5

Chitosan based drug delivery systems

Piegat A, Goszczyńska A., Niemczyk A.

Engineering of Biomaterials

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2016

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Vol. 19, no. 138 spec. iss.

27

EN

One of the research area in which polymeric materials are intensively explored, deals with the controlled drug delivery systems (DDSs), allowing for drugs distribution directly to the desired site of biological activity. The morphology of polymeric colloidal drug carriers can be described as a construction of a core-shell type. Depending on the chemical or physical bonds providing stability of those systems and the type of interactions between the drug and the polymer, among polymeric DDSs the following morphological structures can be distinguished: micelles, dendrimers, liposomes, niosomes, polymerosomes and micro- and nanocapsules [1]. The main advantages of those systems are the preparation of particles with desired size (diameter from nano to micrometers) during their synthesis / formation and high specific surface area, which can be modified by the appropriate chemical composition of the surface improving the efficiency of a drug delivery. Chitosan is biopolymer derived from chitin, that is characterised by biodegradability, biocompatibility, mucoadhesion and antimicrobial activity [2,3]. Taking into account the overall advantages of this polymer and the possibility of modification due to the accessible functional groups i.e. hydroxyl and amine, chemically modified chitosan is one of the most promising biomaterials for DDS. In order to obtain micelle structures by selfassemby in aqueous environment several hydrophobically modified chitosan derivatives, such as – stearic acid-modified chitosan [4], palmitic anhydridemodified chitosan [5], linolenic acid-modified chitosan [6], have been synthesized. The micelles prepared by these derivatives in the aqueous medium contain internal hydrophobic moieties as drug reservoir and external hydrophilic chitosan chains as surrounding shell. The above mentioned micellar systems allow encapsulation of hydrophobic antitumor drugs e.g. doxorubicin or paclitaxel due to the compatibility between the hydrophobic core and hydrophobic drug affecting the drug loading and regulate drug release. Another important group of chitosan based micro- and nanoparticles are those dedicated for gastric infection treatment. The use of chitosan in this specific application is mainly related with the mucoadhesive properties of chitosan resulted from the electrostatic interactions between its positively charged free amine groups and the negatively charged gastric mucins at the acidic stomach pH. Several problems such as high solubility of chitosan under stomach acidic conditions, low retention time and difficulty in crossing the mucus barrier have been observed in those systems [7]. Therefore various crosslinking methods e.g. with glutaraldehyde [8], genipin [9] or sodium triphosphate pentabasic (TPP) solution [10] were investigated in order to minimize these problems. The nanotechnological production of the polymeric drug carriers, as well as the disadvantages of already developed chitosan based drug delivery systems induce the NANOENCAP project concept on the development and characterization of new dendrimeric micelles polymeric systems, with rigidly defined chemical structure, allowing the encapsulation of several drugs and their controlled release, and thus forming the so-called multidrug therapy systems. To provide the biocompatibility of new polymeric materials the monomer / reactant with proven biocompatibility or naturally occurring in the human body are chosen. According to the assumptions of the project the amphiphilic character of the proposed multi-functional polymeric drug delivery systems is going to enable the encapsulation of at least two drugs, matching latest trends in the research on DDS models in multi-therapy. As an exemplary multi-drug therapy in this project, the combine therapy of peptic ulcer disease was chosen. In this work we would like to present the short review of chitosan based drug delivery systems and the concept of the project as well as preliminary studies on new chitosan derivatives and the possibility of synthesis new micellar structures.

6

Morphology of polyamide 6 confined into carbon nanotubes

Piegat A., Staniszewski Z., Poeppel A., El-Fray M.

Materials Science Poland

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2015

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Vol. 33, No. 2

306--311

EN

The preparation of polymer nanocomposites filled with carbon nanotubes requires the nanotubes to be uniformly dispersed and compatible with the polymer matrix. In this work we report a preparation method of polyamide 6 (PA 6) based nano-composite containing multi-walled carbon nanotubes (MWCNT) without any additional surface modification and obtained by in situ polymerization, as a simple method for composites production. The process was assisted by ultrasounds prior to synthesis. With such a method, an interesting morphology of polyamide 6 confined into a multi-walled carbon nanotube as well as grafted on a carbon nanotube surface was observed. For comparative purpose, PA 6 nanocomposites were also prepared from commercially available master batch by melt compounding.

7

Computing with words with the use of inverse RDM models of membership functions

Piegat A., Pluciński M.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 3

675--688

EN

Computing with words is a way to artificial, human-like thinking. The paper shows some new possibilities of solving difficult problems of computing with words which are offered by relative-distance-measure RDM models of fuzzy membership functions. Such models are based on RDM interval arithmetic. The way of calculation with words was shown using a specific problem of flight delay formulated by Lotfi Zadeh. The problem seems easy at first sight, but according to the authors’ knowledge it has not been solved yet. Results produced with the achieved solution were tested. The investigations also showed that computing with words sometimes offers possibilities of achieving better problem solutions than with the human mind.

8

Uncertainty analysis for efficient fuel allocation using info-gap theory

Tomaszewska K., Piegat A.

Information Systems in Management

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2015

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Vol. 4, No. 3

228--238

EN

Theory decision under uncertainty applies different methods to predict future events, physical measurements, which are already unknown. The paper shows one of the decision-making methods in conditions of severe uncertainty in application to a problem. Some aspects of the robustness and opportuneness functions of Info-Gap Theory are presented and used to evaluate the example of efficient fuel allocation. A general outline of decision analysis is presented, including its orientation and models.

9

The effect of catalyst and segmental composition on the crystallization of multiblock polyesters for biomedical applications

Staniszewski Z., Piegat A., Piątek-Hnat M., El Fray M.

Polimery

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2014

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T. 59, nr 7-8

592--598

EN

In the present work, segmented thermoplastic elastomers (TPE) containing hard segments of poly(ethylene terephthalate) (PET) and soft segments comprising amorphous fatty acid ester sequences based on dilinoleic acid (DLA) were synthesized. The aim was to obtain transparent materials with high strength and flexibility. Thermal properties of the obtained PET/DLA copolymers were examined using differential scanning calorimetry (DSC). It was found that segmental composition and new type of catalyst used for the synthesis of PET/DLA copolymers has influence on materials transparency.

PL

W ramach pracy zsyntezowano multiblokowe poliestrowe elastomery termoplastyczne (TPE), zawierające segmenty sztywne, takie jak w poli(tereftalanie etylenu) (PET), i segmenty giętkie zawierające amorficzne kwasy tłuszczowe na bazie kwasu dilinoleinowego (DLA). Celem było uzyskanie przezroczystych materiałów o dużej wytrzymałości i elastyczności. Właściwości termiczne otrzymanych kopolimerów PET/DLA zbadano za pomocą różnicowej kalorymetrii skaningowej (DSC). Stwierdzono, że wielkość udziału segmentów sztywnych i giętkich oraz zastosowanie nowego typu katalizatora do syntezy kopolimerów PET/DLA ma istotny wpływ na przeźroczystość materiałów, a tym samym na ich właściwości użytkowe.

10

The biocompatibility in vitro study of an innovative elastomer for heart assist devices construction

Kościelniak-Ziemniak M., Wilczek P., Kustosz R., Gonsior M., Błachowicz A., El Fray M., Piegat A., Piątek-Hnat M.

Engineering of Biomaterials

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2014

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Vol. 17, no. 128-129

112--113 [wklejka]

11

Chemical purity of new segmented polyester biomaterials

Piegat A., Walenia M., El Fray M.

Engineering of Biomaterials

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2014

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Vol. 17, no. 128-129

83--85

12

Specialized, MSE-optimal m-estimators of the rule probability especially suitable for machine learning

Piegat A., Landowski M.

Control and Cybernetics

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2014

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Vol. 43, no. 1

133--160

EN

The paper presents an improved sample based rule- probability estimation that is an important indicator of the rule quality and credibility in systems of machine learning. It concerns rules obtained, e.g., with the use of decision trees and rough set theory. Particular rules are frequently supported only by a small or very small number of data pieces. The rule probability is mostly investigated with the use of global estimators such as the frequency-, the Laplace-, or the m-estimator constructed for the full probability interval [0,1]. The paper shows that precision of the rule probability estimation can be considerably increased by the use of m-estimators which are specialized for the interval [phmin, phmax] given by the problem expert. The paper also presents a new interpretation of the m-estimator parameters that can be optimized in the estimators.

13

Decision-Making under uncertainty using Info-Gap Theory and a new multi-dimensional RDM interval arithmetic

Piegat A., Tomaszewska K.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 8

71--76

EN

Decision-making is an integral part of technical problem-solving. In this study, two decision theories, which are capable to deal with uncertain information – Info-Gap Theory and RDM (Relative-Distance-Measure) interval arithmetic, are presented. The paper shows some aspects of the robustness function and uses each approach to evaluate the example of charging car battery. The comparison of Info-Gap Theory and RDMarithmetic not only improves understanding of these methods, it also suggests some broader insights into robustness understanding.

PL

Podejmowanie decyzji jest nieodłączną częścią rozwiązywania technicznych problemów. W artykule zaprezentowano dwie metody, które rozwiązują problemy z niepewnymi danymi – Teoria Luk Informacyjnych i arytmetyka interwałowa RDM (Relative-Distance-Measure). Przedstawiono działanie każdej z metod na przykładzie ładowania akumulatora samochodowego. Porównanie Teorii Luk Informacyjnych i arytmetyki RDM nie tylko umożliwia głębsze poznanie tych metod, ale również sugeruje pewne szersze spojrzenie na rozwiązywanie problemów w warunkach niepewności.

14

Mean square error optimal completeness estimator Eph2 of probability

Piegat A., Landowski M.

Journal of Theoretical and Applied Computer Science

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2013

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Vol. 7, nr 3

3--20

EN

The paper presents the optimal estimator of probability for the binomial and multinomial case that was called ”completeness estimator Eph2” and theoretical proof of its optimality. The estimator accuracy was compared with accuracy of the universally used frequency estimator. The comparison was realized both theoretically and experimentally. Both comparison ways show superiority of the completeness estimator Eph2 over the frequency estimator frh = nh=n. A prooved solution of the single case problem is given.

15

Nonlinearity of human multi-criteria in decision-making

Piegat A., Sałabun W.

Journal of Theoretical and Applied Computer Science

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2012

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Vol. 6, nr 3

36-49

EN

In most cases, known methods of multi-criteria decision-making are used in order to make linear aggregation of human preferences. Authors of these methods seem not to take into account the fact that linear functional dependences rather rarely occur in real systems. Linear functions rather imply a global character of multi-criteria. This paper shows several examples of human nonlinear multi-criteria that are purely local. In these examples, the nonlinear approach is used based on fuzzy logic. It allows for better understanding of how important is the non-linear aggregation of human multi-criteria. The paper contains also proposal of an indicator of nonlinearity degree of the criteria. The presented results are based on investigations and experiments realized by authors.

16

New approach to the decision analysis in conditions of uncertainty – Info-Gap Theory

Piegat A, Tomaszewska K.

Journal of Theoretical and Applied Computer Science

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2012

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Vol. 6, nr 1

67-74

EN

The paper presents a new method of decision-making in conditions of severe uncertainty in application to a problem. The method has not been introduced in Poland yet and is still in the early development stage in Europe. Because the method is difficult to understand it was illustrated by the example of its application to evaluation of the project duration time. The paper also presents a proposal of decoupling a hypothesis relating to an outcome from the outcome itself in form of the incompatibility function of the hypothesis.

17

Is the conventional interval arithmetic correct?

Piegat A., Landowski M.

Journal of Theoretical and Applied Computer Science

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2012

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Vol. 6, nr 2

27-44

EN

Interval arithmetic as part of interval mathematics and Granular Computing is unusually important for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic thinking, Computing with Words, grey systems, fuzzy arithmetic and probabilistic arithmetic. However, the mostly used conventional Moore-arithmetic has evident weak-points. These weak-points are well known, but nonetheless it is further on frequently used. The paper presents basic operations of RDM-arithmetic that does not possess faults of Moore-arithmetic. The RDM-arithmetic is based on multi-dimensional approach, the Moore-arithmetic on one-dimensional approach to interval calculations. The paper also presents a testing method, which allows for clear checking whether results of any interval arithmetic are correct or not. The paper contains many examples and illustrations for better understanding of the RDM-arithmetic. In the paper, because of volume limitations only operations of addition and subtraction are discussed. Operations of multiplication and division of intervals will be presented in next publication. Author of the RDM-arithmetic concept is Andrzej Piegat.

18

Optimal estimator of hypothesis probability for data mining problems with small samples

Piegat A, Landowski M.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

629-645

EN

The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "[...] completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik's m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the [...] completeness estimator over the frequency estimator for the probability interval ph (0.1, 0.9). The frequency estimator is better for ph [0, 0.1] and ph [0.9, 1].

19

Composites of polyvinyl alcohol (PVA) hydrogel and calcium and magnesium phosphate formed by enzymatic functionalization

Douglas T. E. L., Piegat A., Schaubroeck D., El Fray M., Dubruel P.

Engineering of Biomaterials

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2012

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Vol. 15, no. 116-117 spec. iss.

137--138

EN

In this study, polyvinyl alcohol (PVA) hydrogels designed for osteochondral regeneration were mineralized with calcium phosphate (CaP) and magnesium phosphate (MgP) by incorporation of the enzyme alkaline phosphatase (ALP) and incubation in solutions of 0.1 M calcium or magnesium glycerophosphate (CaGP, MgGP). Hydrogels incubated in water served as controls. Dry mass percentage, i.e. the percentage consisting of polymer and mineral and not water, was markedly higher for samples incubated in CaGP and MgGP and decreased in the order: CaGP>MgGP>water. CaP and MgP formation was confirmed by FTIR. SEM revealed spherical deposits characteristic for apatite in samples incubated in CaGP and plate-like crystals of the magnesium phosphate bobierrite in samples incubated in MgGP, while samples incubated in water were devoid of deposits. Rheometric testing showed that storage modulus of hydrogels incubated in CaGP and MgGP was markedly higher and decreased in the order: CaGP>MgGP>water. The results prove the principle of enzymatic mineralization of PVA with CaP and MgP to improve their suitability for bone regeneration applications.

20

Zastosowanie samouczącego się trzypunktowego minimodelu do modelowania stopy bezrobocia w Polsce

Piegat A., Wąsikowska B., Korzeń M.

Zeszyty Naukowe. Studia Informatica / Uniwersytet Szczeciński

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2011

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Nr 27

59--69

PL

W artykule przedstawiono koncepcję ograniczonego, lokalnego, trójkątnego minimodelu, którego celem jest udzielenie – na podstawie próbek zależności y = f(x1, x2), jaką dysponujemy w bazie wiedzy – odpowiedzi na zapytania obliczeniowe. Badania wykazały, że dokładność obliczeń realizowanych przez minimodel jest wysoka, a czas obliczeń krótki. Uzyskana wysoka dokładność jest wynikiem lokalności minimodelu. Dalsze prace autorów idą w kierunku opracowania nieliniowych minimodeli o jeszcze wyższej dokładności obliczeń.

DE

Gegenstand des Artikels ist die Konstruktionsmethode des lokalen Minimodels das eine beträchtliche Lerngeschwindigkeit besitzt. Das Model dient hier zur Berechnung schneller Antworten an Anfragen bettreffens der Arbeitslosenquote aufgrund der Daten. Die Anzahl der Daten muss nicht konstant sein und kann mit der Zeit vergrößert werden, falls neue Daten gewonnen werden. Ein großer Vorteil des Minimodels ist seine Fähigkeit zur Interpolation in den Informationslücken in den Daten. Diese Fähigkeit unterscheidet das vorgeschlagene Minimodel von der KNN-Methode (Methode der nahesten Nachbarn). Ausser dem Erklären der Minimodelsidee wurde in dem Artikel ein Beispiel der Anwendung zur Modellierung der Arbeitslosenquote aufgrund statistischer Daten gezeigt. Die Qualität des Minimodels wurde mit der bekannten „leave one out” Methode geprüft.