Andrzej Piegat - Academia.edu (original) (raw)

Papers by Andrzej Piegat

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

Control and Cybernetics, 2014

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Research paper thumbnail of Decision-Making Problems with Local Extremes: Comparative Study Case

Artificial Intelligence and Soft Computing

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

The paper presents a new (to the best of the authors ’ knowledge) estimator of probability called... more The paper presents a new (to the best of the authors ’ knowledge) estimator of probability called the “Ep

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Research paper thumbnail of Control and Cybernetics On practical problems with the explanation of the difference between possibility and probability

ABSTRACT

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Research paper thumbnail of What is Not Clear in Fuzzy Control Systems?

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Research paper thumbnail of Bayes Rule, Piegat A. Alndowski M., ICAISC 2008

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Research paper thumbnail of Andrzej Piegat, Marek Landowski, Correctness-checking of uncertain-equation solutions on example of the interval-modal method. Twelf International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN'2013, organized by System Research Institute of Polish Academy of Sciences, Warsaw...

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

International Journal of Applied Mathematics and Computer Science

For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, ... more 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...

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Research paper thumbnail of Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

Mathematics

To answer the question stated in the title, we present and compare two approaches: first, a stand... more To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded.

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Research paper thumbnail of How to Test Overfitting When There is not Enough Data for a Testing Set?

Neural Networks and Soft Computing, 2003

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Research paper thumbnail of Cyfrowy układ sterowania ruchem bezzałogowego pojazdu podwodnego

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Research paper thumbnail of Child well being estimation as a multi-criteria decision problem

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Research paper thumbnail of Fuzzy Control

Studies in Fuzziness and Soft Computing, 2001

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Research paper thumbnail of Computingwithwords with the Use of Inverse Rdm Models of Membership Functions

International Journal of Applied Mathematics and Computer Science, 2015

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Research paper thumbnail of Fuzzy Number Addition with the Application of Horizontal Membership Functions

The Scientific World Journal, 2015

The paper presents addition of fuzzy numbers realised with the application of the multidimensiona... more The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods use α-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.

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Research paper thumbnail of Are Linguistic Evaluations Used by People of Possibilistic or Probabilistic Nature?

Lecture Notes in Computer Science, 2004

Defining linguistic fuzzy evaluations of various quantities e.g. very small, average, approximate... more Defining linguistic fuzzy evaluations of various quantities e.g. very small, average, approximately 5, a little more than 10, we usually assume that membership functions qualifying for these evaluations are of possibilistic character. The paper presents a comparison of a measurement realization by a technical instrument and of evaluation by man (uncertainty of the measurement realized by technical instrument is mainly

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Research paper thumbnail of Informative value of the possibilistic extension principle

Enhanced Methods in Computer Security, Biometric and Artificial Intelligence Systems, 2000

ABSTRACT

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Research paper thumbnail of Stability checking of a real digital control system with a neuro-fuzzy PD-controller

1997 European Control Conference, Jul 1, 1997

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Research paper thumbnail of Bewegungsverhalten und automatische Kurssteuerung von unbemannten Unterwasserfahrzeugen mit offener Rahmenkonstruktion

ABSTRACT

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Research paper thumbnail of Modelowanie i sterowanie rozmyte

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

Control and Cybernetics, 2014

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Research paper thumbnail of Decision-Making Problems with Local Extremes: Comparative Study Case

Artificial Intelligence and Soft Computing

Bookmarks Related papers MentionsView impact

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

The paper presents a new (to the best of the authors ’ knowledge) estimator of probability called... more The paper presents a new (to the best of the authors ’ knowledge) estimator of probability called the “Ep

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Control and Cybernetics On practical problems with the explanation of the difference between possibility and probability

ABSTRACT

Bookmarks Related papers MentionsView impact

Research paper thumbnail of What is Not Clear in Fuzzy Control Systems?

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Bayes Rule, Piegat A. Alndowski M., ICAISC 2008

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Andrzej Piegat, Marek Landowski, Correctness-checking of uncertain-equation solutions on example of the interval-modal method. Twelf International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN'2013, organized by System Research Institute of Polish Academy of Sciences, Warsaw...

Bookmarks Related papers MentionsView impact

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

International Journal of Applied Mathematics and Computer Science

For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, ... more 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...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

Mathematics

To answer the question stated in the title, we present and compare two approaches: first, a stand... more To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of How to Test Overfitting When There is not Enough Data for a Testing Set?

Neural Networks and Soft Computing, 2003

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Research paper thumbnail of Cyfrowy układ sterowania ruchem bezzałogowego pojazdu podwodnego

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Research paper thumbnail of Child well being estimation as a multi-criteria decision problem

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fuzzy Control

Studies in Fuzziness and Soft Computing, 2001

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Research paper thumbnail of Computingwithwords with the Use of Inverse Rdm Models of Membership Functions

International Journal of Applied Mathematics and Computer Science, 2015

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Research paper thumbnail of Fuzzy Number Addition with the Application of Horizontal Membership Functions

The Scientific World Journal, 2015

The paper presents addition of fuzzy numbers realised with the application of the multidimensiona... more The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods use α-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Are Linguistic Evaluations Used by People of Possibilistic or Probabilistic Nature?

Lecture Notes in Computer Science, 2004

Defining linguistic fuzzy evaluations of various quantities e.g. very small, average, approximate... more Defining linguistic fuzzy evaluations of various quantities e.g. very small, average, approximately 5, a little more than 10, we usually assume that membership functions qualifying for these evaluations are of possibilistic character. The paper presents a comparison of a measurement realization by a technical instrument and of evaluation by man (uncertainty of the measurement realized by technical instrument is mainly

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Informative value of the possibilistic extension principle

Enhanced Methods in Computer Security, Biometric and Artificial Intelligence Systems, 2000

ABSTRACT

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Stability checking of a real digital control system with a neuro-fuzzy PD-controller

1997 European Control Conference, Jul 1, 1997

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Bewegungsverhalten und automatische Kurssteuerung von unbemannten Unterwasserfahrzeugen mit offener Rahmenkonstruktion

ABSTRACT

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Modelowanie i sterowanie rozmyte

Bookmarks Related papers MentionsView impact