Andrzej Piegat - Academia.edu (original) (raw)
Papers by Andrzej Piegat
Control and Cybernetics, 2014
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Artificial Intelligence and Soft Computing
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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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ABSTRACT
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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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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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Neural Networks and Soft Computing, 2003
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Studies in Fuzziness and Soft Computing, 2001
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International Journal of Applied Mathematics and Computer Science, 2015
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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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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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Enhanced Methods in Computer Security, Biometric and Artificial Intelligence Systems, 2000
ABSTRACT
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1997 European Control Conference, Jul 1, 1997
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ABSTRACT
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Control and Cybernetics, 2014
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Artificial Intelligence and Soft Computing
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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
ABSTRACT
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
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
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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Neural Networks and Soft Computing, 2003
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Bookmarks Related papers MentionsView impact
Studies in Fuzziness and Soft Computing, 2001
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International Journal of Applied Mathematics and Computer Science, 2015
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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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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
Enhanced Methods in Computer Security, Biometric and Artificial Intelligence Systems, 2000
ABSTRACT
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1997 European Control Conference, Jul 1, 1997
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ABSTRACT
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