Przemysław Grzegorzewski - Academia.edu (original) (raw)

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Papers by Przemysław Grzegorzewski

The median two-sample test for the location problem is considered. We adopt this nonparametric te... more The median two-sample test for the location problem is considered. We adopt this nonparametric test to interval-valued data perceived from the epistemic perspective, where the available observations are just interval-valued perceptions of the unknown true outcomes of the experiment. Unlike typical generalizations of statistical procedures into the interval-valued framework, the proposed test entails very low computational costs. However, the presence of interval-valued data results in set-valued p-value which leads no longer to a definite binary decision (reject or not reject the null hypothesis) but may indicate the abstention from making a final decision if the information is too vague.

Control and Cybernetics, 1998

The multiple fuzzy linear regression model with fuzzy input–fuzzy output is considered. Assuming ... more The multiple fuzzy linear regression model with fuzzy input–fuzzy output is considered. Assuming that fuzzy inputs and fuzzy outputs are modeled by triangular fuzzy numbers, we prove the consistency and asymptotic normality of the least squares estimators.

Advances in Intelligent Systems and Computing, 2015

Probabilistic models, like the Mallows model, are commonly used for label ranking. However, for i... more Probabilistic models, like the Mallows model, are commonly used for label ranking. However, for incomplete preferences the existing methods are exhaustive in the learning step and therefore the applications of the Mallows model in practical label ranking problems or in recommender systems are limited. In this paper, we show how to improve the Mallows model using IF-sets so it may become more simple and more effective for analyzing vague preferences and creating recommendations.

Communications in Computer and Information Science, 2010

The idea of the membership functions construction form a data sample is suggested. The proposed m... more The idea of the membership functions construction form a data sample is suggested. The proposed method is based on the trapezoidal approximation of fuzzy numbers.

Scientometrics, 2009

Two broad classes of scientific impact indices are proposed and their properties-both theoretical... more Two broad classes of scientific impact indices are proposed and their properties-both theoretical and practical-are discussed. These new classes were obtained as a geometric generalization of the well-known tools applied in scientometric, like Hirsch's h-index, Woeginger's w-index and the Kosmulski's Maxprod. It is shown how to apply the suggested indices for estimation of the shape of the citation function or the total number of citations of an individual. Additionally, a new efficient and simple O(log n) algorithm for computing the h-index is given.

Advances in Soft Computing, 2006

ABSTRACT

Soft Computing, 2008

The problem of measuring association between preference systems in situations with missing inform... more The problem of measuring association between preference systems in situations with missing information or noncomparable outputs is discussed. New correlation coefficient, which generalizes Kendall's correlation coefficients used traditionally in statistics, is suggested. The construction utilizes IF-sets.

Classical statistical tests may be sensitive to vio- lations of the fundamental model assumptions... more Classical statistical tests may be sensitive to vio- lations of the fundamental model assumptions in- herent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. A generalization of the median test for the two-sample problem with

International Journal of Intelligent Systems, 2009

Classical statistical tests may be sensitive to violations of the fundamental model assumptions i... more Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. In the present paper, a distribution-free statistical test for the so-called "many-one problem" with vague data is suggested. This test is a generalization of the k-sample median test. In our approach, we utilize the necessity index of strict dominance, suggested by Dubois and Prade.

The R Journal

The classical bootstrap has proven its usefulness in many areas of statistical inference. However... more The classical bootstrap has proven its usefulness in many areas of statistical inference. However, some shortcomings of this method are also known. Therefore, various bootstrap modifications and other resampling algorithms have been introduced, especially for real-valued data. Recently, bootstrap methods have become popular in statistical reasoning based on imprecise data often modeled by fuzzy numbers. One of the challenges faced there is to create bootstrap samples of fuzzy numbers which are similar to initial fuzzy samples but different in some way at the same time. These methods are implemented in FuzzyResampling package and applied in different statistical functions like single-sample or two-sample tests for the mean. Besides describing the aforementioned functions, some examples of their applications as well as numerical comparisons of the classical bootstrap with the new resampling algorithms are provided in this contribution.

The two-sample dispersion testing problem is considered. Two generalizations of the Sukhatme test... more The two-sample dispersion testing problem is considered. Two generalizations of the Sukhatme test for interval-valued data are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment: the epistemic or the ontic one. Each view yields its own approach to data analysis which results in a different test construction and the way of carrying on the statistical inference.

Information Sciences, 2021

We consider the problem of measuring the degree of inclusion and similarity between interval-valu... more We consider the problem of measuring the degree of inclusion and similarity between interval-valued fuzzy sets. We propose a new idea for constructing indicators of inclusion and similarity measures based on the precedence relation, aggregation and uncertainty assessment. Furthermore, we examine selected properties of the suggested measures and their interactions. Finally, we discuss several similarity measures that appear in the literature and compare them with our novel approach.

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015

Recently, two new families of fuzzy implication functions called probabilistic implications and p... more Recently, two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications were introduced by Grzegorzewski [6, 7, 9]. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this paper we generalize these two classes and propose a new kind of construction methods for fuzzy implications which are based on an a priori given fuzzy implication I and a semicopula B.

Advances in Intelligent Systems and Computing, 2015

Fuzzy opinions are very common in surveys performed by social sciences. A fuzzy multinomial distr... more Fuzzy opinions are very common in surveys performed by social sciences. A fuzzy multinomial distribution for modeling such opinions is proposed. Next, a method for constructing a generalized version of the chi-square test of homogeneity which allows fuzzy data is proposed.

Advances in Soft Computing

ABSTRACT

Frontiers in Statistical Quality Control 6, 2001

A method for designing single sampling plans by attributes with relaxed producer’s and consumer’s... more A method for designing single sampling plans by attributes with relaxed producer’s and consumer’s risks and quality levels is suggested. Since small deviations of the parameter (risk, quality level) from its target value are very often of no importance this soft method for designing sampling plans is more flexible than the conventional one.

The median two-sample test for the location problem is considered. We adopt this nonparametric te... more The median two-sample test for the location problem is considered. We adopt this nonparametric test to interval-valued data perceived from the epistemic perspective, where the available observations are just interval-valued perceptions of the unknown true outcomes of the experiment. Unlike typical generalizations of statistical procedures into the interval-valued framework, the proposed test entails very low computational costs. However, the presence of interval-valued data results in set-valued p-value which leads no longer to a definite binary decision (reject or not reject the null hypothesis) but may indicate the abstention from making a final decision if the information is too vague.

Control and Cybernetics, 1998

The multiple fuzzy linear regression model with fuzzy input–fuzzy output is considered. Assuming ... more The multiple fuzzy linear regression model with fuzzy input–fuzzy output is considered. Assuming that fuzzy inputs and fuzzy outputs are modeled by triangular fuzzy numbers, we prove the consistency and asymptotic normality of the least squares estimators.

Advances in Intelligent Systems and Computing, 2015

Probabilistic models, like the Mallows model, are commonly used for label ranking. However, for i... more Probabilistic models, like the Mallows model, are commonly used for label ranking. However, for incomplete preferences the existing methods are exhaustive in the learning step and therefore the applications of the Mallows model in practical label ranking problems or in recommender systems are limited. In this paper, we show how to improve the Mallows model using IF-sets so it may become more simple and more effective for analyzing vague preferences and creating recommendations.

Communications in Computer and Information Science, 2010

The idea of the membership functions construction form a data sample is suggested. The proposed m... more The idea of the membership functions construction form a data sample is suggested. The proposed method is based on the trapezoidal approximation of fuzzy numbers.

Scientometrics, 2009

Two broad classes of scientific impact indices are proposed and their properties-both theoretical... more Two broad classes of scientific impact indices are proposed and their properties-both theoretical and practical-are discussed. These new classes were obtained as a geometric generalization of the well-known tools applied in scientometric, like Hirsch's h-index, Woeginger's w-index and the Kosmulski's Maxprod. It is shown how to apply the suggested indices for estimation of the shape of the citation function or the total number of citations of an individual. Additionally, a new efficient and simple O(log n) algorithm for computing the h-index is given.

Advances in Soft Computing, 2006

ABSTRACT

Soft Computing, 2008

The problem of measuring association between preference systems in situations with missing inform... more The problem of measuring association between preference systems in situations with missing information or noncomparable outputs is discussed. New correlation coefficient, which generalizes Kendall's correlation coefficients used traditionally in statistics, is suggested. The construction utilizes IF-sets.

Classical statistical tests may be sensitive to vio- lations of the fundamental model assumptions... more Classical statistical tests may be sensitive to vio- lations of the fundamental model assumptions in- herent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. A generalization of the median test for the two-sample problem with

International Journal of Intelligent Systems, 2009

Classical statistical tests may be sensitive to violations of the fundamental model assumptions i... more Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. In the present paper, a distribution-free statistical test for the so-called "many-one problem" with vague data is suggested. This test is a generalization of the k-sample median test. In our approach, we utilize the necessity index of strict dominance, suggested by Dubois and Prade.

The R Journal

The classical bootstrap has proven its usefulness in many areas of statistical inference. However... more The classical bootstrap has proven its usefulness in many areas of statistical inference. However, some shortcomings of this method are also known. Therefore, various bootstrap modifications and other resampling algorithms have been introduced, especially for real-valued data. Recently, bootstrap methods have become popular in statistical reasoning based on imprecise data often modeled by fuzzy numbers. One of the challenges faced there is to create bootstrap samples of fuzzy numbers which are similar to initial fuzzy samples but different in some way at the same time. These methods are implemented in FuzzyResampling package and applied in different statistical functions like single-sample or two-sample tests for the mean. Besides describing the aforementioned functions, some examples of their applications as well as numerical comparisons of the classical bootstrap with the new resampling algorithms are provided in this contribution.

The two-sample dispersion testing problem is considered. Two generalizations of the Sukhatme test... more The two-sample dispersion testing problem is considered. Two generalizations of the Sukhatme test for interval-valued data are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment: the epistemic or the ontic one. Each view yields its own approach to data analysis which results in a different test construction and the way of carrying on the statistical inference.

Information Sciences, 2021

We consider the problem of measuring the degree of inclusion and similarity between interval-valu... more We consider the problem of measuring the degree of inclusion and similarity between interval-valued fuzzy sets. We propose a new idea for constructing indicators of inclusion and similarity measures based on the precedence relation, aggregation and uncertainty assessment. Furthermore, we examine selected properties of the suggested measures and their interactions. Finally, we discuss several similarity measures that appear in the literature and compare them with our novel approach.

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015

Recently, two new families of fuzzy implication functions called probabilistic implications and p... more Recently, two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications were introduced by Grzegorzewski [6, 7, 9]. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this paper we generalize these two classes and propose a new kind of construction methods for fuzzy implications which are based on an a priori given fuzzy implication I and a semicopula B.

Advances in Intelligent Systems and Computing, 2015

Fuzzy opinions are very common in surveys performed by social sciences. A fuzzy multinomial distr... more Fuzzy opinions are very common in surveys performed by social sciences. A fuzzy multinomial distribution for modeling such opinions is proposed. Next, a method for constructing a generalized version of the chi-square test of homogeneity which allows fuzzy data is proposed.

Advances in Soft Computing

ABSTRACT

Frontiers in Statistical Quality Control 6, 2001

A method for designing single sampling plans by attributes with relaxed producer’s and consumer’s... more A method for designing single sampling plans by attributes with relaxed producer’s and consumer’s risks and quality levels is suggested. Since small deviations of the parameter (risk, quality level) from its target value are very often of no importance this soft method for designing sampling plans is more flexible than the conventional one.