Papers by Przemysław Grzegorzewski
Mathematical sciences, Jan 22, 2018
In this paper, we present the novel concept of fuzzy semi-numbers. Then, a method for assigning d... more In this paper, we present the novel concept of fuzzy semi-numbers. Then, a method for assigning distance between every pair of fuzzy semi-numbers is given. Moreover, it is shown that this distance is a metric on the set of all trapezoidal fuzzy semi-numbers with the same height and is a pseudo-metric on the set of all fuzzy semi-numbers. Also, by utilizing this distance, we propose an approximation of a fuzzy semi-number with given height and apply this approximation method in a medical case study.
Soft Computing, Feb 14, 2019
The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the ... more The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26-51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot (n ≥ 2) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems.
In this paper we suggest how to est,imate a mean lifetime in the presence of vague data, especial... more In this paper we suggest how to est,imate a mean lifetime in the presence of vague data, especially imprecise number of failures.
Subsethood measure for intuitionistic fuzzy sets
2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542)
ABSTRACT
Lecture Notes in Computer Science, 2012
We propose a new system which is able to extract informative content from the news pages and divi... more We propose a new system which is able to extract informative content from the news pages and divide it into prescribed sections. The system is based on the machine learning classifier incorporating different kind of information (styles, linguistic information, structural information, content semantic analysis) and conditional learning. According to empirical results the suggested system seems to be a promising tool for extracting information from web.
A Recommender System Based on Customer Reviews Mining
Lecture Notes in Computer Science, 2014
As e-commerce is becoming more and more popular, the number of different products reviews done by... more As e-commerce is becoming more and more popular, the number of different products reviews done by customer grows rapidly. The efficient method for automatic summarization of such reviews is required. The majority of existing approaches classify a review only whether the opinion is positive or negative. In the present paper we show how to extract product features from the set of the reviews to design feature based summaries of available opinions. These summaries, expressed in IF-set framework, are later used to recommend a customer the best product corresponding to his individual demands.
Acceptance Sampling Plans by Variables for Vague Data
Advances in Intelligent and Soft Computing, 2002
All classical sampling plans were constructed for exact data. However, sometimes we are not able ... more All classical sampling plans were constructed for exact data. However, sometimes we are not able to obtain such data but we deal with imprecise or even linguistic data. Therefore, a method for designing acceptance sampling plans by variables for vague data is considered.
Goodness-of-fit tests for fuzzy data
Information Sciences, 2014
ABSTRACT One of the key problems in statistics is to get information about the form of the popula... more ABSTRACT One of the key problems in statistics is to get information about the form of the population from which a sample is drawn. To check compatibility of a set of observed values with a presumed distribution one can apply various, so called, goodness-of-fit tests. It seems that the goodness-of-fit testing problem becomes much more complicated in the presence of imprecise observations. Actually, although many statistical procedure dedicated for specified types of distributions were generalized to fuzzy environment, still there are not too many tools that help under fuzzy data from the unknown distribution. Therefore, in the paper we suggest how to generalize the well-known one-sample goodness-of-fit tests based on the empirical distribution function, like the Kolmogorov test, the Cramér-von Mises test or the Anderson-Darling test, for fuzzy data.
Recommender Systems and BOWA Operators
Advances in Intelligent Systems and Computing, 2015
ABSTRACT When making recommendations based on the aggregated correlations both their absolute val... more ABSTRACT When making recommendations based on the aggregated correlations both their absolute values and signs are meaningful and important. This is the reason why traditional aggregation operators, like OWA functions, may not be satisfactory. Therefore, a generalization of OWA operators which might be useful in aggregating a bipolar information is proposed and examined.
Trapezoidal approximations of fuzzy numbers preserving the expected interval—Algorithms and properties
Fuzzy Sets and Systems, 2008
Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is ... more Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. Algorithms for calculating the proper approximations are proposed and some properties of the approximation operators are discussed. It is shown that an adequate approximation operator might be chosen through the comparisons of some characteristics of the fuzzy number, like its ambiguity, width, its value and weighted expected value.
A new family of implication operators, called probabilistic implications, is introduced. The sugg... more A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic implications. Therefore, it seems that this new family of implication operators might be a useful tool in approximate reasoning.
Two-Sample Median Test for Interval-Valued Data
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.
Approximation of a Fuzzy Number Preserving Entropy-Like Nonspecifity
Statistical inference about the median from vague data
Control and Cybernetics, 1998
On Asymptotic Properties of the Multiple Fuzzy Least Squares Estimator
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.
Soft querying via intuitionistic fuzzy sets
ABSTRACT
On Incomplete Label Ranking with IF-sets
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.
Trapezoidal Approximation of Fuzzy Numbers Based on Sample Data
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.
Friedman’s Test for Ambiguous and Missing Data
Advances in Soft Computing, 2006
ABSTRACT
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Papers by Przemysław Grzegorzewski