Search all articles
14 articles
Research Article
Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation
Przemyslaw Grzegorzewski, Olgierd Hryniewicz, Maciej Romaniuk
Pages: 1650 - 1662
Several new resampling methods for generating bootstrap samples of fuzzy numbers are proposed. To avoid undesired repetitions in the secondary samples we do not draw randomly directly observations from the primary samples but construct them allowing for some modifications in their membership functions,...
Research Article
Fuzzy Semi-Numbers and Their Elementary Arithmetic With a Medical Case Study
Sh. Yeganehmanesh, M. Amirfakhrian, P. Grzegorzewski
Pages: 991 - 1004
A new methodology for processing non-normal fuzzy sets is proposed. To break the predominant constraint on normality of fuzzy numbers the concept of fuzzy semi-numbers is introduced Then it is shown how to generalize operations defined on fuzzy numbers onto a family of fuzzy semi-numbers with possibly...
Proceedings Article
Similarity based one-sided tests for the expected value and interval data
Przemyslaw Grzegorzewski, Ana Belén Ramos-Guajardo
A novel way for addressing one-sided hypothesis tests for the mean of unable to observe real random variables from which we have information provided in terms of interval data is proposed. For this purpose, a measure of similarity between intervals is considered and the classical one-sided hypothesis...
Proceedings Article
Properties of the survival implications and S-implications
Piotr Helbin, Michal Baczynski
Recently, Grzegorzewski [9] introduced two new families of fuzzy implication functions called survival implications and survival S-implications. These two classes of multivalued implications are based on conditional copulas. In the same article the author gave a motivation to his ideas and he analyzed...
Proceedings Article
Fuzzy implications based on semicopulas
Michal Baczynski, Przemyslaw Grzegorzewski, Radko Mesiar
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...
Proceedings Article
Trapezoidal approximations of fuzzy numbers with restrictions on the support and core
Przemyslaw Grzegorzewski, Karolina Pasternak-Winiarska
Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New operators that fulfill additional requirements for the core and support of the fuzzy number are suggested. These supplementary conditions guarantee the proper interpretation of the solution...
Proceedings Article
The Inclusion-Exclusion Principle On the Set of IF-sets
Jana Kelemenová
P. Grzegorzewski [3] has worked the probability version of the inclusion-exclusion principle and made a generalization for IF-events. He had applied two versions of the generalized formula, corresponding to different t-conorms and so defined the union of IF-events. This paper contains the generalization...
Proceedings Article
Epistemic Bootstrap for Fuzzy Data
Przemysław Grzegorzewski, Maciej Romaniuk
Fuzzy data applied for modeling imprecise observations cause many problems in statistical reasoning and data analysis. To handle better such observations a new bootstrap technique designed for epistemic fuzzy data is proposed. Our new method is conceptually simple and is not hard computationally. Some...
Proceedings Article
In Search of a Precise Estimator Based on Imprecise Data
Przemyslaw Grzegorzewski, Joanna Goławska
Statistics with interval-valued data are getting less interest from practitioners than it really deserves. This is partly because the solutions it offers are often too conservative and hence do not fully meet the expectations of potential users. Thus it is necessary to develop methods which, despite...
Proceedings Article
Flexible bootstrap based on the canonical representation of fuzzy numbers
Przemyslaw Grzegorzewski, Olgierd Hryniewicz, Maciej Romaniuk
A new resampling approach for simulating bootstrapped samples of fuzzy numbers is proposed. The secondary samples consist of fuzzy numbers which preserve the canonical representation (i.e., the value and ambiguity) of fuzzy numbers belonging to the primary sample, although may differ from the initial...
Proceedings Article
A fixed-shape fuzzy median of a fuzzy sample
Adrian Ban, Lucian Coroianu, Przemyslaw Grzegorzewski
Since fuzzy numbers are not linearly ordered a median of a fuzzy sample cannot be determined directly as it happens with crisp observations. Even the very notion of a median of a fuzzy sample is not well established. Therefore we propose some definitions of the fixed-shape fuzzy median of a fuzzy sample...
Proceedings Article
Probabilistic Implications
Przemyslaw Grzegorzewski
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....
Proceedings Article
Evaluation and interval approximation of fuzzy quantities
Luca Anzilli, Gisella Facchinetti, Giovanni Mastroleo
In this paper we present a general framework to face the problem of evaluate fuzzy quantities. A fuzzy quantity is a fuzzy set that may be non normal and/or non convex. This new formulation contains as particular cases the ones proposed by Fortemps and Roubens (1996), Yager and Filev (1981,1999) and...
Proceedings Article
Axiomatic characterizations of (quasi-) L-statistics and S-statistics and the Producer Assessment Problem
Marek Gagolewski, Przemyslaw Grzegorzewski
Two classes of aggregation functions: L-statistics and S-statistics and their generalizations called quasi-L-statistics and quasi-S-statistics are considered. Some interesting characterizations of these families of operators are given. The aforementioned functions are useful for various applications....