Flexible resampling for fuzzy data

Grzegorzewski, Przemysław; Hryniewicz, Olgierd; Romaniuk, Maciej

doi:10.34768/amcs-2020-0022

Cited by 15 publications

(13 citation statements)

References 38 publications

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“…We will study the proposed transitivity properties in other real-world problems, e.g., to construct an equivalence measure that we may use in image processing. Moreover, in the future, we will also consider the possibility of using the transitivity and interval interpretation used in the work, taking into account the uncertainty in such interesting areas as the recommender systems (Rutkowski et al, 2019) or bootstrap methods (Grzegorzewski et al, 2020).…”

Section: B Pękala Et Almentioning

confidence: 99%

New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model

Pękala

Grochowalski

Eulalia

2021

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Atanassov's intuitionistic fuzzy sets and especially his intuitionistic fuzzy relations are tools that make it possible to model effectively imperfect information that we meet in many real-life situations. In this paper, we discuss the new concepts of the transitivity problem of Atanassov's intuitionistic fuzzy relations in an epistemic aspect. The transitivity property reflects the consistency of a preference relation. Therefore, transitivity is important from the point of view of real problems appearing, e.g., in group decision making in preference procedures. We propose a new type of optimistic and pessimistic transitivity among the alternatives (options) considered and their use in the procedure of ranking the alternatives in a group decision making problem.

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Section: B Pękala Et Almentioning

confidence: 99%

New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model

Pękala

Grochowalski

Eulalia

2021

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“…To avoid undesired repetitions which often appear in bootstrap Romaniuk and Hryniewicz [17][18][19] proposed a resampling method which enrich secondary samples with fuzzy observations imitating those from the primary sample but containing some incremental spreads on their 𝛼-cuts. Then Grzegorzewski et al [21,28] suggested another approach for generating bootstrap samples which may differ from the primary one but preserve the two-parameter canonical representation of each fuzzy observation, i.e., its value and ambiguity or the expected value and the width. We briefly discuss this method below, before introducing in Section 5 a new flexible bootstrap algorithm which preserves three-parameter canonical representation comprising the value, ambiguity and the fuzziness of a fuzzy number.…”

Section: Value-ambiguity (Va) Bootstrap Algorithmmentioning

confidence: 99%

“…where m denotes the size of the secondary sample (see also Ref. [28]), 𝜃 = 1 and 𝜆 stands for the Lebesgue measure.…”

Section: Standard Error Of the Estimatorsmentioning

confidence: 99%

Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Grzegorzewski¹,

Hryniewicz²,

Romaniuk³

2020

IJCIS

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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, however only such which do not disturb the canonical representation of the initial fuzzy numbers. We consider both two-parameter and three-parameter canonical representations, as well as the triangular and trapezoidal outputs in the secondary samples. Numerical experiments concerning some statistical tests based on fuzzy samples show that the suggested methods may appear helpful in statistical reasoning with imprecise data.

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“…Quantum computing is believed to be a source of new ideas and solutions leading to a very significant increase of computations performance, especially by shortening its duration in many areas of science e.g. applications to fuzzy logic [1], machine [2] and deep learning methods [3]. Unfortunately, quantum computers are still in an early stage of development what may be seen in restricted capabilities and an appearance of a high intensity of errors appearance during the computational process.…”

Section: Introductionmentioning

confidence: 99%

“…The utilised Python distribution is dedicated for Intel One API 2022.0.22 package. The numerical experiments were performed in virtual environment WSL2 for Windows 11 (version 10.0.22000.613), Linux kernel 5.10.102 1. The speedup values for different sizes of quantum system given by (112), where N is the number of qubits.…”

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confidence: 99%

Classical Computer Assisted Analysis of Small Multiqudit Systems

et al. 2022

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Quantum computation model is regarded as a model which can overcome barriers in calculations efficiency of problems which appear in modern science. In spite of hardware development, in particular a recent emergence of several different physical installations of the pioneering quantum machines, the contemporary and numerical analysis of problems concerning quantum computing is very important. In the first part of this article, some useful computing techniques for quantum registers processed by a quantum circuits are presented. Applied classical parallel computational techniques are utilised to shorten the whole computational time. New methods of processing state vectors for qudits and density matrices are presented, indicating which operations may be performed in parallel in the context of the implementation of local unitary operations. There is also shown, how to use the reduction operation in parallel implementation of the von Neumann measurement by performing local measurements on a system of qudits. In addition to the purely technical results as described above, the paper includes also a bunch of purely theoretical results which substitute a solid mathematical ground for the computations performed with the help of the computational routines as described in Section III. In particular, a discussion concerning general multi-qudit quantum states through the prism of Entropy and Negativity measures of entanglement included in has been presented. Additionally, the notion of the total entanglement has been introduced. For certain classes of popular multi-qudit states, the introduced deficits of entanglement defined with the use of von Neumann Entropy and Negativity have been discussed. In particular, by the use of Gram matrix technique, the corresponding deficits of entanglement in the analysed states have been computed in an explicite way. Additionally, some new results on AME states for some multiqudit systems are also included in Section V. The last part of the article presents some numerical experiments on multi-qudit entanglement and determination of total entanglement values for convex combinations of GHZ and W states. Some details concerning technical nature of results are included in the attached Appendix A.

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Flexible resampling for fuzzy data

Cited by 15 publications

References 38 publications

New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model

New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model

Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Classical Computer Assisted Analysis of Small Multiqudit Systems

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