Kronecker (tensor) models of fuzzy sets defined granules

Authors

  • Ю. Н. Минаев Национальный авиационный университет
  • О. Ю. Филимонова Национальный авиационный университет
  • Ю. И. Минаева Национальный авиационный университет

DOI:

https://doi.org/10.18372/2073-4751.1.7702

Keywords:

тензор, нечеткое множество, Кронекерово произведение, норма, информационная гранула, SVD-разложение

Abstract

Rassmatryvayutsya questions, svyazannыe with hranulyrovanyem Information and hranulyarnыmy vыchys-mined (hranulyrovannыy kompyutynh) at presentation of HM-hranulы as text Kronekerova works. Shown unyversalnost predlozhennoy model. Examples Pryvedenы, pokazы-vayuschye Efficiency of application tenzornыh ynformatsyonnыh granules poluchennыh As for HM, and so for a multitude of data yshodnыh, predstavlennыh as text mnohomernыh massyvov

Author Biographies

Ю. Н. Минаев, Национальный авиационный университет

д.т.н.

О. Ю. Филимонова, Национальный авиационный университет

к.т.н.

Ю. И. Минаева, Национальный авиационный университет

к.т.н.

References

Минаев Ю.Н., Филимонова О.Ю., Минаева Ю.И. Гранулярный компьютинг в системе нечетких множеств на уровне тензорных гранул// Проблемы информатизации и управления. – 2012. – № 4(40). – С.51-61.

Zadeh L.A. Toward a theory of fuzzy information granulation and its centralityin human reasoning and fuzzy logic// Fuzzy Sets and Systems. – 1997. – № 90. – P. 111-127.

Zadeh L.A. Toward a perceptionbased theory of probabilistic reasoning with impre-cise probabilities// Journal of Statistical Planning and Inference. – 2002. – №105. – P. 233-264.

Aja-Fern´andez S., AlberolaL´opez C. Fuzzy Granules as a BasicWord Representation for Computing with Words//SPECOM’2004: 9th Conference Speech and ComputerSt. Petersburg, Russia September 20-22, 2004.ISCA Archive http://www.iscaspeech. org/archive

Lin T., Yao Y., Zadeh L. Data Mining, Rough Sets and Granular Computing. Heidelberg.: – Physica-Verlag Heidelberg, – 2002.

Тарасов В.Б. Нестандартные множества и гранулированные вычисления//5-ые Поспеловские чтения «Искусственный интеллект – проблемы и перспективы». Интернет-ресурс: http:// www. posp.raai.org/data/posp 2011/tarasov.ppt

Тарасов В.Б. Теория нечетких множеств: новый виток развития. Интеллектуальные системы и технологии //Научная сессия МИФИ-2006. Том 3. Интернет-ресурс: http://www.library. mephi.ru/elbib/ izdvuza /scientificsessions? Year=2006...2

Вопенка П. Альтернативная теория множеств: Новый взгляд на бесконечность: Пер. со словац. – Новосибирск: Изд-во Института математики, 2004. – 611 с.

Пегат А. Нечеткое моделирование и управление. – М. : БИНОМ. Лаборатория знаний, 2009. – 798 с.

Zadeh L. A. Generalized theory of uncertainty-principal concepts and ideas.//Computational Statistics & Data Analysis.– 2006. – Vol. 51.– P. 15-46.

Wang Yi., Zadeh L. A., Yao Y. On the System Algebra Foundations for Granular Com-putting// Int. J. of Software Science and Computational Intelligence.- 2009. – 1, № 1. – P. 64-86.

Давыдов А.А. Системная социология. М.: КомКнига, 2006. – 192 c.

The Structural Representation of Proximity Matrices With MATLAB //cda_toolbox_ manual. Интернет-ресурс: http://cda.psych.uiuc.edu/matlab_class_mate rial/clusteringchapter_r1

Castellano G., Fanelli A.-M., Mencar C. Fuzzy Information Granules: a Compact, Transparent and Efficient Representation. COMPUTATIONAL INTELLIGENCE. In press.

Pedrycz W. Fuzzy Sets as a User-Centric Processing Framework of Granular Computing. In Handbook of Granular Computing. Edited by W. Pedrycz, A. Skowron and V. Kreinovich.- John Wiley & Sons, Ltd, 2008. – 1150 р.

Yao Y.Y. Granular Computing: basic issues and possible solutions. Интернет-ресурс:

Lin T.Y. Measure theory on granular fuzzy sets.// Fuzzy Information Processing Society, 1999. NAFIPS. 18th Internationa Conference of the North American: Jul 1999, – P. 809 – 813. (Conference Publications).

Langville A.N. , Stewart W.J. The Kronecker product and stochastic automata networks// Journal of Computational and Applied Mathematics. – 2004. – N 167. – P. 429-447.

Van Loan C.The Ubiquitous Kronecker Product// Journal of

Computational and Applied Mathematics. – 2000, №. 123. – P. 85-100.

Van Loan C. and Pitsianis N. Approximation with Kronecker Products//Linear Algebra for Large Scale and Real Time Applications, M. S. Moonen and G. H. Golub, eds.// Kluwer Publications, 1993. – P. 293-314. (See also http://www.cs.duke.edu/˜nikos/KP/home.html).

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Published

2014-03-29

How to Cite

Минаев, Ю. Н., Филимонова, О. Ю., & Минаева, Ю. И. (2014). Kronecker (tensor) models of fuzzy sets defined granules. Problems of Informatization and Management, 1(45), 77–88. https://doi.org/10.18372/2073-4751.1.7702

Issue

Vol. 1 No. 45 (2014)

Section

Статті

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