Special Types of Fuzzy Relations S. Nadaban*, I. Dzițac*,** *Aurel Vlaicu University of Arad,...
-
Upload
mercedes-gloster -
Category
Documents
-
view
214 -
download
0
Transcript of Special Types of Fuzzy Relations S. Nadaban*, I. Dzițac*,** *Aurel Vlaicu University of Arad,...
Special Types of Fuzzy Relations
S. Nadaban*, I. Dzițac* ,**
*Aurel Vlaicu University of Arad, Department of Mathematics and Computer Science
**Agora University of Oradea, Department of Social SciencesRomania
Moscow, Russia, June 3-5, 2014.
Slide 2 of 26
Corresponding authorDr. IOAN DZITAC, Senior Member of IEEEB. & M.Sc. In Mathematics (1977), Ph.D. in Information Sci. (2002) (Babes-Bolyai University of Cluj-Napoca, RO)Professor of informatics at Aurel Vlaicu University of Arad, RO (tenured since 2009)Senior Researcher at Agora University of Oradea & Director of R&D Agora , RO (2012-2016)Adjunct Professor of the School of Management, University of Chinese Academy of Sciences, China (May 2013-May 2016)
Co-founder and General Chair of International Conference on Computers Communications and Control (ICCCC, since 2006)http://univagora.ro/en/icccc2014/
Co-Founder and Associate Editor in Chief of International Journal of Computers Communications & Control (since 2006), In Science Citation Index Expanded (ISI Thomson Reuters, Impact Factor(IF) in JCR2009 = 0.373; JCR2010 = 0.650; JCR2011 = 0.438; JCR2012 = 0.441); A) Automation & Control Systems [Q4, 49 of 59] ; 2B) Computer Science, Information Systems [Q4, 109 of 132].In Scopus (SJR2012 =0.297): A) Computational Theory and Mathematics [Q4] , B) Computer Networks and Communications [Q3] , C) Computer Science Applications [Q3]. http://univagora.ro/jour/index.php/ijccc
Rector of Agora University (2012-2016)[email protected]
Co-Chair of SS03in ITQM2013Suzhou, China
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Co-Chair of SS07in ITQM2014Moscow, Russia
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
•Abstract• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 3 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Abstract
• The aim of this paper is to present, in an unitary way, some special
types of fuzzy relations: affine fuzzy relations, linear fuzzy relations, convex fuzzy relations, M-convex fuzzy relations,
in order to build a fertile ground for application, in further papers, of these fuzzy relations in decision making. • All these fuzzy relations are characterized and we established
the inclusions between these classes of fuzzy relations.
Slide 4 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
• Abstract
• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 5 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Preliminaries (1/5)
Slide 6 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Preliminaries (2/5)
Slide 7 of 26
D. Tufis, I. Dzitac, L.A. Zadeh, M.J. Manolescu and F.G. Filip at ICCCC 2008, Oradea, Romania
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Preliminaries (3/5)
Slide 8 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Preliminaries (4/5)
Slide 9 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Preliminaries (5/5)
Slide 10 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
• Abstract
• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 11 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Affine Fuzzy Relations (1/2)
Slide 12 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Affine Fuzzy Relations (2/2)
Slide 13 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
• Abstract
• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 14 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Linear Fuzzy Relations (1/2)
Slide 15 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Linear Fuzzy Relations (2/2)
Slide 16 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
• Abstract
• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 17 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Convex Fuzzy Relations (1/2)
Slide 18 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Convex Fuzzy Relations (2/2)
Slide 19 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
• Abstract
• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 20 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
M-Convex Fuzzy Relations (1/2)
Slide 21 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
M-Convex Fuzzy Relations (2/2)
Slide 22 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Contents
• Abstract
• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References
Slide 23 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Conclusions & References (1/2)
Slide 24 of 26
•In this paper we have build a fertile ground to study, in further papers, special types of closed fuzzy relations between topological vector spaces. •The results obtained in this paper leave to foresee that there are solutions to theproblem afore mentioned. •These fuzzy relations can be proven to be a powerful tool for decision making.
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Conclusions & References (2/2)
Slide 25 of 26
S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow
Thank you for your attention!AcknowledgmentsThis work was supported in part by research centers:
1) Cercetare Dezvoltare Agora (R&D Agora) of Agora University of Oradea
(Director: I. Dzitac)
and
2) Mathematical Models and Information Systems, Faculty of Exact Sciences
of Aurel Vlaicu University of Arad.
(Director: I. Dzitac)