Special Types of Fuzzy Relations

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.

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Dr. IOAN DZITAC, Senior Member of IEEEB. & M.Sc. In Mathematics (1977), Ph.D. in Information Sciences (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)

IOAN DZITAC [email protected]

www.univagora.ro

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)

Co-Chair of SS07in ITQM2014

S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

http://univagora.ro/en/icccc2014/

http://univagora.ro/jour/index.php/ijccc


Contents

•Abstract• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References

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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.

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Contents

• Abstract

• Preliminaries• Affine Fuzzy Relations• Linear Fuzzy Relations• Convex Fuzzy Relations• M-Convex Fuzzy Relations• Conclusions & References

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Preliminaries (1/5)

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Preliminaries (2/5)

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D. Tufis, I. Dzitac, L.A. Zadeh, M.J. Manolescu and F.G. Filip at ICCCC 2008, Oradea, Romania


Preliminaries (3/5)

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Preliminaries (4/5)

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Preliminaries (5/5)

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Contents

• Abstract


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Affine Fuzzy Relations (1/2)

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Affine Fuzzy Relations (2/2)

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Contents

• Abstract


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Linear Fuzzy Relations (1/2)

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Linear Fuzzy Relations (2/2)

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Contents

• Abstract


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Convex Fuzzy Relations (1/2)

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Convex Fuzzy Relations (2/2)

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Contents

• Abstract


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M-Convex Fuzzy Relations (1/2)

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M-Convex Fuzzy Relations (2/2)

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Contents

• Abstract


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Conclusions & References (1/2)

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•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.


Conclusions & References (2/2)

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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)

Special Types of Fuzzy Relations

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