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Special Types of Fuzzy Relations

Moscow , Russia , June 3-5, 2014. Special Types of Fuzzy Relations. S. Nadaban * , I. Dzi ț ac* ,** * Aurel Vlaicu University of Arad , Department of Mathematics and Computer Science **Agora University of Oradea, Department of Social Science s Romania.

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Special Types of Fuzzy Relations

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  1. Moscow, Russia, June 3-5, 2014. Special Types of Fuzzy Relations S. Nadaban*, I. Dzițac* ,** *AurelVlaicu University of Arad, Department of Mathematics and Computer Science **Agora University of Oradea,Department of Social Sciences Romania

  2. 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 AurelVlaicu 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/ IOAN DZITAC rector@univagora.ro www.univagora.ro Co-Chair of SS07 in ITQM2014 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) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  3. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

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

  5. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

  6. Preliminaries (1/5) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  7. Preliminaries (2/5) 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

  8. Preliminaries (3/5) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  9. Preliminaries (4/5) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  10. Preliminaries (5/5) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  11. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

  12. Affine Fuzzy Relations (1/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  13. Affine Fuzzy Relations (2/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  14. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

  15. Linear Fuzzy Relations (1/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  16. Linear Fuzzy Relations (2/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  17. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

  18. Convex Fuzzy Relations (1/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  19. Convex Fuzzy Relations (2/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  20. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

  21. M-Convex Fuzzy Relations (1/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  22. M-Convex Fuzzy Relations (2/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  23. Contents S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow Abstract Preliminaries Affine Fuzzy Relations Linear Fuzzy Relations Convex Fuzzy Relations M-Convex Fuzzy Relations Conclusions & References

  24. Conclusions & References (1/2) • 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 the • problem 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

  25. Conclusions & References (2/2) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

  26. Thank you for your attention! Acknowledgments This work was supported in part by research centers: • CercetareDezvoltare Agora (R&D Agora) of AgoraUniversity of Oradea (Director: I. Dzitac) and 2) Mathematical Models and Information Systems, Faculty of Exact Sciences of AurelVlaicu University of Arad. (Director: I. Dzitac) S. Nadaban, I. Dzitac, Special Types of Fuzzy Relations, 4rd of June, 2014, Moscow

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