Relations on Interval Valued Neutrosophic Soft Sets

Year 2014, Volume: 3 Issue: 5, 0 - 1, 01.05.2014

Said Broumi Irfan Deli Florentin Smarandache

Abstract

– Mukherjee [34] introduced the concept of interval valued intuitionistic fuzzy soft relation. In this paper we will extend this concept to the case of interval valued neutrosophic soft relation (IVNSS relation for short) which can be discussed as a generalization of soft relations, fuzzy soft relation, intuitionistic fuzzy soft relation, interval valued intuitionistic fuzzy soft relations and neutrosophic soft relations. Basic operations are presented and the various properties like reflexivity, symmetry, transitivity of IVNSS relations are also studied

Keywords

-

References

• S. Aggarwal, R. Biswas and A. Q. Ansari, Neutrosophic Modeling and Control, Computer and Communication Technology (2010) 718-723.
• B. Ahmad, and A. Kharal, On Fuzzy Soft Sets, Hindawi Publishing Corporation, Advances in Fuzzy Systems, (2009) Doi: 10.1155/2009/586507.
• S. Alkhazaleh, A. R. Salleh and N. Hassan, Possibility Fuzzy Soft Set, Advances in Decision Sciences, (2011) Doi:10.1155/2011/479756.
• M. Arora, R. Biswas and U.S. Pandy, Neutrosophic Relational Database Decomposition, International Journal of Advanced Computer Science and Applications, 2/ 8 (2011) 121-125.
• M. Arora and R. Biswas, Deployment of Neutrosophic Technology to Retrieve Answers for Queries Posed in Natural Language, in 3rdInternational Conference on Computer Science and Information Technology, (2010) 435-439.
• Ansari, Biswas, Aggarwal, Proposal for Applicability of Neutrosophic Set Theory in Medical AI, International Journal of Computer Applications, 27/5 (2011) 5-11.
• K. Atanassov. Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
• K.V. Babitha and J. J. Sunil,”Generalized Intuitionistic Fuzzy Soft Sets and Its Applications “, Gen. Math. Notes, 7/ 2 (2011) 1-14.
• M. Bashir, A.R. Salleh, and S. Alkhazaleh, Possibility Intuitionistic Fuzzy Soft Set, Advances in Decision Sciences, doi:10.1155/2012/404325.
• M. Bhowmik and M. Pal, Intuitionistic Neutrosophic Set, Journal of Information and Computing Science, 4/ 2, (2009) 142-152.
• M. Bhowmik and M. Pal, Intuitionistic Neutrosophic Set Relations and Some of Its Properties, Journal of Information and Computing Science, 5/3 (2010) 183-192.
• M. Borah, T. J. Neog and D. K. Sut, A study on some operations of fuzzy soft sets, International Journal of Modern Engineering Research, 2/ 2 (2012) 157-168.
• S. Broumi and F. Smarandache, Intuitionistic Neutrosophic Soft Set, Journal of Information and Computing Science, 8/ 2 (2013) 130-140.
• S. Broumi, “Generalized Neutrosophic Soft Set”, International Journal of Computer Science, Engineering and Information Technology, 3/2 (2013) 17-30.
• S. Broumi and F. Smarandache, ”More on Intuitionistic Neutrosophic Soft Sets”, Computer Science and Information Technology, 1/4 (2013) 257-268.
• S. Broumi and F. Smarandache, Several Similarity Measures of Neutrosophic Sets, Neutrosophic Sets and Systems, 1 (2013) 54-62.
• S. Broumi and F. Smarandache , Correlation Coefficient of Interval Neutrosophic set, Periodical of Applied Mechanics and Materials, Proceedings of the International Conference ICMERA, Bucharest, 436 2013.
• S. Broumi and F. Smarandache, New operations on interval neutrosophic set, 2013, accepted.
• P. Chi and L. Peide, An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic, Neutrosophic Sets and Systems, 1 (2013) 63-70.
• N. Çağman, I. Deli, Product of FP-Soft Sets and its Applications, Hacettepe Journal of Mathematics and Statistics, 41/3 (2012) 365 - 374.
• N. Çağman, I. Deli, Means of FP-Soft Sets and its Applications, Hacettepe Journal of Mathematics and Statistics, 41/5 ( 2012) 615–625.
• I. Deli, Interval-valued neutrosophic soft sets and its decision making http://arxiv.org/abs/1402.3130.
• I. Deli and S. Broumi, Neutrosophic soft relation and some properties (submitted). K. Georgiev, A simplification of the Neutrosophic Sets. Neutrosophic Logic and Intuitionistic Fuzzy Sets, 28. Int. Conf. on IFSs, Sofia, NIFS, 11/2 (2005), 28-31.
• Y. Jiang, Y. Tang, Q. Chen, H. Liu, J.Tang, “Interval-valued intuitionistic fuzzy soft sets and their properties”, Computers and Mathematics with Applications, 60 (2010) 906-918.
• A. Kharal, A Neutrosophic Multicriteria Decision Making Method, New Mathematics and Natural Computation, Creighton University, USA, 2013.
• F.G. Lupiáñez, On neutrosophic topology, Kybernetes, 37/6 (2008) 797 – 800.
• P. K. Maji, A. R. Roy and R. Biswas, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9/3 (2001) 589-602.
• P. K. Maji, R. Biswas and A. R. Roy, Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9/3 (2001) 677-692.
• P. K. Maji, Neutrosophic Soft Set, Annals of Fuzzy Mathematics and Informatics, 5/ 1 (2013) 2287-623.
• P. Majumdar and S.K. Samanta, On similarity and entropy of neutrosophic sets, Journal of Intelligent and Fuzzy Systems, 26/3 (2014) 1245-1252.
• P. Majumdar, S. K. Samanta, Generalized Fuzzy Soft Sets, Computers and Mathematics with Applications, 59 (2010) 1425-1432.
• D. A. Molodtsov, Soft Set Theory First Result, Computers and Mathematics with Applications, 37 (1999) 19-31.
• A. Mukherjee, A. Saha and A.K. Das, ”Interval valued intuitionistic fuzzy soft set relations”, Annals of Fuzzy Mathematics and Informatics, (2014) accepted.
• T. J. Neog and D. K. Sut, On Fuzzy Soft Complement and Related Properties, International Journal of Energy Information and Communications (IJEIC), 3/1 (2012) 24-34.
• A. A. Salama and S.A. Alblowi, Generalized Neutrosophic Set and Generalized Neutrosophic Topological Spaces, Computer Science and Engineering, 2/7 (2012) 129
• F. Smarandache, “A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic”. Rehoboth: American Research Press, 1999.
• I. Turksen, “Interval valued fuzzy sets based on normal forms”, Fuzzy Sets and Systems, 20 (1968) 191–210.
• H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, Single valued neutrosophic sets, Multispace and Multistructure, 4 (2010) 410–413.
• H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis, Phoenix, AZ, 2005.
• H. L. Yang, Notes On Generalized Fuzzy Soft Sets, Journal of Mathematical Research and Exposition, 31/ 3 (2011) 567-570.
• J. Ye, Single valued netrosophic minimum spanning tree and its clustering method Journal of Intelligent System, (2014) DOI: 10.1515/jisys-2013-0075.
• J. Ye, Similarity measures between interval neutrosophic sets and their multicriteria decision-making method, Journal of Intelligent and Fuzzy Systems, 26/1 (2014) 165-172.
• L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-353.