More on neutrosophic soft rough sets and its modification

This paper aims to introduce and discuss anew mathematical tool for dealing with uncertainties, which is a combination of neutrosophic sets, soft sets and rough sets, namely neutrosophic soft rough set model. Also, its modification is introduced. Some of their properties are studied and supported with proved propositions and many counter examples. Some of rough relations are redefined as a neutrosophic soft rough relations. Comparisons among traditional rough model, suggested neutrosophic soft rough model and its modification, by using their properties and accuracy measures are introduced. Finally, we illustrate that, classical rough set model can be viewed as a special case of suggested models in this paper.

[1]  Armin R. Mikler,et al.  Temporal analysis of infectious diseases: influenza , 2005, SAC '05.

[2]  Generalized Near Rough Probability in Topological Spaces , 2011 .

[3]  B. K. Tripathy,et al.  On Some Topological Properties of Pessimistic Multigranular Rough Sets , 2012 .

[4]  Salvatore Greco,et al.  Rough approximation by dominance relations , 2002, Int. J. Intell. Syst..

[5]  Xiaole Bai,et al.  Topological characterizations of covering for special covering-based upper approximation operators , 2012, Inf. Sci..

[6]  XuJiuping,et al.  Rough approximation-based random model for quarry location and stone materials transportation problem , 2013 .

[7]  A. M. Kozae,et al.  Near Approximations in Topological Spaces , 2009 .

[8]  J.W.T. Lee,et al.  On the upper approximations of covering generalized rough sets , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[9]  Eric C. C. Tsang,et al.  The parameterization reduction of soft sets and its applications , 2005 .

[10]  Young Bae Jun,et al.  Applications of soft sets in ideal theory of BCK/BCI-algebras , 2008, Inf. Sci..

[11]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[12]  Mustafa Mat Deris,et al.  Soft Decision Making for Patients Suspected Influenza , 2010, ICCSA.

[13]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[14]  M. Gorzałczany.  A method for inference in approximate reasoning based on interval-valued fuzzy sets , 1987 .

[15]  Florentin Smarandache,et al.  Neutrosophic set - a generalization of the intuitionistic fuzzy set , 2004, 2006 IEEE International Conference on Granular Computing.

[16]  Yiyu Yao,et al.  Two views of the theory of rough sets in finite universes , 1996, Int. J. Approx. Reason..

[17]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[18]  Qinghua Hu,et al.  On rough approximations of groups , 2013, Int. J. Mach. Learn. Cybern..

[19]  Nirmala Rebecca Paul,et al.  Mathematical Innovations of a Modern Topology in Medical Events , 2012 .

[20]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

[21]  Y. Y. Yao.  Generalization of Rough Sets Using Relationships Between Attribute Values , 2005 .

[22]  Young Bae Jun,et al.  Soft sets and soft rough sets , 2011, Inf. Sci..

[23]  A. R. Roy,et al.  An application of soft sets in a decision making problem , 2002 .

[24]  Pabitra Kumar Maji,et al.  FUZZY SOFT SETS , 2001 .

[25]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[26]  Pabitra Kumar Maji,et al.  Neutrosophic Soft Set , 2013 .

[27]  Ming-Wen Shao,et al.  Generalized fuzzy rough approximation operators determined by fuzzy implicators , 2013, Int. J. Approx. Reason..

[28]  Marzena Kryszkiewicz,et al.  Rules in Incomplete Information Systems , 1999, Inf. Sci..

[29]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[30]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[31]  William Zhu,et al.  Topological approaches to covering rough sets , 2007, Inf. Sci..

[32]  Yee Leung,et al.  Maximal consistent block technique for rule acquisition in incomplete information systems , 2003, Inf. Sci..

[33]  D. Molodtsov.  Soft set theory—First results , 1999 .

[34]  Tsau Young Lin,et al.  Combination of interval-valued fuzzy set and soft set , 2009, Comput. Math. Appl..