Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.

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

[2]  Wei-Zhi Wu,et al.  Generalized fuzzy rough sets , 2003, Inf. Sci..

[3]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

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

[5]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[6]  Young Bae Jun,et al.  Soft BCK/BCI-algebras , 2008, Comput. Math. Appl..

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

[8]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[9]  Bijan Davvaz,et al.  Soft sets combined with fuzzy sets and rough sets: a tentative approach , 2010, Soft Comput..

[10]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[11]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

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

[13]  Yiyu Yao,et al.  A Comparative Study of Fuzzy Sets and Rough Sets , 1998 .

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

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

[16]  A. R. Roy,et al.  A fuzzy soft set theoretic approach to decision making problems , 2007 .

[17]  Keyun Qin,et al.  On soft equality , 2010, J. Comput. Appl. Math..

[18]  Xiaoyan Liu,et al.  On some new operations in soft set theory , 2009, Comput. Math. Appl..

[19]  Steven Li,et al.  The normal parameter reduction of soft sets and its algorithm , 2008, Comput. Math. Appl..

[20]  Zhi Xiao,et al.  A combined forecasting approach based on fuzzy soft sets , 2009 .

[21]  A. R. Roy,et al.  Soft set theory , 2003 .

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

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

[24]  Young Bae Jun,et al.  Soft semirings , 2008, Comput. Math. Appl..