Type-2 soft sets

In this paper the concept of type-2 soft sets has been introduced for the first time. Various operations are defined on them and their properties are studied. The notion of the image of a type-2 soft set under a mapping has been defined. An application of type-2 soft sets in the form of a decision making problem using the concept of type-2 weighted soft sets has been shown.

[1]  J. Goguen.  L-fuzzy sets , 1967 .

[2]  Ajoy Kumar Ray,et al.  Texture Classification Using a Novel, Soft-Set Theory Based Classification Algorithm , 2006, ACCV.

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

[4]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

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

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

[7]  Jerry M. Mendel,et al.  Operations on type-2 fuzzy sets , 2001, Fuzzy Sets Syst..

[8]  Pinaki Majumdar,et al.  On soft mappings , 2010, Comput. Math. Appl..

[9]  Muhammad Shabir,et al.  On soft topological spaces , 2011, Comput. Math. Appl..

[10]  Jerry M. Mendel,et al.  $\alpha$-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications , 2009, IEEE Transactions on Fuzzy Systems.

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

[12]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

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

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

[15]  Athar Kharal,et al.  MAPPINGS ON SOFT CLASSES , 2010, 1006.4940.

[16]  Daowu Pei,et al.  From soft sets to information systems , 2005, 2005 IEEE International Conference on Granular Computing.

[17]  S. K. Samanta,et al.  SIMILARITY MEASURE OF SOFT SETS , 2008 .

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

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

[20]  Yan Zou,et al.  Data analysis approaches of soft sets under incomplete information , 2008, Knowl. Based Syst..

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

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

[23]  radwa mohamed hassan,et al.  On Soft Metric Spaces , 2016 .

[24]  Naim Çagman,et al.  Soft set theory and uni-int decision making , 2010, Eur. J. Oper. Res..

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