Properties of Multigranular Rough Sets on Fuzzy Approximation Spaces and their Application to Rainfall Prediction

Basic rough set model introduced by Pawlak in 1982 has been extended in many directions to enhance their modeling power. One such attempt is the notion of rough sets on fuzzy approximation spaces by De et al in 1999. This basic model uses equivalence relation for its definition, which decompose the universal set into disjoint equivalence classes. These equivalence classes are called granules of knowledge. From the granular computing point of view the basic rough set model is unigranular in character. So, in order to handle more than one granular structure simultaneously, two types of multigranular rough sets, called the optimistic and pessimistic multigranular rough sets were introduced by Qian et al in 2006 and 2010 respectively. In this paper, we introduce two types of multigranular rough sets on fuzzy approximation spaces (optimistic and pessimistic), study several of their properties and illustrate how this notion can be used for prediction of rainfall. The introduced notions are explained through several examples.

[1]  Tsau Young Lin,et al.  Granular Computing on Binary Relations , 2002, Rough Sets and Current Trends in Computing.

[2]  Theresa Beaubouef,et al.  Rough Sets , 2019, Lecture Notes in Computer Science.

[3]  Yiyu Yao,et al.  On modeling data mining with granular computing , 2001, 25th Annual International Computer Software and Applications Conference. COMPSAC 2001.

[4]  Y. Yao.  Information granulation and rough set approximation , 2001 .

[5]  B.K.Tripathy,et al.  Some Algebraic Properties of Multigranulations and an Analysis of Multigranular Approximations of Classifications , 2013 .

[6]  Witold Pedrycz,et al.  Granular Computing - The Emerging Paradigm , 2007 .

[7]  Yiyu Yao,et al.  Granular Computing: Past, Present, and Future , 2008, Rough Sets and Knowledge Technology.

[8]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[9]  Witold Pedrycz,et al.  Granular Computing: Perspectives and Challenges , 2013, IEEE Transactions on Cybernetics.

[10]  Y. H. Qian,et al.  Rough Set Method Based on Multi-Granulations , 2006, 2006 5th IEEE International Conference on Cognitive Informatics.

[11]  B. K. Tripathy,et al.  On the approximate equalities of multigranular rough sets and approximate reasoning , 2013, 2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT).

[12]  B. K. Tripathy,et al.  On algebraic and topological properties of Neighbourhood Based Multigranular Rough Sets , 2014, 2014 International Conference on Computer Communication and Informatics.

[13]  Andrzej Bargiela,et al.  Granular clustering: a granular signature of data , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Yiyu Yao,et al.  A Unified Framework of Granular Computing , 2008 .

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

[16]  Yao,et al.  Three Perspectives of Granular Computing , 2006 .

[17]  B. K. Tripathy,et al.  Rough Sets on Fuzzy Approximation Spaces and Intuitionistic Fuzzy Approximation Spaces , 2009 .

[18]  Jiye Liang,et al.  International Journal of Approximate Reasoning an Efficient Rough Feature Selection Algorithm with a Multi-granulation View , 2022 .

[19]  D. Vanderpooten.  Similarity Relation as a Basis for Rough Approximations , 1995 .

[20]  B. K. Tripathy,et al.  Multi-Granular Computing through Rough Sets , 2014 .

[21]  B. K. Tripathy,et al.  On Covering Based Pessimistic Multigranular Rough Sets , 2014, 2014 International Conference on Computational Intelligence and Communication Networks.

[22]  B. Tripathy,et al.  On Multigranular Approximate Rough Equivalence of Sets and Approximate Reasoning , 2015 .

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

[24]  Jiye,et al.  Pessimistic Rough Decision , 2010 .

[25]  W. Pedrycz,et al.  Granular computing and intelligent systems : design with information granules of higher order and higher type , 2011 .

[26]  B. K. Tripathy,et al.  On Some Topological Properties of Multigranular Rough Sets , 2011 .

[27]  B. K. Tripathy,et al.  Topological Properties of Incomplete Multigranulation Based on Rough Fuzzy Sets , 2011 .

[28]  D.P. Acharjya,et al.  Rough sets on fuzzy approximation spaces and applications to distributed knowledge systems , 2008, Int. J. Artif. Intell. Soft Comput..

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

[30]  G. K. Panda,et al.  Some Concepts of Incomplete Multigranulation Based on Rough Intuitionistic Fuzzy Sets , 2012 .

[32]  B. K. Tripathy,et al.  Some Properties of Rough Sets on Fuzzy Approximation Spaces and Applications , 2016, FICTA.