A comparative review on nondeterministic sets for association rule mining

Nowadays decision making based on data mining mostly deals with imprecise environment. Managing various uncertainties is one of the main challenging areas in decision support systems. The aim of this paper is to compare the relationship among four paramount uncertain sets namely, soft, grey, rough and fuzzy sets. The origin of these vague names is investigated and how they could be combined to make effective usage is shown. A systematic consideration is accomplished with respect to data mining approaches. The analysis demonstrates that these uncertain sets provide different but overlapping approaches for uncertainty representation and reasonable consolidation of them in rule mining could lead to more appropriate results.

[1]  Pawan Lingras,et al.  Survey of Rough and Fuzzy Hybridization , 2007, 2007 IEEE International Fuzzy Systems Conference.

[2]  Didier Dubois,et al.  Putting Rough Sets and Fuzzy Sets Together , 1992, Intelligent Decision Support.

[3]  M. Nagai,et al.  Reviewing crisp, fuzzy, grey and rough mathematical models , 2007, 2007 IEEE International Conference on Grey Systems and Intelligent Services.

[4]  Naime Tozlu,et al.  Soft Covering Based Rough Sets and Their Application , 2014, TheScientificWorldJournal.

[5]  Hongxiang Tang,et al.  A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster-Shafer theory of evidence , 2015, Appl. Soft Comput..

[6]  Wu Shunxiang,et al.  Study of integrate models of rough sets and grey systems , 2005 .

[7]  Mahour Mellat-Parast,et al.  Developing a grey-based decision-making model for supplier selection , 2012 .

[8]  Tsau Young Lin,et al.  A New Rough Sets Model Based on Database Systems , 2003, Fundam. Informaticae.

[9]  Chris Cornelis,et al.  Computing fuzzy rough approximations in large scale information systems , 2014, 2014 IEEE International Conference on Big Data (Big Data).

[10]  Muhammad Irfan Ali,et al.  A note on soft sets, rough soft sets and fuzzy soft sets , 2011, Appl. Soft Comput..

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

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

[13]  Jie Li,et al.  Modeling of Grey Neural Network and Its Applications , 2008, ISICA.

[14]  Yiyu Yao.  Combination of Rough and Fuzzy Sets Based on α-Level Sets , 1997 .

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

[16]  Cheng Wang,et al.  Research and application of fuzzy grey multi-attribute group decision making , 2008, 2008 Chinese Control and Decision Conference.

[17]  Desire L. Massart,et al.  Rough sets theory , 1999 .

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

[19]  Dan Meng,et al.  Soft rough fuzzy sets and soft fuzzy rough sets , 2011, Comput. Math. Appl..

[20]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[21]  Pinaki Majumdar,et al.  Generalised fuzzy soft sets , 2010, Comput. Math. Appl..

[22]  Hossam Abd Elmaksoud Mohamed,et al.  A Probabilistic Rough Set Approach to Rule Discovery , 2011, UCMA.

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

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

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

[28]  Chyi Hwang,et al.  An FFT-based algorithm for 2D power series expansions , 1999 .

[29]  Binu Thomas,et al.  Integration of Fuzzy Logic in Data Mining to Handle Vagueness and Uncertainty , 2008, ICIC.

[30]  Charu C. Aggarwal,et al.  Managing and Mining Uncertain Data , 2009, Advances in Database Systems.

[31]  Satchidananda Dehuri,et al.  Usage of Fuzzy, Rough, and Soft Set Approach in Association Rule Mining , 2012, Int. J. Artif. Life Res..

[32]  Daisuke Yamaguchi,et al.  On the Combination of Rough Set Theory and Grey Theory Based on Grey Lattice Operations , 2006, RSCTC.

[33]  Reynold Cheng,et al.  Uncertain Data Mining: A New Research Direction , 2005 .

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

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

[36]  Chen Guo-hong,et al.  Rough grey sets , 2004 .

[37]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .