Towards theories of fuzzy set and rough set to flow graphs

Mathematical rough set theory and fuzzy set theory have attracted both practical and theoretical researchers from their efficiently and effectively to analyze real-world data. A novel and significant extension is called flow graphs. In this paper, we introduced how to calculate certainty, coverage and strength coefficients of decision rules from fuzzy attributes in a flow graph. Furthermore, we relax concept of mutual exclusion and introduced four new propositions of certainty and coverage coefficients for decision rules extracted from flow graph. An example calculation of these coefficients is provided. We also demonstrate real-world experiment on POSN data set. Several case studies illustrate a desirable outcome.

[1]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[2]  Zdzisław Pawlak,et al.  Decision algorithms and flow graphs: A rough set approach , 2003 .

[3]  Wen Yan,et al.  The Computational Complexity of Inference Using Rough Set Flow Graphs , 2005, RSFDGrC.

[4]  Jigui Sun,et al.  An Interpretation of Flow Graphs by Granular Computing , 2006, RSCTC.

[5]  Alicja Mieszkowicz-Rolka,et al.  Flow Graphs and Decision Tables with Fuzzy Attributes , 2006, ICAISC.

[6]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[7]  Vilém Novák,et al.  Fuzzy Set , 2009, Encyclopedia of Database Systems.

[8]  Roman Słowiński,et al.  Generalized Decision Algorithms, Rough Inference Rules, and Flow Graphs , 2002, Rough Sets and Current Trends in Computing.

[9]  Zdzislaw Pawlak,et al.  Decision Trees and Flow Graphs , 2006, RSCTC.

[10]  Zdzislaw Pawlak,et al.  Rough Sets and Flow Graphs , 2005, RSFDGrC.

[11]  Zdzislaw Pawlak,et al.  Flow Graphs and Decision Algorithms , 2003, RSFDGrC.

[12]  Zdzislaw Pawlak,et al.  Rough sets, decision algorithms and Bayes' theorem , 2002, Eur. J. Oper. Res..

[13]  Zdzislaw Pawlak,et al.  Flow Graphs and Data Mining , 2005, Trans. Rough Sets.

[14]  Alicja Mieszkowicz-Rolka,et al.  Fuzzy Implication Operators in Variable Precision Fuzzy Rough Sets Model , 2004, ICAISC.

[15]  Nick Cercone,et al.  Rule learning: Ordinal prediction based on rough sets and soft-computing , 2006, Appl. Math. Lett..