Generalised approximate equalities based on rough fuzzy sets & rough measures of fuzzy sets

In an attempt to incorporate user knowledge in order to decide about the equality of sets, the concepts of approximate equalities using rough sets were introduced. These notions have been generalised in several ways and very recently [1] extended four types of approximate equalities using rough fuzzy sets instead of only rough sets. To be precise, a concept of leveled approximate equality was introduced and properties were studied. In this paper we extend this work with case studies to illustrate the applications of the concepts and compare them respectively. We also introduce and discuss the rough measures of basic sets, fuzzy sets and interpret four types of approximate equalities in terms of the accuracy measure as well as rough measures. The analysis had provided a clear distinguish notion in terms of the measures.

[1]  Honghai Liu,et al.  Fuzzy Qualitative Human Motion Analysis , 2009, IEEE Transactions on Fuzzy Systems.

[2]  Honghai Liu,et al.  A fuzzy qualitative approach to human motion recognition , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[3]  Van-Nam Huynh,et al.  An approach to roughness of fuzzy sets , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[4]  Anirban Mitra,et al.  On Rough Equalities and Rough Equivalences of Sets , 2008, RSCTC.

[5]  Sankar K. Pal,et al.  Roughness of a Fuzzy Set , 1996, Inf. Sci..

[6]  Chee Seng Chan,et al.  A fuzzy qualitative approach for scene classification , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[7]  Zdzisław Pawlak,et al.  On rough equalities , 1985 .

[8]  B. K. Tripathy,et al.  An Analysis of Generalised Approximate Equalities Based on Rough Fuzzy Sets , 2011, SocProS.

[9]  B. K. Tripathy,et al.  An Analysis of Approximate Equalities based on Rough Set Theory , 2011 .

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

[11]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[12]  Zdzisław Pawlak,et al.  Black box analysis and rough top equalities , 1985 .

[13]  Honghai Liu,et al.  Recognition of Human Motion From Qualitative Normalised Templates , 2007, J. Intell. Robotic Syst..

[14]  B. K. Tripathy,et al.  Rough equivalence and algebraic properties of rough sets , 2009, Int. J. Artif. Intell. Soft Comput..

[15]  B. K. Tripathy,et al.  On Approximation of Classifications, Rough Equalities and Rough Equivalences , 2009 .