RIFs as the Formal Tool of Measuring Similarity between Sets (short paper)

In my paper, I will present some results towards the formalization of Rough Inclusion Functions (RIFs) and their complementary mappings using the Mizar system. Following the lines established by Anna Gomolińska, we reuse the notions which are already present in the Mizar Mathematical Library, in the theory of metric spaces, in order to establish the connections between the theory of such metrics and the theory of rough sets.

[1]  Adam Grabowski,et al.  Formal Development of Rough Inclusion Functions , 2019, Formaliz. Math..

[2]  Adam Grabowski,et al.  Automated Comparative Study of Some Generalized Rough Approximations , 2018, CS&P.

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

[4]  Adam Grabowski,et al.  Lattice Theory for Rough Sets - A Case Study with Mizar , 2016, Fundam. Informaticae.

[5]  Adam Grabowski,et al.  Binary Relations-based Rough Sets – an Automated Approach , 2016, Formaliz. Math..

[6]  Adam Naumowicz,et al.  Four Decades of Mizar , 2015, Journal of Automated Reasoning.

[7]  Adam Naumowicz,et al.  Mizar: State-of-the-art and Beyond , 2015, CICM.

[8]  Adam Grabowski,et al.  Mechanizing Complemented Lattices Within Mizar Type System , 2015, Journal of Automated Reasoning.

[9]  Adam Grabowski,et al.  Efficient Rough Set Theory Merging , 2014, CS&P.

[10]  Adam Grabowski,et al.  Automated Discovery of Properties of Rough Sets , 2013, Fundam. Informaticae.

[11]  Lech Polkowski,et al.  Approximate Reasoning by Parts - An Introduction to Rough Mereology , 2011, Intelligent Systems Reference Library.

[12]  Anna Gomolinska,et al.  On Certain Rough Inclusion Functions , 2008, Trans. Rough Sets.

[13]  William Zhu,et al.  Generalized rough sets based on relations , 2007, Inf. Sci..

[14]  Anna Gomolinska,et al.  On Three Closely Related Rough Inclusion Functions , 2007, RSEISP.

[15]  Andrzej Skowron,et al.  Monitoring, Security, and Rescue Techniques in Multiagent Systems (Advances in Soft Computing) , 2005 .

[16]  Adam Grabowski,et al.  On the Computer-Assisted Reasoning about Rough Sets , 2004, MSRAS.

[17]  Anna Gomolinska,et al.  A Comparative Study of Some Generalized Rough Approximations , 2002, Fundam. Informaticae.

[18]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

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

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