Open AccessDeveloping Complementary Rough Inclusion Functions
Author(s) -
Adam Grabowski
Publication year - 2020
Publication title -
formalized mathematics
Language(s) - English
Resource type - Journals
eISSN - 1898-9934
pISSN - 1426-2630
DOI - 10.2478/forma-2020-0009
Subject(s) - jaccard index , metric space , metric (unit) , mathematics , continuation , rough set , inclusion (mineral) , index (typography) , computer science , data mining , theoretical computer science , algebra over a field , discrete mathematics , pure mathematics , statistics , programming language , economics , cluster analysis , sociology , operations management , gender studies
Summary We continue the formal development of rough inclusion functions (RIFs), continuing the research on the formalization of rough sets [15] – a well-known tool of modelling of incomplete or partially unknown information. In this article we give the formal characterization of complementary RIFs, following a paper by Gomolińska [4]. We expand this framework introducing Jaccard index, Steinhaus generate metric, and Marczewski-Steinhaus metric space [1]. This is the continuation of [9]; additionally we implement also parts of [2], [3], and the details of this work can be found in [7].
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