While it was exceptionally warm weather outside, we stayed inside in a comfortable atmosphere in one of the aulas at the University of Milano-Bicocca, who had organised the first Rough Sets Theory workshop, 25-27 May 2009. With an emphasis on theory: there are many applications of rough sets, but “Even though this attention to application is of great importance, it is not excluded that theoretical aspects concerning with foundations of rough sets, both logical and mathematical, must be taken into account.”
As I’m no expert on rough sets (but there is an interesting relationship between rough sets and granularity, which was the topic of my presentation), the different topics covered by the programme were very interesting to me and gave a useful overview of the range of research topics. As it appears, there there’s plenty of work still to be done on rough sets theory—even though the basic description of rough sets is elegant and simple—and the ambience provided ample opportunity for exchange of ideas and lively discussions.
Topics ranged from using roughs sets with ordinal data and substituting the indistinguishability relation with a dominance relation presented by Salvatore Greco to discussions what are the essential ‘ingredients’ of rough sets to presentations on definitions of rough sets by Mihir Chakraborty and on the differences between Pawlak rough sets versus probabilistic rough sets by Yiyu Yao. For instance, on the latter, Pawlak rough sets consider qualitative aspects and has zero tolerance for errors whereas probabilistic rough sets are about quantitative aspects and acceptance of error; Yao proposed a solution to deal with both, called decision-theoretic rough sets. Also organizer Gianpiero Cattaneo talked about foundational and mathematical aspects of rough sets, but then using a binary relations approach (more detailed information can be found here).
Fertile ground for discussion and misunderstandings, due to the different backgrounds and assumptions of the attendees, was the notion of incompleteness. Simply put, given some ‘data table’ (which is not necessarily a database table), there may be null values, but what does that represent? Incomplete information? To make a long story short: it depends on the context (the semantics of the structure you use, language). Didier Dubois approached it from, among others, a setting of incomplete information in database integration and considered “ill-known attributes” and “ill-known rough sets” as cases of incomplete information about the data. Ill-known attributes are another rendering of the usage at the intensional level of a value range for an attribute of a class so that each object in the class’s extension does have only one value that falls within the defined range of allowed values. Ill-known rough sets are about the ill-observation of attribute values and the lack of discrimination of the set of attributes, and then there is the issue of “potential similarity”. His proposal is about covering-based generalisation of rough sets.
I have more notes of the presentations and the panel session, but I’ll leave it at that (for now at least). If you want to know more about these and the other programme topics, I’d suggest you attend next year’s workshop, but also related conferences may be of interest (e.g., RSKT, GrC, RSFDGrC) or, if you would like to see a closer link with fuzzy and with ontologies, then you may be interested in attending the WI-IAT’09 workshop on managing vagueness and uncertainty in the Semantic Web (VUSW’09) on 15-9-’09 in Milan.
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