scholarly journals Rough Set Approximation as Formal Concept

2006 ◽  
Vol 10 (5) ◽  
pp. 606-611 ◽  
Author(s):  
Nozomi Ytow ◽  
◽  
David R. Morse ◽  
David McL. Roberts ◽  
◽  
...  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
The Other ◽  
Formal Concept ◽  
Object Based ◽  
Formal Concepts ◽  
Set Approximation

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

Semantic Search Exploiting Formal Concept Analysis, Rough Sets, and Wikipedia

2020 ◽  
pp. 1436-1458
Author(s):  
Yuncheng Jiang ◽  
Mingxuan Yang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Formal Concept Analysis ◽  
Web Search ◽  
Rough Set Theory ◽  
Concept Analysis ◽  
Semantic Search ◽  
Formal Concept ◽  
Importance Ranking ◽  
Keyword Searches

This article describes how the traditional web search is essentially based on a combination of textual keyword searches with an importance ranking of the documents depending on the link structure of the web. However, one of the dimensions that has not been captured to its full extent is that of semantics. Currently, combining search and semantics gives birth to the idea of the semantic search. The purpose of this article is to present some new methods to semantic search to solve some shortcomings of existing approaches. Concretely, the authors propose two novel methods to semantic search by combining formal concept analysis, rough set theory, and similarity reasoning. In particular, the authors use Wikipedia to compute the similarity of concepts (i.e., keywords). The experimental results show that the authors' proposals perform better than some of the most representative similarity search methods and sustain the intuitions with respect to human judgements.

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