A macroscopic approach to FCA and its various fuzzifications

Authors:
Tim B. Kaiser;Stefan E. Schmidt
Affiliations:
SAP AG, Walldorf, Germany;Institut für Algebra, Technische Universität Dresden, Germany
Venue:
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Year:
2012

Citing 6
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Abstract

We promote biresiduation as a fundamental unifying principle in Formal Concept Analysis, including fuzzification and factor analysis. In particular, we show that maximal formal rectangles are exactly formal concepts within the presented framework of biresiduated maps on ordered sets. Macroscopic implications yield the particular derivation operators in specific settings such as Fuzzy Formal Concept Analysis, Factor Analysis, and degree of containment (i.e. degree of being a subset).