Probabilistic generalization of formal concepts

A comprehensive survey on formal concept analysis, its research trends and applications

“…Subsequently, FCA is extended into different Mining similar concepts Aswani Kumar, 2011b Knowledge discovery Aswani Kumar, 2012 Rule mining Belohlavek et al, 2011aIPAQ questionnaires Belohlavek et al, 2013b Background knowledge Dau, 2013 Analyzing a triple store Fowler, 2013 Order in taxonomy Galitsky et al, 2013 Pattern on parse thickets Macko, 2013 Fuzzy FCA Missaoui and Kwuida, 2011 Triadic rules Nguyen et al, 2011 Mathematical search Nguyen and Yamamoto, 2012 Learning from graph Li et al, 2011b Symbolic data analysis Pavlovic, 2012 Quantitative data analysis Rouane et al, 2013 Multi relational data Li and Tsai, 2013 Sentiments analysis Trabelsi et al, 2012 Analyzing folksonomies Vityaev et al, 2012 Probabilistic concepts Watmough, 2014 ERP analysis Yang et al, 2011b Decision-making Zhao and Liu, 2011…”

“…In general, the information granule regarded as a collection of elements drawn together by their closeness (resemblance, proximity, functionality, etc.) articulated in terms of some useful spatial (Ciobanu and Vaideanu, 2014;Singh and Gani, 2015;, bidrectional (Aswani Kumar et al, 2015b), temporal (Belohlavek and Trnecka, 2013;, or functional relationships (Singh and Aswani Kumar, 2012b;Vityaev et al, 2012;Zhang et al, 2012). Selecting the level to find some important concepts in the large context is based on user requirements.…”

Consciousness as a logically consistent and prognostic model of reality

“…Our model is directly based on cyclic causal relationships, represented by fundamentally new mathematical models -fixed points of predictions on causations. To formalize such fixed points, a probabilistic generalization of formal concepts was defined (Vityaev, et al, 2012. Formal concepts emerging in the Formal Concept Analysis (FCA) may be specified as fixed points of deterministic implications (with no exceptions) (Ganter andWille, 1999, Ganter, 2003).…”

“…Formal concepts emerging in the Formal Concept Analysis (FCA) may be specified as fixed points of deterministic implications (with no exceptions) (Ganter andWille, 1999, Ganter, 2003). We generalize formal concepts for probabilistic case through introducing probabilistic implications and defining fixed points for probabilistic implications (Vityaev, et al, 2012. Generalization is made so, that in certain conditions probabilistic formal concepts and formal concepts coincide.…”

“…Generalization is made so, that in certain conditions probabilistic formal concepts and formal concepts coincide. A computer experiment is performed (Vityaev, et al, 2012, which demonstrates that probabilistic formal concepts might "restore" formal concepts after superimposition of noise.…”