Pseudo-rank functions on certain lattices

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
M. Wasadikar ◽  
S. Nimbhorkar
Keyword(s):  
Boolean Lattice ◽  
Choquet Simplex ◽  
Rank Functions

AbstractPseudo-rank functions on bounded lattices are introduced and their properties are studied. It is shown that if the set of all pseudo-rank functions on a Boolean lattice is nonempty then it is a Choquet simplex.

Partitioning the Boolean lattice into a minimal number of chains of relatively uniform size

2003 ◽  
Vol 24 (2) ◽  
pp. 219-228 ◽  
Author(s):  
Tim Hsu ◽  
Mark J. Logan ◽  
Shahriar Shahriari ◽  
Christopher Towse
Keyword(s):  
Boolean Lattice ◽  
Uniform Size

Projective rank functions compatible with pure-injective envelopes

1995 ◽  
Vol 23 (5) ◽  
pp. 1847-1866 ◽  
Author(s):  
Claudi Busqué ◽  
Alberto Facchini∗∗
Keyword(s):  
Rank Functions

Flowers and Steps in the Boolean Lattice of Hexagrams

2004 ◽  
Vol 31 (4) ◽  
pp. 489-504
Author(s):  
Andreas Schöter
Keyword(s):  
Boolean Lattice

A FCA-Based Cognitive Diagnosis Model for CAT

2011 ◽  
pp. 151-170
Author(s):  
Yang Shuqun ◽  
Ding Shuliang
Keyword(s):  
Large Scale ◽  
Matrix Theory ◽  
Estimation Method ◽  
Boolean Lattice ◽  
Cognitive Diagnosis ◽  
Remedial Measure ◽  
Concept Lattices ◽  
Knowledge States ◽  
Attribute Hierarchy ◽  
Developing Area

There is little room for doubt about that cognitive diagnosis has received much attention recently. Computerized adaptive testing (CAT) is adaptive, fair, and efficient, which is suitable to large-scale examination. Traditional cognitive diagnostic test needs quite large number of items, the efficient and tailored CAT could be a remedy for it, so the CAT with cognitive diagnosis (CD-CAT) is prospective. It is more beneficial to the students who live in the developing area without rich source of teaching, and distance education is adopted there. CD is still in its infancy (Leighton at el.2007), and some flaws exist, one of which is that the rows/columns could form a Boolean lattice in Tatsuoka’s Q-matrix theory. Formal Concept Analysis (FCA) is proved to be a useful tool for cognitive science. Based on Rule Space Model (RSM) and the Attribute Hierarchy Method (AHM), FCA is applied into CD-CAT and concept lattices are served as the models of CD. The algorithms of constructing Qr matrice and concept lattices for CAT, and the theory and methods of diagnosing examinees and offering the best remedial measure to examinees are discussed in detail. The technology of item bank construction, item selection strategies in CD-CAT and estimation method are considered to design a systemic CD-CAT, which diagnoses examinees on-line and offers remedial measure for examinees in time. The result of Monte Carlo study shows that examinees’ knowledge states are well diagnosed and the precision in examinees’ abilities estimation is satisfied.

scholarly journals On blockers in bounded posets

2001 ◽  
Vol 26 (10) ◽  
pp. 581-588 ◽  
Author(s):  
Andrey O. Matveev
Keyword(s):  
Boolean Lattice ◽  
Bounded Poset ◽  
Finite Set ◽  
Bounded Posets

Antichains of a finite bounded poset are assigned antichains playing a role analogous to that played by blockers in the Boolean lattice of all subsets of a finite set. Some properties of lattices of generalized blockers are discussed.

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