Binary Matrix Model: Difference between revisions
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A '''Binary Matrix Model''' is a binary matrix and three associations (indicated by colons), i.e. <br> | A '''Binary Matrix Model''' is a binary matrix and three associations (indicated by colons), i.e. <br> | ||
M = { N, V: I<sub>s</sub>, H: I<sub>t</sub>, ''R̂'': ''R'' } | |||
N: | N: a binary matrix | ||
V: a set of contextual elements associated in a one-to-one manner with the vertical index | V: a set of contextual elements associated in a one-to-one manner with the vertical index | ||
set Is of N, H is a set of contextual elements associated in a one-to-one manner with the horizontal index set I, of N | set Is of N, H is a set of contextual elements associated in a one-to-one manner with the horizontal index set I, of N | ||
I: a contextual relation associated with the binary relation induced on I,xI, | I: a contextual relation associated with the binary relation induced on I, xI, by N. | ||
The set V is called the vertical index set of the model, and H is its horizontal index set. | |||
called the vertical index set of the model, and H is its horizontal index set. | |||
The contextual relation I is called | The contextual relation I is called the model relation, and the matrix N is called the model | ||
the model relation, and the matrix N is called the model | |||
matrix. Also, N may often be given a specific name for a | matrix. Also, N may often be given a specific name for a | ||
specific kind of binary-matrix model. | specific kind of binary-matrix model. | ||
Latest revision as of 09:48, 18 January 2022
A Binary Matrix Model is a binary matrix and three associations (indicated by colons), i.e.
M = { N, V: Is, H: It, R̂: R }
N: a binary matrix
V: a set of contextual elements associated in a one-to-one manner with the vertical index
set Is of N, H is a set of contextual elements associated in a one-to-one manner with the horizontal index set I, of N
I: a contextual relation associated with the binary relation induced on I, xI, by N.
The set V is called the vertical index set of the model, and H is its horizontal index set.
The contextual relation I is called the model relation, and the matrix N is called the model matrix. Also, N may often be given a specific name for a specific kind of binary-matrix model.
Warfield, J. N. (1976). Implication structures for system interconnection matrices. IEEE Transactions on Systems, Man, and Cybernetics, (1), 18-24. https://en.wikipedia.org/wiki/Logical_matrix