By Igor Chikalov, Vadim Lozin, Irina Lozina, Mikhail Moshkov, Hung Son Nguyen, Andrzej Skowron, Beata Zielosko
In this e-book, the next 3 techniques to facts research are presented:
- attempt thought, based by way of Sergei V. Yablonskii (1924-1998); the 1st guides seemed in 1955 and 1958,
- tough units, based by means of Zdzisław I. Pawlak (1926-2006); the 1st guides seemed in 1981 and 1982,
- Logical research of knowledge, based through Peter L. Hammer (1936-2006); the 1st courses seemed in 1986 and 1988.
These 3 ways have a lot in universal, yet researchers lively in a single of those components frequently have a constrained wisdom concerning the effects and strategies constructed within the different . however, all the methods exhibits a few originality and we think that the trade of data can stimulate additional improvement of every of them. this may bring about new theoretical effects and real-life functions and, particularly, new effects in response to mixture of those 3 info research methods should be expected.
- Logical research of knowledge, based by way of Peter L. Hammer (1936-2006); the 1st guides seemed in 1986 and 1988.
These 3 methods have a lot in universal, yet researchers energetic in a single of those parts frequently have a restricted wisdom concerning the effects and techniques constructed within the different . nonetheless, all the techniques indicates a few originality and we think that the alternate of information can stimulate additional improvement of every of them. this may bring about new theoretical effects and real-life purposes and, particularly, new effects according to mixture of those 3 info research methods will be expected.
These 3 methods have a lot in universal, yet researchers energetic in a single of those parts usually have a restricted wisdom in regards to the effects and techniques constructed within the different . however, all the techniques indicates a few originality and we think that the alternate of data can stimulate extra improvement of every of them. this may bring about new theoretical effects and real-life functions and, particularly, new effects in accordance with mixture of those 3 information research techniques may be expected.
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Additional info for Three Approaches to Data Analysis: Test Theory, Rough Sets and Logical Analysis of Data
Sample text
Step 1: We set SEP(T ) = {T } and pass to the second step. After the first step T is not labeled as a treated table. Suppose s ≥ 1 steps have been made already. Step (s + 1): Let all tables in the set SEP(T ) be labeled as treated tables. In this case, we finish the first part of the algorithm W computation. 1 Decision Trees, Rules and Tests 19 D ∈ SEP(T ) which is not treated. We add to the set SEP(T ) all subtables of the kind D( fi , δ ), where fi ∈ E(D) and δ ∈ E(D, fi ), which were not in SEP(T ), mark the table D as treated and pass to the step (s + 2).
P ∈ B p the system of equations { f1 (x) = δ1 , . . 2) is compatible on the set A (has a solution from A). If for any natural p there exists a subset of the set F, which cardinality is equal to p and which is an independent set, then we will say that the information system U has infinite I-dimension. Otherwise, I-dimension of U is the maximum cardinality of a subset of F, which is an independent set. 34 1 Test Theory: Tools and Applications The notion of I-dimension is closely connected with well known notion of VapnikChervonenkis dimension [70].
If T is a degenerate table (all rows of the table are labeled with the same value t of the decision attribute) then instead of T we mark the node v by the number t and proceed to the step (s + 2). Let T be a nondegenerate table. Then, for i = 1, . . , n, we compute the value Q( fi ) = max{P(T ( fi , 0)), . . , P(T ( fi , k − 1))} . We mark the node v by the attribute fi0 where i0 is the minimum i for which Q( fi ) has minimum value. For each δ ∈ {0, . , k − 1} such that the subtable T ( fi0 , δ ) is nonempty, we add to the tree G the node v(δ ), mark this node by the table T ( fi0 , δ ), draw the edge from v to v(δ ), and mark this edge by δ .