Rauszer, C. (1991). Reducts in information systems. Fundamenta Informaticae, 15:1--12.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sets It is easy to see the models that rough set theory gives matches the tasks researchers are dealing with in the area of data mining. However, an expressive model does not necessarily imply efficient algorithms. It has been shown that finding a smallest reduct of an arbitrary set Q is NP hard [30]. Obviously, finding all reducts can have exponential time. As we have seen RSDA has successfully modeled deterministic and indeterministic rules. A usual interest on indeterministic rules is its confidence. Because rough set uses partitions as a basic mechanism to describe problems and calculate ....

C. Rauszer. Reducts in information systems. Foundamenta Informaticae, 15:1--12, 1991.

....indispensable for Q. If q # Q,andq is not an element of any reduct of Q, then we call q redundant for Q.IfQ## we just speak of reducts of #, core of # etc. The set of all reducts of # is denoted by Red###. Reducts correspond to keys of a relational database; consequently, as was pointed out in [57] the problem of finding a reduct of minimal cardinality is, in general, NP hard, and finding all reducts has exponential complexity [66] A transparent method to find the core and the reducts of an information system # via discernibility matrices was given in [66] Define a discernibility ....

Rauszer, C. (1991). Reducts in information systems. Fundamenta Informaticae, 15, 1--12.

....dense in the dependence space (A; Theta wsim ) Thus, fag; fa; cg) 2 Theta wsim implies that for all X 2 K, fag X if and only if fa; cg X . 5. 4 Independent Sets and Reducts In the literature there are many articles which concern independent sets and reducts in information systems (see e.g. [9, 44, 50]) In this section we review cores, independent sets and reducts defined in dependence spaces. We compare the independence defined in dependence spaces with some notions of independence studied in universal algebra. Our main result of this section gives a characterization of the reducts of a given ....

....on A. In the next example we show that this abstract dependence is not necessarily transitive even if D is finite. Example 5.4.6. In the dependence space of Example 5.1.3, hf1gi = f1; 4g and hhf1gii = f1; 2; 4g. The notion of reducts is important in the theory of information systems (see [50], for example) Here we study reducts in the more general setting of dependence spaces. Let D = A; Theta) be a dependence space. For any B A, a subset C B is called a reduct of B, if B ThetaC and C 2 INDD . The set of all reducts of B is denoted by REDD (B) Lemma 5.4.7. Let D = A; ....

C. M. RAUSZER, Reducts in Information Systems, Fundamenta Informaticae 15 (1991), 1-- 12.

.... r 1 (t 1 , v) u 2 (t) t 1 #= t) #( t 0 , t n , r 2 (t n 1 , v) u 2 (t) t # R,t ## t 0 , t n , t n 1 , #( t 0 , t n , r 2 (t n 1 , v) # if t 0 , t n , t n 1 determines an object, where R is a reduct of the information system (see [6] 7] [9]) For this strategy max E[s, s 2 ] depends on card(R) # card(T ) provided the weight coe#cients equal 1) By finding a minimal reduct and by improving the strategy so that only the values of the corresponding attributes are required, we can obtain optimal results for this type of strategies. ....

Rauszer, C.M.: Reducts in Information Systems, Fundamenta Informaticae, 15(1991), pp. 1-12.

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Rauszer, C. (1991). Reducts in information systems. Fundamenta Informaticae, 15:1--12.

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