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The monograph is devoted to the study of inhibitory rules. In contrast to deterministic (standard) rules which have the relation attribute = value on the right-hand side, inhibitory rules have on the right-hand side the relation attibute ≠ value. For information systems [60, 63, 72], we consider inhibitory association rules which on the right-hand side can have an arbitrary attribute. For decision...
The idea of representation of concurrent system by information system is due to Z. Pawlak [61, 73, 74] In such a representation attributes are interpreted as local processes of a concurrent system, values of attributes – as states of local processes, and objects (tuples of values of attributes on objects) – as global states of the considered concurrent system. The knowledge encoded in an information...
There are three approaches to use inhibitory rules in classifiers: (i) lazy algorithms based on an information about the set of all inhibitory rules, (ii) standard classifiers based on a subset of inhibitory rules constructed by a heuristic, and (iii) standard classifiers based on the set of all minimal (irreducible) inhibitory rules. The aim of this chapter is to show that the last approach is not...
In this chapter, we consider algorithms for construction of partial inhibitory decision rules and some bounds on the length such rules. These investigations are based on the use of known results for partial covers. We show that: Under some natural assumptions on the class NP, the greedy algorithm is close to the best polynomial approximate algorithms for the minimization of...
In this chapter, we consider the case, where each subset, used for covering, has its own weight, and we should minimize the total weight of subsets in partial cover. The same situation is with partial inhibitory decision rules: each conditional attribute has its own weight, and we should minimize the total weight of attributes occurring in partial inhibitory decision rule. If weights of attributes...
In this chapter, we consider the following problem of classification (prediction): for a decision table T and a new object v, given by values of conditional attributes from T, it is required to generate a decision corresponding to v. We compare qualities of classifiers based on exact deterministic and inhibitory decision rules. The first type of classifiers is the following: for a given...
In this chapter, we consider the same classification problem as in Chap. 5: for a given decision table T and a new object v it is required to generate a value of the decision attribute on v using values of conditional attributes on v. To this end, we divide the decision table T into a number of information systems Si, i ∈ Dec(T), where Dec(T) is the set of values...
In this chapter, we consider the same classification problem as in Chaps. 5 and 6: for a given decision table T and a new object v it is required to generate a value of the decision attribute on v using values of conditional attributes on v. We compare two lazy [1] classification algorithms based on deterministic and inhibitory decision rules of the forms $$ (a_1(x)=b_1)\wedge \ldots \wedge...
In this monograph, we studied inhibitory decision and association rules. We showed that using inhibitory rules one can describe more knowledge encoded in information and decision systems than in the case of deterministic (standard) rules. Unfortunately, for almost all k-valued information systems with the polynomial number of objects in the number of attributes the number of minimal (irreducible)...
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