DECISION LOGIC


Decision logic has been proposed by Pawlak. Z. (1995), the author of the Rough Set Theory. The procedure we have implemented in SEMANA follows the specifications given in [BOLC L., CYTOWSKI J. & STACEWICZ P. (1996) On Logic and Rough Reasoning, Institute of Computer Science, Polish Academy of Sciences, Report 822 (in Polish)].

The table to examine is an AV table (or 'multi-valued table'). The procedure is as follows:

 Step 1) The user has to decide which are the attributes that constitute the decision, the remaining attributes being considered as conditional. Each object is thus considered as a rule:

         IF {set of condional attributes} THEN decision

 Step 2) Check for inconsistencies and eliminate inconsistent objects. Inconsistents objects are objects that have exactly the same conditional attributes, but different decisions.

 Step 3) For each object-rule, eliminate all superfluous attributes. Each attribute is virtually eliminated and the apparition of new inconsistencies is checked. If no inconsistency appears, the attribute is eliminated. Thus are obtained so-called first generation reducts.
The reducts of first generation are checked again for the possibility to reduce further the number of attributes and the operation is repeated until no more reduction is possible.

Step 4)
Duplicates are eliminated and the reduced rules are compared with the subset of objects having the same decision. Only the rules which apply to the whole subset of objects are maintained. If no rule applies to the whole subset, all the rules are maintained. The resulting set of rules is called minimal rules.

 A report gives the list of the minimal rules and the objects to which each rule applies, and indicates the strength of each attribute (i.e. the number of rules in which each attribute appears).

N.B.: the user should be cautious with the reliability of the rules which is strongly dependent on the representativeness of the corpus.


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