Applying Rough Sets to Information Tables Containing Possibilistic Values

Rough sets are applied to information tables containing imprecisevalues that are expressed in a normal possibility distribution. Amethod of weighted equivalence classes is proposed, where each equivalenceclass is accompanied by a possibilistic degree to which it is an actualone. By using a family of weighted equivalence classes, we derive lowerand upper approximations. The lower and upper approximations coincidewith ones obtained from methods of possible worlds. Therefore, themethod of weighted equivalence classes is justified. When this method isapplied to missing values interpreted possibilistically, it creates the samerelation for indiscernibility as the method of Kryszkiewicz that gave anassumption for indiscernibility of missing values. Using weighted equivalenceclasses correctly derives a lower approximation from the viewpointof possible worlds, although using a class of objects that is not an equivalenceclass does not always derive a lower approximation.

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