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Rough Sets in Possibilistic Information Data Tables
Michinori Nakata, Hiroshi Sakai and Takeshi Fujiwara
Rough sets and rule induction are described in possibilistic information data tables with values expressed in normal possibility distributions. A possibilistic information data table is transformed into the set of incomplete information data tables with possible degrees by using α-cut. Every incomplete information data table is dealt with from the viewpoint of possible world semantics used by Lipski and creates possible tables. We obtain the binary relation expressing object indiscernibility in each possible table. Aggregating the relations, we derive the minimum and maximum of lower and lower approximations in the level of possible degree α. Using these minimum and maximum, we represent the minimum and the maximum of approximations in the form of possibility distributions. The real approximation exists between the minimum and the maximum. This representation allows us to grasp the overall picture of approximations. We introduce a descriptor-explicit expression in order to derive rule sets from the overall configuration of approximations. By this introduction, we can also grasp the whole structure of the rule sets that we can obtain. Each rule is evaluated by three indices: support, coverage and accuracy. We induce only valuable rule sets from using the criterion of meaningful rule sets that is obtained using certain and possible degrees.
Keywords: Rough sets, rule induction, possibility distributions, lower and upper approximations, descriptor-explicit expression, possible world semantics