Extracting Fuzzy Rules Under Uncertainty and Measuring Definability Using Rough Sets

Although computers have come a long way since their invention, they are basically able to handle only crisp values at the hardware level. Unfortunately, the world we llve in consists of problems which fail to fall into this category, i.e. uncertainty is all too common. In this work, we look at a problem which involves uncertainty. To be specific we deal with attributes which are fuzzy sets. Under this condition we acquire knowledge by looking at examples. In each example a condition as well as a decision is made available. Based on the examples given to us, we will extract two sets of rules namely: certain and possible. Furthermore we will construct measures of how much we believe these rules, and finally we will define the decisions as a function of the terms used in the conditions.