Research On The Relationships Between Probability Distribution And Possibility Distribution

Randomness and fuzziness are two types of uncertainties in our objective and subjective world. Usually probability distribution is used to measure randomness, and possibility distribution is used to measure fuzziness. Therefore the research on the two distributions becomes more and more significant. This dissertation analyzes the differences and relationships between the two distributions based on their definitions, characteristics and corresponding measurements which are probability entropy and fuzziness respectively. Finally we discuss the applications of the two distributions in the selection of expanding attributes during the growing of decision trees. In the generation of crisp decision tree, the class distribution of examples is a probability distribution, which is measured by probability entropy. In the generation of fuzzy decision tree, the class distribution of examples is a possibility distribution which is measured by fuzziness. Based on the discussion, we draw the differences and relationships between the two distributions by comparing the two types of decision trees.