Artificial Intelligence with Uncertainty

2.3 Algorithm of Forward Gaussian Cloud -- 2.3.1 Description -- 2.3.1.1 Forward Gaussian Cloud Algorithm -- 2.3.1.2 Two-Dimensional Forward Gaussian Algorithm -- 2.3.2 Contributions Made by Cloud Drops to the Concept -- 2.3.3 Using Gaussian Cloud Model to Understand the 24 Solar Terms in the Chinese Lunar Calendar -- 2.4 Mathematical Properties of the Gaussian Cloud -- 2.4.1 Statistical Analysis of the Distribution of Cloud Drops -- 2.4.2 Statistical Analysis of Certainty Degree of Cloud Drops -- 2.4.3 Expectation Curves of Gaussian Cloud -- 2.4.4 From Cloud to Fog -- 2.5 Algorithm of Backward Gaussian Cloud -- 2.5.1 Description -- 2.5.1.1 Backward Gaussian Cloud Algorithm with Certainty Degree -- 2.5.1.2 Backward Cloud Algorithm Based on the First-Order Absolute Central Moment and the Second-Order Central Moment -- 2.5.1.3 Backward Cloud Algorithm Based on the Second- and Fourth-Order Central Moments of Samples -- 2.5.2 Parameter Estimation and Error Analysis of Backward Gaussian Cloud -- 2.5.2.1 Error Analysis of Ex -- 2.5.2.2 Error Analysis of En and He -- 2.5.2.3 Determining the Number of Samples under the Condition of Given Errors and Confidence Level -- 2.6 Further Understanding of the Cloud Model -- 2.6.1 Judgment Shooting -- 2.6.2 Fractal with Uncertainty -- 2.7 Universality of the Gaussian Cloud -- 2.7.1 Universality of Gaussian Distribution -- 2.7.2 Universality of Bell-Shaped Membership Function -- 2.7.3 Universal Relevance of Gaussian Cloud -- References -- Chapter 3: Gaussian Cloud Transformation -- 3.1 Terminology in Granular Computing -- 3.1.1 Scale, Level, and Granularity -- 3.1.2 Concept Tree and Pan-Concept Tree -- 3.2 Gaussian Transformation -- 3.2.1 Parameter Estimation of Gaussian Transform -- 3.2.2 Gaussian Transform Algorithm -- 3.3 Gaussian Cloud Transformation