## Abstract

In this chapter, we develop the foundation of a new theory for decision trees based on new modeling of phenomena with soft numbers. Soft numbers represent the theory of soft logic that addresses the need to combine real processes and cognitive ones in the same framework. At the same time, soft logic develops a new concept of modeling and dealing with uncertainty: the uncertainty of time and space. It is a language that can talk in two reference frames and also suggest a way to combine them. In the classical probability, in continuous random variables, there is no distinguishing between the probability involving strict inequality and non-strict inequality. Moreover, a probability involves equality collapse to zero, without distinguishing among the values that we would like that the random variable will have for comparison. This chapter presents soft probability, by incorporating of soft numbers into probability theory. Soft numbers are a set of new numbers that are linear combinations of multiples of “ones” and multiples of “zeros.” In this chapter, we develop a probability involving equality as a “soft zero” multiple of a probability density function (PDF). Based on soft probability, we introduced an approach to implement C4.5 algorithm as an example for a soft decision tree.

Original language | English |
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Title of host publication | Machine Learning for Data Science Handbook |

Subtitle of host publication | Data Mining and Knowledge Discovery Handbook, Third Edition |

Publisher | Springer International Publishing |

Pages | 143-170 |

Number of pages | 28 |

ISBN (Electronic) | 9783031246289 |

ISBN (Print) | 9783031246272 |

DOIs | |

State | Published - 1 Jan 2023 |

## ASJC Scopus subject areas

- General Computer Science
- General Mathematics