Decision Trees with Soft Numbers

TL;DR

This paper introduces Soft Probability by integrating Soft Numbers into probability theory, allowing for a nuanced distinction between strict and non-strict inequalities in continuous random variables.

Contribution

It develops a novel probability framework using Soft Numbers, addressing the collapse of probability involving equality to zero in classical theory.

Findings

Soft Probability distinguishes between strict and non-strict inequalities.

It models probabilities involving equality as soft zero multiples.

The approach enhances the expressiveness of probability models.

Abstract

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 work presents Soft Probability by incorporating of Soft Numbers into probability theory. Soft Numbers are set of new numbers that are linear combinations of multiples of ones and multiples of zeros. In this work, we develop a probability involving equality as a soft zero multiple of a probability density function.