A decision system is a system that makes a decision based on several input parameters. A decision system is built on decision theories. Being human involves making decisions for almost life cases.

The following are examples of decisions that humans take:

Generally speaking, we teach a machine such as a computer in order to understand and achieve a specific goal. This case is called machine learning. Varieties of programs are implemented in machines so they can make decisions.

Machine learning consists of various algorithms to build a decision system. In this book, I use fuzzy logic and Bayesian algorithms to make a decision system. I...

Bayesian uses the manipulation of conditional probabilities approach to interpret data. In this section, we build a decision system using the Bayesian method.

Consider D, called the decision space, which denotes the space of all possible decisions d that could be chosen by the decision maker (DM). Θ is the space of all possible outcomes or state of nature ω, ω∈Θ.

Decision system-based Bayesian is built by Bayesian theory. For illustration, I show a simple spam filter using Bayesian. Imagine the sample space X is the set of all possible datasets of words, from which a single dataset word x will result. For each ω∈Θ and x∈X, the sampling model P(ω) describes a belief that x would be the outcome of spam probability. P(x|ω), prior distribution, is the true population characteristics and supposes a spam probability for x.P(ω|x)., posterior distribution, describes a belief that ω is the true value of spam, having observed dataset x.

The posterior distribution is obtained...

Consider you want to make a decision based on the current temperature, for instance, if the room's temperature is 30°C, then you turn on a cooler machine. Otherwise, if the room's temperature is 18°C, you turn on a heater machine.

This decision happens because we already defined exact values for turning on the machines. What's happening is that we say that we want to turn on the cooler machine if the room's temperature is hot. Furthermore, we also want to turn on the heater machine if the room's temperature is cold.

Cold and hot are two terms related to human linguistics. We should determine how cold and hot criteria are. A human differentiates the criteria for cold and hot, but how can a computer and machine know?

This problem can be solved using fuzzy logic. The idea of fuzzy logic was first introduced by Dr. Lotfi Zadeh from the University of California at Berkeley in the 1960s. The theory of fuzzy logic is developed with fuzzy sets and memberships.

In general...

In this section, we explore some Python libraries to build our decision system. I focus on Bayesian and fuzzy logic models for implementing the decision system.

Bayesian

We can implement Bayesian probability using Python. For our demo, we generate output values from two independent variables, x₁ and x₂. The output model is defined as follows:

c is a random value. We define α, β₁, β₂, and σ as 0.5, 1, 2.5, and 0.5.

These independent variables are generated using a random object from the NumPy library. After that, we compute the model with these variables.

We can implement this case with the following scripts:

import matplotlib
matplotlib.use('Agg')

import numpy as np
import matplotlib.pyplot as plt

# initialization
np.random.seed(100)
alpha, sigma = 0.5, 0.5
beta = [1, 2.5]
size = 100

# Predictor variable
X1 = np.random.randn(size)
X2 = np.random.randn(size) * 0.37

# Simulate outcome variable
Y = alpha + beta[0]*X1 + beta[1]*X2 + np.random.randn...

In this section, we build a simple decision system using Bayesian theory. A smart water system is a smart system that controls water. In general, you can see the system architecture in the following figure:

After using a sensing process on water to obtain the water quality, you can make a decision. If the water quality is good, we can transfer the water to customers. Otherwise, we purify the water.

To implement a decision system-based Bayesian theory, firstly we define the state of nature. In this case, we define two states of nature:

For inputs, we can declare x₁ and x₁ as negative and positive as the observation results.

We define prior values and class conditional probabilities as follows:

To build a decision, we should make a loss function The following is a loss function for our program:

Now you can write the complete scripts for the program.

# decision action
# d1 = distribute...