Understanding Fuzzy Logic in Python (with Animations)

Welcome to the world of fuzzy logic, where we move beyond simple true and false!Let's first look at classical logic, where things are either true or false, one or zero.In classical logic, we might say temperatures below 75 degrees are cold, and above are hot. There's no middle ground.But real life isn't so black and white. This is where fuzzy logic comes in.In fuzzy logic, membership in a category is not absolute. Instead, we use degrees of truth between zero and one.We can have multiple overlapping categories: cold, warm, and hot. A temperature can belong to more than one category at the same time.For example, a temperature of 75 degrees Fahrenheit might be considered point eight warm and point two hot simultaneously.This approach is particularly useful in real-world applications where precise boundaries don't exist.To get started with fuzzy logic in Python, we first need to install the required packages.After installation, we import the necessary modules: NumPy for numerical operations, and scikit-fuzzy for fuzzy logic functionality.Let's create our first fuzzy system by defining the universe of discourse - the range of possible input values.We'll create a coordinate system to visualize our membership functions. The x-axis represents temperature, and the y-axis shows the degree of membership.Now we'll define three triangular membership functions for cold, warm, and hot temperatures.The cold membership function starts at zero degrees, peaks at zero, and decreases to zero at fifty degrees.The warm membership function overlaps with both cold and hot, peaking at fifty degrees.The hot membership function increases from fifty degrees and remains at full membership until one hundred degrees.Finally, we create a control system by defining our temperature as an antecedent variable and assigning our membership functions.When we input a crisp value, like sixty degrees Fahrenheit, it will have partial membership in both the warm and hot sets.Membership functions map specific temperature values to degrees of membership in fuzzy sets.We define three overlapping membership functions for our temperature control system: cold, comfortable, and hot.Let's see how a temperature of 65 degrees Fahrenheit maps to our fuzzy sets.At 65 degrees, the temperature has a membership value of 0.8 in the comfortable set.And simultaneously, it has a membership value of 0.2 in the hot set.Fuzzy rules define how the system should respond to different temperature conditions.When the temperature is 65 degrees, two rules are activated simultaneously with different strengths.These activated rules determine the AC power output through a process called fuzzy inference.The final AC power setting will be determined by combining these activated rules using a defuzzification process.The fuzzy inference process consists of three main steps: fuzzification, rule evaluation, and defuzzification.In fuzzification, we convert a crisp input value into fuzzy membership values using membership functions.For example, if we have an input temperature of 70 degrees Fahrenheit, it activates multiple membership functions.These membership values then activate our fuzzy rules in parallel.Each rule contributes to the final output based on its activation level.Finally, in defuzzification, we combine the outputs of all rules to determine the final crisp output value.The centroid method calculates the center of mass of the combined fuzzy output to determine the final crisp value.In this case, our fuzzy system determines that the air conditioner should run at 65 percent power.In this practical example, we'll control an air conditioner using fuzzy logic based on temperature and humidity inputs.Our temperature input has three membership functions: cold, comfortable, and hot.Similarly, humidity is classified as dry, normal, or humid.The fuzzy rules determine how the system responds to different combinations of temperature and humidity.The AC power output is determined by these membership functions, representing low, medium, and high power settings.Let's see how the system responds to changing conditions. As temperature increases...And when both temperature and humidity are high, the system responds with maximum cooling power.This fuzzy logic system provides smooth, continuous control of the AC unit based on multiple input variables.