Fuzzy Set Theory Basics and Membership Functions
📌 The discussion introduces concepts for solving problems, exemplified by a washing machine case, requiring knowledge of different fuzzy curves.
⚙️ Linear curves (increasing or decreasing) are used to represent relative truth values between 0 (False) and 1 (True), unlike Boolean logic where values are strictly 0 or 1.
🔺 The three main shapes discussed for membership functions are linear increasing, linear decreasing, and trapezoidal curves, which define ranges for absolute truth (0 or 1) and fuzzy areas (between 0 and 1).

Fuzzy Inference System (FIS) Components
🤖 The process of using Fuzzy Logic for AI involves five main stages: Input, Fuzzification, Inference, Defuzzification, and an underlying Knowledge Base.
🔬 Fuzzification transforms crisp input values into linguistic variables using membership functions stored in the Knowledge Base (often expert rules).
⚙️ Inference applies the established rule base (e.g., IF-THEN rules derived from experts) to the fuzzy inputs to determine fuzzy outputs.
🎯 Defuzzification converts the fuzzy results from inference back into a crisp, actionable output value that the user can understand (e.g., a specific RPM).

Case Study: Washing Machine Speed Control (Sukamoto Method)
🧺 The case involves setting the washing machine's rotational speed (RPM) based on two inputs: Amount of Clothes (Little/Much) and Dirtiness Level (Low/Medium/High).
💡 Defined crisp ranges: Speed is Slow ($\le 500$ RPM) or Fast ($\ge 1200$ RPM). Clothes amount threshold is $40$ (Little) and $80$ (Much). Dirtiness Low ($\le 40$), Medium ($50$), High ($\ge 60$).
📜 Six expert-defined rules link the two inputs to the output speed (e.g., Rule 1: IF Clothes=Little AND Dirtiness=Low THEN Speed=Slow).

Fuzzification Calculations for Specific Inputs
📊 Given input: Clothes = 63 and Dirtiness = 56.
👚 For Clothes = 63: $\mu_{\text{Little}} = 0.425$ (using the decreasing linear formula) and $\mu_{\text{Much}} = 0.575$ (using the increasing linear formula).
🧼 For Dirtiness = 56: $\mu_{\text{Low}} = 0$, $\mu_{\text{Medium}} = 0.40$ (decreasing slope part of the fuzzy set), and $\mu_{\text{High}} = 0.60$ (increasing slope part of the fuzzy set).

Inference and Defuzzification (Sukamoto Method)
🔥 Inference uses the $\alpha$-predicate, calculated as the minimum of the combined input MUs (since the rules use AND/intersection).
📉 Rule 2 (Little AND Medium) yielded $\alpha$-predicate$_2 = \min(0.425, 0.40) = 0.40$, resulting in an inferred speed ($Z_2$) of 920 RPM.
📈 The final Defuzzification uses the weighted average formula:
$$\text{Output Speed} = \frac{\sum (\alpha_i \cdot Z_i)}{\sum \alpha_i}$$
⭐ The resulting crisp output speed for Clothes=63 and Dirtiness=56 is calculated to be 854 RPM, ensuring efficiency and electricity savings.

Key Points & Insights
➡️ The core of the Sukamoto method relies on MIN for AND operations during inference ($\alpha$-predicate) and a weighted average for defuzzification.
➡️ The general formula for a linear decreasing curve between points A and B for a variable Z is $\frac{B - Z}{B - A}$.
➡️ The general formula for a linear increasing curve between points A and B for a variable Z is $\frac{Z - A}{B - A}$.
➡️ The final output of 854 RPM demonstrates that fuzzy logic provides a nuanced, non-rounded speed adjustment rather than fixed settings, leading to potential energy optimization.

📸 Video summarized with SummaryTube.com on Nov 10, 2025, 11:27 UTC