Fuzzy Inference System Walkthrough | Fuzzy Logic, Part 2

Summary

In this video, Brian explores a Fuzzy Inference System to determine tipping amounts based on food and service quality. The system walks through fuzzification, inference, and defuzzification processes, explaining how linguistic variables, membership functions, and fuzzy logic operators (like AND, OR, NOT) interact. Using MATLAB, Brian demonstrates how different rule sets influence tipping outcomes, with the added flexibility of easily adjusting the system's rules. He also showcases how lookup tables can optimize the system for limited hardware while maintaining the intuitive nature of fuzzy logic. This example, though based on restaurant tipping, can be applied to various control problems.

Takeaways

• 😀 Fuzzy Inference Systems (FIS) are used to make decisions based on human-interpretable terms (linguistic variables) like 'delicious' or 'poor'.
• 😀 Membership functions shape the relationship between crisp inputs and fuzzy variables. For example, food quality could be categorized into 'delicious', 'fine', and 'rancid'.
• 😀 Membership functions are determined using polling or expert knowledge, creating overlapping regions where inputs can partially belong to multiple categories.
• 😀 Different shapes of membership functions, such as trapezoidal and Gaussian, are chosen based on real-world data or expert knowledge.
• 😀 Fuzzification converts crisp inputs into fuzzy variables, like turning a rating of 7 for food into partial memberships (45% delicious, 55% fine).
• 😀 Logical operators such as 'or', 'and', and 'not' are applied in fuzzy inference, using maximum, minimum, and subtraction methods for aggregation.
• 😀 Rule firing strength represents the degree to which a rule influences the output of the system, and it is important in systems with multiple rules.
• 😀 Defuzzification converts fuzzy results into crisp outputs, often using methods like the centroid technique to determine a precise output value.
• 😀 A lookup table can be used as an alternative to a fuzzy inference system, where inputs directly map to outputs without needing real-time inference calculations.
• 😀 The flexibility of fuzzy systems allows easy updates to rules and membership functions, as demonstrated by adding a new rule to adjust tipping behavior based on food quality.
• 😀 Practical applications of fuzzy logic systems go beyond simple examples like tipping and can be applied to more complex control systems, such as balancing a pole on a moving cart.

Q & A

What is the main purpose of this video?

The main purpose of the video is to explain a more complex example of fuzzy inference systems, focusing on concepts such as membership function shapes, fuzzy operators, multiple input inference systems, and rule firing strength. It aims to provide a better understanding of fuzzy logic in real-world decision-making processes.

Why is the restaurant tipping example used in this video?

The restaurant tipping example is used because, although it may seem simple, it helps explain key fuzzy logic concepts that can be applied to other systems. The example demonstrates how fuzzy inference works with two input variables: food quality and service quality.

What are the three distinct sections of the fuzzy inference process discussed in the video?

The three distinct sections of the fuzzy inference process are fuzzification, inference, and defuzzification.

What are linguistic variables in the context of fuzzy inference systems?

Linguistic variables are human-interpretable adjectives used to describe the input variables in a fuzzy system. For example, food quality can be described as 'delicious', 'fine', or 'rancid', and these adjectives are associated with membership functions that quantify their meaning in numerical terms.

How are the membership functions for food quality and service quality represented?

In the video, the membership functions for food quality are represented by trapezoidal functions, while the service quality is modeled using Gaussian functions.

What is the role of fuzzy logic operators in this system?

Fuzzy logic operators are used to combine fuzzy variables based on logical statements. In this video, operators like 'or', 'and', and 'not' are used to determine how the input variables interact and impact the output decision (tip).

How does the 'or' operator function in fuzzy logic?

The 'or' operator in fuzzy logic takes the maximum value between two fuzzy inputs. For example, if the fuzzy variables are 0.2 and 0.8, the output of the 'or' operator will be 0.8.

What is rule firing strength in fuzzy inference systems?

Rule firing strength represents the degree to which each rule in the fuzzy inference system is activated based on the input values. It helps determine how much influence each rule has on the final output decision.

What is defuzzification and how is it used in this system?

Defuzzification is the process of converting a fuzzy output back into a crisp value. In this system, the centroid method is used for defuzzification, which calculates the x-coordinate of the centroid of the combined membership functions to determine the final tip percentage.

Why would you use a lookup table instead of running a fuzzy inference system in real-time?

A lookup table can replace a fuzzy inference system in real-time applications, especially on devices with limited computational power. The table stores pre-calculated output values based on inputs, making the process more efficient and requiring fewer computations than the full fuzzy inference process.