Fuzzy Inference Systems (FIS) Overview

Introduction to FIS

• FIS uses fuzzy logic to handle reasoning that is approximate rather than precise.
• Key to FIS is the use of "IF...THEN" rules along with connectors like AND for decision-making.

Components of FIS

• Fuzzification Interface: Converts crisp inputs into fuzzy quantities.
• Knowledge Base: Comprises a rule base (IF-THEN rules) and a database defining fuzzy sets.
• Decision-Making Unit: Performs operations on the rules.
• Defuzzification Interface: Converts fuzzy outputs back to crisp data.

FIS Types

• Mamdani FIS:
  • Uses fuzzy sets as rule consequents.
  • Membership functions expected to be fuzzy sets.
  • Popular for its acceptance in universal approximations.
• Sugeno FIS:
  • Uses linear functions of input variables as rule consequents.
  • Computationally efficient and suited for mathematical analysis.

Comparison of Mamdani and Sugeno

• Mamdani is widely accepted for its intuitive human-like approach.
• Sugeno is more computationally efficient and suitable for optimization techniques.
• Sugeno has more adjustable parameters than Mamdani.

Fuzzy Logic Controller (FLC) System

Architecture

• Consists of a fuzzifier, fuzzy rule base, fuzzy knowledge base, inference engine, and defuzzifier.
• Aims to simulate human decision-making through approximate reasoning.

Design Steps

1. Identify input, output, and state variables of the plant.
2. Split the universe of discourse into fuzzy subsets.
3. Obtain membership functions for each fuzzy subset.
4. Assign fuzzy relationships to form the rule base.
5. Choose appropriate scaling factors for normalization.
6. Execute the fuzzification process.
7. Identify output from each rule using fuzzy reasoning.
8. Combine fuzzy outputs into a single output.
9. Apply defuzzification for a crisp output.

Genetic Algorithms & Encoding Techniques

Selection Techniques

• Roulette Wheel Selection: Assigns a slice of a wheel proportional to fitness value for selection.
• Tournament Selection: Selects individuals by holding tournaments among a set number.
• Rank Selection: Based on the rank of individuals within the population.
• Boltzmann Selection: Uses temperature to control the selection pressure.

Crossover Techniques

• Single-point Crossover: Randomly selects a crossover point to exchange bits.
• Two-point Crossover: Uses two crossover points for exchange.
• Uniform Crossover: Parents contribute genes randomly to offspring.
• Precedence Preserving Crossover: Used in scheduling problems.

Mutation Techniques

• Randomly alters genes to maintain genetic diversity.
• Techniques include bit-flipping, inversion, and others to ensure genetic variety.

Termination Criteria

• Can include reaching a defined time limit, achieving a specific fitness level, or other criteria.

Conclusion

• FIS and genetic algorithms provide robust frameworks for dealing with complex, non-linear, and dynamic systems.
• Both systems require careful design of rules, parameters, and techniques to achieve desired outcomes.