Lecture 4: Fuzzy Inference Systems

Lecture 4 introduces fuzzy inference systems (FIS), which have been successfully applied in areas like automatic control, data classification, decision analysis, expert systems, and computer vision [1]. Because of its multidisciplinary nature, a fuzzy inference system is also known as a fuzzy-rule-based system, fuzzy expert system, fuzzy model, fuzzy associative memory, or fuzzy logic controller [1].

Here's a summary of the key aspects of fuzzy inference systems covered in Lecture 4:

• Course Content: The lecture covers fuzzy inference systems with a problem-based learning assignment due [2].

• Limitation of Expert Systems: Traditional expert systems may not handle borderline cases well, or they may struggle with vague terms [3]. For example, a rule might not be triggered if a value is exactly at a boundary, and terms like "GOOD" may be subjective [3].

• Architecture of FIS: Fuzzy inference systems involve several key components [4]:

• Fuzzy Knowledge Base: Contains a rule base of fuzzy IF-THEN rules and a database defining the membership functions of the fuzzy sets used in these rules [4, 5]. The fuzzy knowledge base consists of a rule base and a database [5].

• Fuzzifier: Converts crisp inputs into linguistic variables using membership functions stored in the fuzzy knowledge base [4, 6].

• Inference Engine: Converts fuzzy inputs into fuzzy outputs using IF-THEN type fuzzy rules [4, 7].

• Defuzzifier: Converts the fuzzy output of the inference engine into a crisp output using membership functions [4, 8].

• Steps of Fuzzy Reasoning:

1. Fuzzification: Input variables are compared with membership functions to obtain membership values for each linguistic label [6].

2. Firing Strength: Membership values are combined to determine the firing strength of each rule [6].

3. Qualified Consequents: Qualified consequents (fuzzy or crisp) are generated for each rule based on the firing strength [6].

4. Defuzzification: Qualified consequents are aggregated to produce a crisp output [6].

• Connectives: Three sample connectives introduced include Gӧdel, Product, and Lukasiewicz, with corresponding t-norms, t-conorms, and negations [7].

• Fuzzy Inference Methods: The two most important fuzzy inference methods are Mamdani and Sugeno [8]. The main difference lies in the consequence of fuzzy rules and the fuzzy inference process [9].

• Mamdani Fuzzy Models: The most commonly used inference method [8]. To compute the output, you determine fuzzy rules, fuzzify inputs, combine fuzzified inputs, find the consequence of the rule, combine the consequences to get an output distribution, and defuzzify to get a crisp output [9, 10].

• Sugeno Fuzzy Models: Another well-known inference method [8].

• Mamdani Fuzzy Method Example: Calculating a tip based on food and service quality [10]. This involves defining fuzzy inputs and outputs with membership functions [11]. The example goes through the steps of fuzzifying inputs, applying fuzzy operators, and implication [12-16].

• Qualification & Experience Scorer Example: Designing a scoring mechanism based on theoretical knowledge and practical capacity [17]. This includes defining fuzzy sets for inputs like theoretical knowledge and practical capacity, as well as for the output score [18]. The example includes using triangular membership functions and fuzzy rules to determine the score [19, 20].

• Applying Rules: The fuzzy values for given inputs are determined, fuzzy membership functions are activated, and fuzzy rules are applied [20]. A minimum function is used to combine antecedents connected by AND [21].

• Rule Aggregation: Output membership functions are combined, typically using a maximum operator [22].

• Defuzzification: Different methods can be used, including centroid, mean of maximum, min of maximum, and max of maximum [23].

• Fuzzy Logic Applications: Include modeling, evaluation, optimization, decision-making, and control [23, 24].

• Advantages of Fuzzy Logic Systems: Easy to understand, facilitates dealing with uncertainties, can be easily modified, robust to noisy input, and doesn't require precise inputs [24].

• Disadvantages of Fuzzy Logic Systems: Results are based on assumptions, may not offer accurate reasoning, lacks the pattern recognition capabilities of some ML methods, and validation/verification can be extensive [24, 25]. Setting precise fuzzy rules and accurate membership functions can be challenging [25].