Fuzzy logic handles situations that binary true-or-false rules represent poorly. Medical symptoms, for example, vary by degree: patients may describe headaches or fatigue as sometimes, usually, mild, or severe. section 2.4
It is a mathematical framework for reasoning with uncertainty and imprecision in decision-making and control systems. Rather than assigning only completely true or completely false values, it permits intermediate degrees of truth. Fuzzy sets represent partial membership and gradual transitions between categories. section 2.4
Tall and short as gradual categories
Classical logic might declare someone tall only when their height reaches 6 feet 2 inches. Under that rule, a 6-foot-1-inch person is not tall and a 6-foot-3-inch person is tall. Fuzzy sets instead treat height as a continuum, allowing a person to belong to the tall and short sets to different degrees. section 2.4
Table 2.1 Determining the values of tall and short based on height
|
Name
|
Height
|
Tall
|
Short
|
|---|---|---|---|
|
Gary
|
6’1”
|
0
|
1
|
|
Joe
|
6’3”
|
1
|
0
|
|
Sandy
|
5’6”
|
0
|
1
|
|
Sue
|
6’1”
|
0
|
1
|
The comparison table makes the abrupt boundary of binary tall/short classification visible before introducing graded membership. section 2.4
Fuzzy logic is particularly useful when:
- Questions require nuanced interpretations instead of yes-or-no answers. section 2.6
- A system must represent uncertainty or imprecision in real-world observations. section 2.4
- It is combined with other techniques, such as rule-based systems, data mining, case-based reasoning, deep learning, genetic algorithms, or smart agents. section 11.7
