Fuzzy Systems
Aristotle came up with the “Law of the Excluded Middle”.
- Classical sets
- Fuzzy sets
- an element can belong to a set to a degree k (0 k 1), in contrast to classical set theory where an element must definitely belong or not to a set
- Crisp Sets
A crisp set is defined in such a way that all the individuals in a given universe can be partitioned into two classes:
- those who belong to the set
- and those who do not belong to the set
- Fuzzy Logic – represents partial truth
- reply to a yes-no question with a not-quite-yes-or-no answer
- fuzzy logic is actually a superset of conventional boolean logic
- Membership Function (μ)
can be any function ranging from a simple linear straight line to a complicated spline function or a polynomial of a higher degree
- Truth values range between 0.0 and 1.0
- fuzzy operators
- fuzzy logic is actually a superset of conventional boolean logic
- chooses min (minimum) operator in place for AND
- chooses max (maximum) operator in place for OR
- Fuzzy rules – revise the concept of simple If-Then rules
- Antecedents can have multiple parts – using OR, AND
- consequent can have multiple parts as well
- Types of facts
- Single-valued or multiple – valued
- Uncertain facts
- Fuzzy facts
- Object-Attribute-Value triplets
- FIS (Fuzzy inference system)
process of formulating the mapping from a given input to an output using fuzzy logic
Five parts
- Fuzzification of the input variables
- Application of fuzzy operator in the antecedent (premises)
- Implication from antecedent to consequent
- Aggregation of consequents across the rules
- Defuzzification of output
Last updated: March 19, 2014
