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Fuzzy Expert Systems: Fuzzy Logic - Coggle Diagram
Fuzzy Expert Systems: Fuzzy Logic
Fuzzy logic
a set of mathematical principles for knowledge representation based on degrees of membership.
multi-valued
deals with
degrees of membershi
p and
degrees of truth
logical values between 0 (completely false) and 1 (completely true)
Fuzzy sets
In the fuzzy theory, fuzzy set A of universe X is defined by function A(x) called the membership function of set A
In classical set theory, crisp set A of X is defined as function fA(x) called the characteristic function of A
Fuzzy boundries
Linguistic variables and hedges
The range of possible values of a linguistic variable represents the universe of discourse of that variable.
For example, the universe of discourse of the linguistic variable speed might have the range between 0 and 220 km/h and may include such fuzzy subsets as very slow, slow, medium, fast, and very fast.
IF wind is strong THEN sailing is good
hedges
Hedges are terms that modify the shape of fuzzy sets. They include adverbs such as very, somewhat, quite, more or less and slightly.
Representation of hedges in fuzzy logic
a linguistic variables carries with it the concept of fuzzy set qualifiers
Fuzzy variable. for example, the statement "John is tall" implies that the linguistic variable John takes the linguistic value tall
Operations of fuzzy sets
Containment
. Crisp sets: Which sets belong to which other sets?
. Fuzzy sets: Which sets belong to other sets?
The smaller set is called the subset.
Intersection
. Crisp sets: Which element belongs to both sets?
. Fuzzy sets: How much of the element is in both sets?
Complement
. Crisp sets: Who does not belong to the set?
. Fuzzy sets: How much do elements not belong to the set?
Union
. Crisp sets: Which element belongs to either set?
. Fuzzy sets: How much of the element is in either set?
