The term was introduced by Lotfi Zadeh, the father of fuzzy sets, to denote programming techniques not related to traditional programming languages:
A set of techniques to model systems (input-output mapping) by approximating them.
Considers a small sample of the entity to make an approximate model,
Is a representation of some entity, defined for a specific purpose.
Is limited to aspects of the entity represented which are relevant for the purpose
A model is different to the represented entity ex: map vs land
Models lead to approximation, uncertainty, imprecision.
The model features are similar to the real ones but not the same.
We are not sure that the features of the model are the same of the entity.
The model features values are not precise.
Correct model in a finite number of points, smooth transistion (approximation) among them.
ex: in a thermal control system we fix the normal working point and the critical one, and the system approximates the behaviour between.
input-output samples, learning algorithms to define output values for unknown values.
Optimal solution, obtained by evaluating populations of tentative solutions and combining their parts (sort of copying from nature).
From washing machines to helicopters, to rice cookers
Were created in 1965 by Lotfi Zadeh
The principle is to make computation with words.
Is a set whose membership function can range on the interval [0,1].
On contrary to crisp sets that admit only {0,1}
μ: U -> [0,1]
#####Membership functions can also overlap, and this quality is useful for example in classification of a noisy input, in fact with overlapping MF we have a smooth transition from a label to another
MFs define fuzzy sets
Labels denote fuzzy sets
Fuzzy sets can be considered as conceptual representations
Reason in terms of concepts and grounds them to reality.