Characteristic Function in Fuzzy Set Theory
In classical mathematics, characteristic functions of sets only take values 1 (members) or 0 (non-members). In fuzzy set theory, characteristic functions are generalized to take value in the real unit interval, or more generally, in some algebra or structure (usually required to be at least a poset or lattice). Such generalized characteristic functions are more usually called membership functions, and the corresponding "sets" are called fuzzy sets. Fuzzy sets model the gradual change in the membership degree seen in many real-world predicates like "tall", "warm", etc.
Read more about this topic: Indicator Function
Famous quotes containing the words function, fuzzy, set and/or theory:
“The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
—Erik H. Erikson (1904–1994)
“What do you think of us in fuzzy endeavor, you whose directions are sterling, whose lunge is straight?
Can you make a reason, how can you pardon us who memorize the rules and never score?”
—Gwendolyn Brooks (b. 1917)
“Ceremony was but devised at first
To set a gloss on faint deeds, hollow welcomes,
Recanting goodness, sorry ere ‘tis shown;
But where there is true friendship, there needs none.”
—William Shakespeare (1564–1616)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)