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
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