Fuzzy measure theory

In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ) which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures; possibility/necessity measures; and probability measures which are a subset of classical measures.

Let ${\displaystyle \mathbf {X} }$ be a universe of discourse, ${\displaystyle {\mathcal {C}}}$ be a class of subsets of ${\displaystyle \mathbf {X} }$, and ${\displaystyle E,F\in {\mathcal {C}}}$. A function ${\displaystyle g:{\mathcal {C}}\to \mathbb {R} }$ where

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