An **MV-algebra** is an algebraic structure consisting of

- a non-empty set
- a binary operation on
- a unary operation on and
- a constant denoting a fixed element of

which satisfies the following identities:

- and

By virtue of the first three axioms, is a commutative monoid. Being defined by identities, MV-algebras form a variety of algebras. The variety of MV-algebras is a subvariety of the variety of BL-algebras and contains all Boolean algebras.

An MV-algebra can equivalently be defined (Hájek 1998) as a prelinear commutative bounded integral residuated lattice satisfying the additional identity

Read more about MV-algebra: Examples of MV-algebras, Relation To Łukasiewicz Logic, Relation To Functional Analysis, In Software

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**MV-algebra**- In Software

... There are multiple frameworks implementing fuzzy logic (type II), and most of them implement what has been called a multi-adjoint logic ... This is no more than the implementation of a MV-algebra ...

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