lattice-valued map

noun
UK /ˈlætɪs ˈvæljuːd mæp/
US /ˈlætɪs ˈvæljuːd mæp/

A map that gives each point a value from a special ordered set called a lattice.

The fuzzy controller uses a lattice-valued map to assign each sensor reading a truth degree.

SYNONYMS

lattice-valued functionlattice-valued mappinglattice homomorphismorder-preserving map

RELATED WORDS

latticefuzzy setposetvaluationmembership function

OTHER MEANINGS

2. A function from a set into a lattice, often required to preserve joins or meets.

Every lattice-valued map on the Boolean algebra corresponds to a fuzzy subset.

3. In topology, a map whose codomain is a lattice equipped with a topology, used to study continuous order structures.

The researcher proved that the lattice-valued map is continuous with respect to the Scott topology.

4. A mapping used in many-valued logic that assigns each formula a truth value from a lattice of truth degrees.

The semantics of the logic is given by a lattice-valued map from formulas to the truth lattice.