L-fuzzy grammars

Abstract An L -fuzzy grammar is defined by assigning the element of lattice to the rewriting rules of a formal grammar. According to the kind of lattice, say, distributive lattice, lattice-ordered group, and lattice-ordered monoid, two type of L -fuzzy grammars are defined. It is shown that some context-sensitive languages can be generated by type 3 ∗-L- fuzzy grammars with cut points. It is also shown that for type 2 L -fuzzy grammars, Chomsky and Greibach normal form can be constructed as an extension of corresponding notion in the theory of formal grammars.