Extended hedge algebras and their application to fuzzy logic

This paper continues our investigation on hedge albebras [6]. We extend hedge algebras by two additional operations corresponding to infimum and supremum of the so-called concept category of an element x, i.e. the set which is generated from x by means of the hedge operations. It is shown that every extended hedge algebra with a lattice of the primary generators is a lattice. In the symmetrical extended hedge algebras we are able to define negation and implication, called concept-negation and conceptimplication. Furthermore, it is proved that there exists an isomorphism from a subaigebra of a symmetrical extended hedge algebra of a linguistic truth variable into the closed unit interval [0, 1], under which the concept-negation and the concept-implication correspond to the negation and a kind of implication in multiple-valued logic based on the unitinterval [0, 1].