Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras

In the paper, we shall examine the fuzziness measure (FM) of terms or of complete and linear hedge algebras of a linguistic variable. The notion of semantically quantifying mappings (SQMs) previously examined by the first author will be redefined more generally and a closed relation between the FM of linguistic terms and a family of SQMs with the parameters to be the FM of primary terms and linguistic hedges will be established. A semantics-based topology of hedge algebras and a closed and interesting relation between this topology, the FM and the above family of SQMs will be discovered and examined. An applicability of the FM and SQMs will be shown by an examination of some application examples.