Hedge Algebras: An Algebraic Approach to Domains of Linguistic Variables and Their Applicability

The paper is an overview on an algebraic approach to domains of linguistic variables and some first applications to show the applicability of this new approach. In this approach, each linguistic domain can be considered as a hedge algebra (HA for short) and based on the structure of HAs, a notion of fuzziness measure of linguistic hedges and terms can be defined. In order to apply hedge algebras to those problems, the results of which are needed, a notion of semantically quantifying mappings (SQMs) will be introduced. It shown that there is a closed connection between SQMs and fuzziness measure of hedge and primary terms (the generators of linguistic domains). To show the applicability of this approach, new methods to solve a Fuzzy Multiple Conditional Reasoning problem, the problem of Balancing an Inverted Pendulum will be presented.