Ordered structure-based semantics of linguistic terms of linguistic variables and approximate reasoning

The paper will present an overview of an algebraic approach to approximate reasoning problems. It is shown that there exists a natural semantic ordering relation on domains of linguistic variables, and this relation makes each linguistic domain a complete distributive lattice. For linguistic variables having a unique positive primary term and negative one, their domains have sufficiently rich algebraic-logic properties for investigating fuzzy logic and approximate reasoning. The algebraic structures which model linguistic domains are called hedge algebras, because their axioms formulate directly semantics of linguistic hedges. As an example of the application of this theory, we introduce a method in linguistic reasoning, which allows us to handle directly linguistic terms. We consider this approach as having qualitative characteristics. Since, quantitative characteristics also play an important role in approximate reasoning methods, we introduce a mapping which transforms each linguistic domain into a rea...