Hedge Algebras of Linguistic Values

Abstract

Hedge algebras on the set of linguistic values establish an algebraic approach for CWW. From the philological point of view, there exists an ordering relation among linguistic values that is determined by natural meanings of linguistic values, which is called the semantics ordering relation of linguistic values. Based on the semantics ordering relation, Ho and Wechler (1990) proposed hedge algebras. Whereafter, extensions of hedge algebras are proposed, e.g., extended hedge algebras [Ho and Wechler (1992)], refined hedge algebras [Ho and Nam (1999a,c); Ho (2007)], complete hedge algebras, the topologies and fuzziness measures on complete hedge algebras [Ho and Long (2007)]. In this chapter, we introduce some interesting works of hedge algebras and some applications based on hedge algebras. We refer to [Ho and Son (1995); Ho (1996); Ho and Nam (1996, 1999b); Ho et al. (1999); Ho and Nam (2002); Ho (2003); Ho and Nam (2009)] for more details about hedge algebras. Readers may need the background knowledge of logical algebras and logic systems to understand hedge algebras and their related works, e.g., free algebras, lattice theory, Boolean algebras, Heyting algebras, multi-valued logic systems and fuzzy logic systems.