Linguistic algebras - an algebraic concept for describing modelling with words
Helmut Thiele · 2002
Starting with some well-known concepts from algebra, i.e., the concepts of universal algebra and homomorphism, the author introduces a general notion of model and modelling. Then he describes the construction method I generating a universal algebra ALG which is a model of a given universal algebra ALG'. The described construction method II solves the "inverse" problem, i.e., to a given universal algebra ALG a universal algebra ALG' is generated such that ALG is a model of ALG'. Furthermore, the concept of linguistic variable is updated to the notion of linguistic (universal) algebra. Finally, the construction method I is applied to generate a linguistic model for a given fuzzy (universal) algebra, and vice versa, and a fuzzy algebra such that a given linguistic algebra is a linguistic model for the generated fuzzy algebra (by applying the construction method II). A decisive means in this considerations is the concept of context dependent fuzzy set introduced previously by the author (1999).