Evaluating Linguistic Expressions and Functional Fuzzy Theories in Fuzzy Logic

In this paper, we introduce a new mathematical model of the meaning of the basic linguistic trichotomy, which are the canonical words “small”, “medium” and “big”. The model is based on the concept of horizon as elaborated in the Alternative Set Theory. Such a model makes also possible to include naturally the linguistic hedges which form a consistent class of functions. Each linguistic hedge is thus characterized by one number only.Then it is shown that continuous functional dependences between x and y can be described (precisely or approximately) by the collections of logical formulas of implicative form with predicates interpreted by fuzzy sets with meaning of the basic linguistic trichotomy. It demonstrates the expressive power of modified by linguistic hedges membership functions of fuzzy sets from the basic triplet.