A numerical approach to linguistic variables and linguistic space

The paper introduces an approach to translate linguistic variables (LV) into numerical ones without using the concept of membership. It achieves this goal in three steps: (1) arrange all the atomic terms of a LV inside the interval (0,1|; 2) put a restriction on any compound term of a LV that it can only be formed by the product of a weight vector and the standard vector of this LV; (3) use a standard matrix to describe a linguistic space (LS). Every state of a problem space corresponds to a numerical point of a LS whose numerical coordinates can be calculated by the product of its weight matrix and the standard matrix. The paper also discusses several possible applications of this approach