A numerical approach to linguistic variables and linguistic space
Chengan Liu, A. Shindhelm, Dapeng Li, Kun Jin · Proceedings of IEEE 5th International Fuzzy Systems · 2002
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.