Analytical solution for the linguistic weighted average problem

The linguistic weighted average (LWA) of interval type-2 fuzzy sets is an extension of the fuzzy weighted average (FWA) of type-1 fuzzy sets. Currently, the commonly used methods of both FWA and LWA are based on a-cuts decomposition of the type-1 of type-2 fuzzy sets, which involves large amount of calculations, and the result is not accurate. In this paper, we propose a new algorithm to obtain the analytical solution methods, which is more accurate and efficient than the current a-cuts methods. Some properties of the algorithms are discussed. A numerical example is used to illustrate our new proposed algorithms.