An extension method for fully fuzzy Sylvester matrix equation

An extension method is proposed to solve a class of fully fuzzy Sylvester matrix equation (FFSME) under some mild assumptions. This method consists of two steps. Firstly, the fully fuzzy system is transferred into a series of interval Sylvester matrix equations through alpha-cut. Secondly, these interval systems are extended into crisp systems which is easy to be solved. The solutions of FFSME are not presumed to be triangular-type fuzzy numbers. Moreover, some examples are presented to show the validity of our method.

Automated summary

An extension method is proposed to solve fully fuzzy Sylvester matrix equation by transferring the system into interval systems and then extending them into crisp systems. The solutions are not presumed to be triangular-type fuzzy numbers and the validity of the method is demonstrated through examples.