SOLVING BIPOLAR FULLY FUZZY SYLVESTER MATRIX EQUATIONS WITH NEGATIVE FUZZY NUMBERS

Abstract

Sylvester matrix equations play a crucial role in control theory for controller design. Bipolar Fully Fuzzy Sylvester Matrix Equations (FFSME), incorporating both positive and negative components, are employed in controller design to address uncertainties that may affect a system’s performance and stability. However, there is not much existing research on combining bipolar fuzzy numbers and FFSME,and most of them mainly deal with positive coefficients. Thus, this paper presents a method that enables solving the negative coefficient of bipolar FFSME in the form of Left-Right (LR) triangular fuzzynumbers using an Associated Bipolar Linear System (ABLS). To obtain the ABLS, bipolar FFSME is transformed into a bipolar Fully Fuzzy Linear System (FFLS) using the Kronecker product and Vecoperator. Subsequently, the solution is derived through the inverse method, and the equation of the ABLS is rearranged as a bipolar fuzzy matrix. Additionally, this paper provides two numerical examples to illustrate the applicability of the constructed method.