General Algebraic Solutions of Fuzzy Dual Number Linear Systems

In this paper, we define fuzzy dual number linear systems (FDLSs) expressed as , where C represents a crisp dual number matrix and denotes a fuzzy dual number vector. Our study focuses on three primary objectives. First, we obtain the existence of strong fuzzy solutions to the FDLS by analyzing the CMP inverse of coefficient matrix. Second, we investigate the existence of nonnegative CMP inverse by analyzing their block structure. Third, we derive general strong fuzzy solutions for the FDLS and develop a corresponding computational algorithm based on the CMP inverse. Meanwhile, a method for obtaining general solutions of the FDLS is proposed under the premise of a strong fuzzy solution. To illustrate our theoretical framework, we present numerical examples demonstrating the efficacy of the proposed methodology.