An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

TL;DR: Analytical and numerical methods for solving a couple of trapezoidal fully fuzzy Sylvester matrix equations (CTrFFSMEs) to overcome the drawbacks of the existing crisp methods are constructed.

TL;DR: In this article , a new numerical method for solving arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations (TrFFSME) is proposed, which includes near-zero trapezoidal fuzzy numbers to overcome this limitation.

TL;DR: This paper proposes a new analytical method for solving a family of arbitrary FMEs, able to solve Arbitrary Generalized Trapezoidal Fully Fuzzy Sylvester Matrix Equations (AGTrFFSME), and is better to use in several engineering and scientific applications.

TL;DR: In this article , a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers was proposed, which provides a wider scope of trapezoid fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications.

TL;DR: It is proved that finding all of the real solutions which satisfy in a system with interval coefficients is NP-hard, and some heuristics based methods on Dubois and Prade’s approach are employed, finding some positive fuzzy vector x which satisfies A ˜ x ˜ = b ˜, where A and b are a fuzzy matrix and a fuzzy vector respectively.

TL;DR: This book provides an introduction to fuzzy numbers and the operations using them.

TL;DR: The fuzzy Sylvester matrix equation in which are and crisp matrices, respectively, and is an LR fuzzy numbers matrix is investigated, and the Kronecker product of matrices is converted into anLR fuzzy linear system and extended into two systems of linear equations.