This note gives a theory of state transition matrices for linear systems of fuzzy di#erential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations...

In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective funct...

This paper studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary condition and a sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI ...

In this paper, necessary and sufficient conditions are given for the k-regularity of block fuzzy matrices in terms of the schur complements of its k-regular diagonal blocks. A formula for k-g-inverse of a block fuzzy matrix is established. A set of conditions for a block matrix to be expressed as the sum of k-regular block matrices is obtained. Mathematics Subject Classification: 15B15; 15A09

In this paper, we consider the system of linear equations Ax̃ = b̃, where A ∈ Rn×n is a crisp H-matrix and b̃ is a fuzzy n-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical r...

In this paper, characterizations of secondary κkernel symmetric fuzzy matrices are obtained. Relation between sκkernel symmetric, skernel symmetric, κkernel symmetric and kernel symmetric matrices are discussed. Necessary and sufficient conditions are determined for a matrix to be sκkernel symmetric.

In this paper, we develop an interactive method for multiple attribute group decision making under fuzzy environment. The method can be used in situations where the information about attribute weights is partly known, the weights of decision makers are expressed in exact numerical values or triangular fuzzy numbers, and the attribute values are triangular fuzzy numbers. The method transforms fu...

In paper the fuzzy linear system d x C x A ~ ~ ~   where A and C are crisp matrices and n m  d~ is a LR fuzzy numbers vector, is investigated in detail. We generalize the definition and arithmetic operations of LR fuzzy numbers and convert the dual fuzzy linear system to two crisp systems of linear equations. Then the minimal fuzzy solution of the original fuzzy system is obtained by solving...