Least squares solutions of linear inequality systems: a pedestrian approach

Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

H2 optimal semistable control for linear dynamical systems: An LMI approach

In this paper, we develop H2 semistability theory for linear dynamical systems. Using this theory, we design H2 optimal semistable controllers for linear dynamical systems. Unlike the standard H2 optimal control problem, a complicating feature of the H2 optimal semistable stabilization problem is that the closed-loop Lyapunov equation guaranteeing semistability can admit multiple solutions. An ...

NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS

We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. T...

Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations