Annelies Vroman

Solving systems of linear fuzzy equations by parametric functions---An improved algorithm

Buckley and Qu proposed a method to solve systems of linear fuzzy equations. Basically, in their method the solutions of all systems of linear crisp equations formed by the @a-levels are calculated. We propose a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system. By observing the monotonicity of the parametric functions in each variable, i.e. each fuzzy coefficient in the system, we improve the algorithm by calculating less parametric functions and less evaluations of these parametric functions. We show that our algorithm is much more efficient than the method of Buckley and Qu.

Solving Systems of Linear Fuzzy Equations by Parametric Functions

Buckley and Qu proposed a method to solve systems of linear fuzzy equations. Basically, in their method the solutions of all systems of linear crisp equations formed by the alpha-levels are calculated. We propose in this paper a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system. We show that our algorithm is much more efficient than the method of Buckley and Qu.

A SOLUTION FOR SYSTEMS OF LINEAR FUZZY EQUATIONS IN SPITE OF THE NON-EXISTENCE OF A FIELD OF FUZZY NUMBERS

In this paper we investigate whether the fuzzy arithmetic based on Zadehs extension principle could be improved by redefining the fuzzy addition and multiplication so that the class of fuzzy numbers combined with these operations would constitute a field. We will prove that such a fuzzy arithmetic does not exist. This has important consequences for solving systems of linear fuzzy equations. Despite the lack of inverses, we propose a method to solve approximately such systems.

Real-Time Constrained Fuzzy Arithmetic

Klir introduced constrained fuzzy arithmetic (CFA) as a solution to the unnecessary precision loss when dealing with fuzzy quantities that represent linguistic variables. Since then, some attempts have been made to make CFA efficient, but none of these solutions is suitable for real-time applications. In this paper, we will propose a new CFA algorithm that can be used in such environments.

Using parametric functions to solve systems of linear fuzzy equations: an improved algorithm

Buckley and Qu proposed a method to solve systems of linear fuzzy equations. Basically, in their method the solutions of all systems of linear crisp equations formed by the a-levels are calculated. We proposed a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system. By observing the monotonicity of the parametric functions in each variable, i.e. each fuzzy coefficient in the system, we improve the algorithm by calculating less parametric functions and less evaluations of these parametric functions. We show that our algorithm is much more efficient than the method of Buckley and Qu.