Ghassan Malkawi

A note on \The nearest symmetric fuzzy solution for a symmetric fuzzy linear system"

Abstract This paper provides accurate approximate solutions for the symmetric fuzzy linear systems in (Allahviranloo et al:[1]).

The consistency of positive fully fuzzy linear system

In this paper, the consistency of fuzziness of positive solution of the n × n fully fuzzy linear system (P – FFLS) is studied based on its associated linear system (P – ALS). That can consist of the whole entries of triangular fuzzy numbers in a linear system without fuzzy operations. The nature of solution is differentiated in case of fuzzy solution, non-fuzzy solution and fuzzy non-positive solution. Moreover, the analysis reveals that the P – ALS is applicable to provide the set of infinite number of solutions. Numerical examples are presented to illustrate the proposed analysis.

A preliminary study on the solution of fully fuzzy Sylvester matrix equation

Sylvester matrix equation is one of the most popular equations used in control theory. In applying the uncertainty, vague, ambiguity and incomplete real problem, this equation can be employed with the fuzzy theory. In this study, we present a preliminary study on how the Sylvester matrix equation is solved when its parameters are fuzzy or known as fully fuzzy Sylvester matrix equation (FFSME). This study shows that the FFSME can be transferred to linear system, as in the case of crisp linear Sylvester matrix equation. We also show that the transformation of FFSME to linear system passes on fully fuzzy linear system (FFLS), subsequently the solution of FFLS is obtained by its associated linear system, which equivalent to fuzzy solution of FFSME. A numerical example is given to illustrate this transformation. Finally, we draw some conclusions concerning the related future directions towards this study.

Finite solutions of fully fuzzy linear system

The solution of Fully Fuzzy Linear System (FFLS) is normally categorized as unique, finite and infinitely many solutions. However, in the case of more than one solution, the finite or alternative solution is not detected when linear programming is considered. Therefore this paper aims to provide a method of using min-max system and absolute system to append new concept for the consistency of FFLS, which is called finite solution of FFLS, where the FFLS have more than two solutions, and not only an infinite solution.