A novel approach for solving fully fuzzy linear systems and their duality

This paper deals with uncertain linear systems called fully fuzzy linear systems (FFLSs) and dual FFLSs. The aim is to solve FFLSs and their duality. To get the purpose, a new approach based on the relative-distance-measure fuzzy interval arithmetic (RDM-FIA) is proposed. So far, many approaches based on fuzzy standard interval arithmetic (FSIA) have been suggested for solving FFLSs, and dual FFLSs. However, the suggested approaches suffer from some limitations, e.g. unnatural behavior in modeling (UBM) phenomenon. The limitations are regarded as either the sign of fuzzy numbers or the type of fuzzy numbers considered in systems. However, in this paper, the proposed approach does not have the limitations. Using two theorems, the general form of solutions of FFLSs and dual FFLSs are presented. By a corollary it was demonstrated that a dual FFLS can be regarded as an FFLS. In addition, restrictions associated to the FSIA-based approaches dealing with the FFLSs and dual FFLSs were pointed out. Furthermore, the effectiveness and efficiency of the proposed approach are demonstrated using some comparative examples.