Abstract
We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-calledgeneral solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.
Highlights
Systems of simulations linear equations play major role in various areas such as mathematics, statistics, and social sciences
We provide some useful result to show the difference between proposed method and the symmetric solutions [34, 39]
We presented a practicl method for determining the general solutions of a fully fuzzy linear system
Summary
Systems of simulations linear equations play major role in various areas such as mathematics, statistics, and social sciences. Based on their works, Muzzioli and Reynaerts in [26] studied FFLS of the form A1x + b1 = A2x + b2, while for implementing their method 2n(n+1) crisp systems should be solved. In [30], Allahviranloo and Mikaeilvand proposed an analytical method to obtain solution of FFLS by an embedding method. Allahviranloo et al [34] have proposed a new practical method to solve an FFLS based on the 1-cut expansion In their method, some spreads and some new solutions have been derived that belong to TSS or CSS.
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