The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modelling, which can formulate the uncertainty in the actual environment. The aim of this paper is to present an efficient algebraic method which is called an eigenvalue method for solving fully fuzzy polynomial equations systems. First of all, the system of fully fuzzy polynomial equations is transformed to an equivalent crisp polynomial equations system. In eigenvalue method, the solutions of a system of fully fuzzy polynomial equations are obtained employing linear algebra benefits. One of the great benefits of our approach is that it gives all solutions at a time. Finally, some applied numerical examples are illustrated to demonstrate the proficiency of the given approaches.

fuzzy number, fully fuzzy polynomial equations system, Gröbner basis, eigenvalue, Positive solution.