LAUSR

In this paper, the single-variable fuzzy polynomial equations are studied. We firstly define two solution types for the equations, called solution and r-cut solution. Then, sufficient and necessary conditions are proposed for existence of the solution and r-cut solution of the equations, respectively. Also, a new algorithm is designed to find all the solutions and r-cut solutions of the equations using algebraic computations. Based on Descartes’ rule of signs, we express and prove a fuzzy version of fundamental theorem of algebra to obtain the number of real roots of a single-variable fuzzy polynomial. Moreover, we present an upper bound on the number of solutions of the equations and show that each single-variable fuzzy polynomial equation has at most two distinct solutions.