Minimal generalized solutions of fuzzy polynomial equations

Abstract

Fuzzy polynomial equations ($FPEs$) don't have algebraic solutions, generally. In this paper, we first, express and prove some relationships between Husdroof meter and length function on classes of triangular fuzzy numbers. We appraise the behavior of fuzzy polynomials by using the length function properties. Next, we transform a $FPE$ into a generalized fuzzy polynomial equation ($GFPE$) and introduce generalized solutions and minimal generalized solutions concepts of $FPEs$. Finding minimal generalized solutions are discussed theoretically, in details. Finally, some numerical examples are given, illustrating our results.