<p>Ranking the fuzzy numbers plays an important role in decision-making. Although there are a lot of methods for ranking fuzzy numbers, some of them are non-intuitive and inconsistent. In this paper, a theorem is strictly presented by mathematical proof, and then some special cases are given to point out the shortcomings of these existing methods: (a) The results of Hajjari’s method and Gu and Xuan’s method do not satisfy the theorem which considers the symmetric fuzzy numbers with 0 as the possibilistic means are equivalent; (b) The ranking results of Abbasbandy’s method and Liu’s method cannot differentiate fuzzy numbers when possibilistic means are the same; (c) The ranking results of Gu and Xuan’s method exist inconsistency. To overcome the limitations, we propose an improved ranking method based on a new perspective: the weighted average distribution value of fuzzy number is jointly determined by the possibilistic mean and skewness, rather than only by the possibilistic mean. Then, we use some numerical examples to illustrate that the proposed method can well overcome these shortcomings. To illustrate the advantages of our proposed method in application, we construct the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S - V\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mo>-</mo> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation> portfolio model which incorporates the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(M - V\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo>-</mo> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation> model in theory, and the models based on other ranking methods. Finally, a specific stock selection problem is verified by these constructed models. The results show that the portfolio model based on our proposed new method is better than the other models in terms of the solution effect and the problem scope.</p>