To design novel anion-conducting polymer electrolyte membranes (AEMs), this paper proposes a basicity index (BI) that is defined by the ion-exchange ratios of AEMs from the OH- to Cl- forms in a neutral aqueous solution as a parameter for Arrhenius basicity (dissociation constant). Using a radiation-induced graft polymerization technique, three iminium cations are introduced into fluorinated polymer films. The BI of the iminium-containing AEMs is less than that of a conventional ammonium-type AEM. The conductivity and water uptake correlate positively with the BI, whereas the thermal and chemical stabilities correlate negatively with the BI. The dependence on the BI stems from the stabilization of the iminium hydroxide in proportion to the basicity of the original diaza-compounds, resulting in a decrease in conductivity and water uptake with keeping higher thermal and chemical stabilities. Notably, ion conductivity is sufficient and water uptake is less in AEMs with a medium BI. (c) 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 503-510