In the present paper, a new fuzzy inaccuracy measure is proposed to measure the inaccuracy of a fuzzy set with respect to another fuzzy set. This measure is a modified version of fuzzy inaccuracy proposed in our earlier work. The measure is demonstrated to satisfy some interesting properties, which prepare ground for applications in multi-criteria decision making problems. A method to solve multi-criteria decision making problems with the help of new measure is developed. Finally, a numerical example is given to illustrate the proposed method to solve multi-criteria decision-making problem under fuzzy environment.