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The knowledge measure can be considered as a dual measure of entropy for fuzzy sets. In the present work, a new entropy-based knowledge measure is proposed for FSs, which complies with the extended idea of De Luca and Termini axioms. Besides this, some of its major properties are also discussed. Comparison of the proposed measure with various existing fuzzy measures indicates that the proposed knowledge measure has a greater ability in discrimination of various FSs. Moreover, a fuzzy inaccuracy measure is introduced based on the proposed measure and investigated some properties. Considering the significance of integrated weights, a new multiple attribute decision-making (MADM) model is introduced under fuzzy set environment. The proposed knowledge measure is utilized to calculate the weights vector, when weights are partially known and other when weights are completely unknown. Finally, an example is employed to illustrate the effectiveness and consistency of the new MADM method.