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Based on importance measures and fuzzy integrals, a new assessment method for image coding quality is presented in this paper. The proposed assessment is based on two subevaluations. In the first subevaluation, errors on edges, textures, and flat regions are computed individually. The errors are then assessed using an assessment function. A global evaluation with Sugeno fuzzy integral is then obtained based on the importance measure of edge, texture, and flat region. In the second subevaluation, an importance measure is first established depending on the types of regions where errors occur, a subtle evaluation is then obtained using Sugeno fuzzy integral on all pixels of the image. A final evaluation is obtained based on the two subevaluations. Experimental results show that this new image quality assessment closely approximates human subjective tests such as mean opinion score with a high correlation coefficient of 0.963, which is a significant improvement over peak signal-to-noise ratio, picture quality scale, and weighted mean square error, three other image coding quality assessment methods, which have the correlation coefficients of 0.821, 0.875, and 0.716, respectively.