Hamming-Hausdorff距离下区间直觉模糊知识测度及应用

提出了一种基于改进Hamming-Hausdorff距离的区间直觉模糊知识测度（interval-valued intuitionistic fuzzy knowledge measure，IVIFKM），并应用于图像阈值分割中，获得了更好的图像分割结果.最新研究成果表明，直觉模糊环境下的知识度量包括两个重要方面，即信息量与信息清晰度.基于这种理解，提出新的区间直觉模糊知识测度公理系统.同时，改进并推广标准Hamming-Hausdorff距离，结合理想解法（technique for order preference by similarity to ideal solution，TOPSIS），建立新的满足所提公理系统要求的区间直觉模糊知识测度.随后，将所提测度模型应用于图像阈值分割中，并根据区间直觉模糊集自身结构特点，进一步提出一种精炼而高效的像素分类规则及图像区间直觉模糊化算法.最后，利用所提测度模型计算图像的区间直觉模糊知识量，确定最佳分割阈值，实现图像分割.实验结果表明，该基于知识驱动的图像阈值分割方法性能表现稳定、可靠，所生成的二值图具有更加优良的性能指标，明显优于其他同类算法.将知识测度新理论引入图像处理领域，为该理论在其他相关领域的潜在应用提供了实例.

Interval-valued Intuitionistic Fuzzy Knowledge Measure with Applications Based on Hamming-Hausdorff Distance

A Hamming-Hausdorff distance-based interval-valued intuitionistic fuzzy knowledge measure (IVIFKM) is presented in this paper, upon with a methodology for image thresholding is based so as to achieve a better segmentation result. The latest achievement shows that there are two significant facets of knowledge measurement associated with an intuitionistic fuzzy set (IFS), i.e., the information content and the information clarity. With this understanding, a novel axiomatic system of IVIFKM is proposed. The normalized Hamming-Hausdorff distance is also improved and extended. Combined with the technique for order preference by similarity to ideal solution (TOPSIS), a novel IVIFKM is then established, complying fully with the requirement of the developed axiomatic system. The proposed measure is subsequently applied to image thresholding. Given the structural features of an interval-valued IFS (IVIFS) in itself, a more effective classification rule of pixels and a more efficient algorithm for interval-valued intuitionistic fuzzification of an image are suggested, respectively. The developed measure is finally used to calculate the amount of knowledge associated with the image to determine the best threshold for segmentation. Experimental results show that the developed knowledge-driven methodology, characterized by high stability and reliability, can produce much more satisfactory binary images with excellent performance metrics, routinely outperforming other thresholding ones. By this work, the latest IVIFKM theory is introduced into the field of image processing, thus providing a concrete instance for the potential applications of this theory in other related areas.