The purpose of this paper is to establish a new mathematical framework for knowledge measure (KM) from fuzzy sets (FSs) through interval-valued intuitionistic fuzzy sets (IVIFSs). A novel KM is developed first in the context of intuitionistic fuzzy sets (IFSs) based on the normalized Hamming distance combined with the technique for order preference by similarity to ideal solution (TOPSIS), complying with the latest axiomatic definition. More efforts are made to investigate this new kind of axiomatic system and measuring model in the contexts of IVIFSs and FSs, respectively. This allows us to further recognize the nature of knowledge and present a unified framework for KM from FSs through IVIFSs. The developed technique is then used for image thresholding as a brand-new KM application, in which a new classification rule of pixels and a more efficient method for (interval-valued) intuitionistic fuzzification of images are proposed, thus leading to a knowledge-driven thresholding methodology. Experimental results show the outperformance of the developed technique with application. This is the first attempt to apply the latest KM theory to image processing, with which we undoubtedly create a new instance for the potential application areas of this theory.

本文的目的是从模糊集 (FS) 到区间值直觉模糊集 (IVIFS) 为知识度量 (KM) 建立一个新的数学框架。一种新颖的 KM 首先在基于归一化汉明距离的直觉模糊集 (IFS) 的背景下开发，并结合了通过与理想解相似的顺序偏好技术 (TOPSIS)，符合最新的公理定义。分别在 IVIFS 和 FS 的背景下研究这种新的公理系统和测量模型做出了更多努力。这使我们能够进一步认识知识的性质，并为从 FS 到 IVIFS 的 KM 提供统一的框架。然后将开发的技术用于图像阈值处理作为全新的 KM 应用程序，其中提出了一种新的像素分类规则和一种更有效的图像（区间值）直觉模糊化方法，从而产生了一种知识驱动的阈值方法。实验结果表明，所开发的技术在应用方面的表现优于其他技术。这是将最新的知识管理理论应用于图像处理的首次尝试，无疑为该理论的潜在应用领域创造了新的实例。