A unified framework for knowledge measure with application: From fuzzy sets through interval-valued intuitionistic fuzzy sets

Abstract 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.