Also referred to as “hesitancy margin” or “indeterminacy index”. It represents the degree of indeterminacy regarding the assignment of an element of the universe to a particular set. It is calculated as the difference between unity and the sum of the corresponding membership and non-membership values.
Published in Chapter:
Intuitionistic Fuzzy Image Processing
Ioannis K. Vlachos (Aristotle University of Thessaloniki, Greece) and George D. Sergiadis (Aristotle University of Thessaloniki, Greece)
Copyright: © 2009
|Pages: 8
DOI: 10.4018/978-1-59904-849-9.ch143
Abstract
Since its genesis, fuzzy sets (FSs) theory (Zadeh, 1965) provided a flexible framework for handling the indeterminacy characterizing real-world systems, arising mainly from the imprecise and/or imperfect nature of information. Moreover, fuzzy logic set the foundations for dealing with reasoning under imprecision and offered the means for developing a context that reflects aspects of human decision-making. Images, on the other hand, are susceptible of bearing ambiguities, mostly associated with pixel values. This observation was early identified by Prewitt (1970), who stated that “a pictorial object is a fuzzy set which is specified by some membership function defined on all picture points”, thus acknowledging the fact that “some of its uncertainty is due to degradation, but some of it is inherent”. A decade later, Pal & King (1980) (1981) (1982) introduced a systematic approach to fuzzy image processing, by modelling image pixels using FSs expressing their corresponding degrees of brightness. A detailed study of fuzzy techniques for image processing and pattern recognition can be found in Bezdek et al and Chi et al (Bezdek, Keller, Krisnapuram, & Pal, 1999) (Chi, Yan, & Pham, 1996). However, FSs themselves suffer from the requirement of precisely assigning degrees of membership to the elements of a set. This constraint raises some of the flexibility of FSs theory to cope with data characterized by uncertainty. This observation led researchers to seek more efficient ways to express and model imprecision, thus giving birth to higher-order extensions of FSs theory. This article aims at outlining an alternative approach to digital image processing using the apparatus of Atanassov’s intuitionistic fuzzy sets (A-IFSs), a simple, yet efficient, generalization of FSs. We describe heuristic and analytic methods for analyzing/synthesizing images to/from their intuitionistic fuzzy components and discuss the particular properties of each stage of the process. Finally, we describe various applications of the intuitionistic fuzzy image processing (IFIP) framework from diverse imaging domains and provide the reader with open issues to be resolved and future lines of research to be followed.