Ambiguous Set Theory: A New Approach to Deal with Unconsciousness and Ambiguousness of Human Perception

Abstract

Recently, precise measurement of uncertainty of data with fuzzy attributes is considered as one of the main problems. For this purpose, fuzzy sets, intuitionistic fuzzy sets, and neutrosophic set theory are extensively introduced. The problem arises in computing the complement of true or false membership values in the case of indeterminacy. Instead of indeterminacy as discussed in neutrosophic set theory, it can be completely true, partially true, or partially false. To deal with this, the theory of ambiguous sets has recently been introduced. A real-time example of dealing with unconsciousness and ambiguousness in relation to human perception is discussed, illustrating the motivation of the ambiguous set theory. Finally, this study focuses on the definition of the ambiguous set, its mathematical representation, and the associated concepts.