Vague sets or intuitionistic fuzzy sets for handling vague data: Which one is better?

In the real world there are vaguely specified data values in many applications, such as sensor information. Fuzzy set theory has been proposed to handle such vagueness by generalizing the notion of membership in a set. Essentially, in a Fuzzy Set (FS) each element is associated with a point-value selected from the unit interval [0,1], which is termed the grade of membership in the set. A Vague Set (VS), as well as an Intuitionistic Fuzzy Set (IFS), is a further generalization of an FS. Instead of using point-based membership as in FSs, interval-based membership is used in a VS. The interval-based membership in VSs is more expressive in capturing vagueness of data. In the literature, the notions of IFSs and VSs are regarded as equivalent, in the sense that an IFS is isomorphic to a VS. Furthermore, due to such equivalence and IFSs being earlier known as a tradition, the interesting features for handling vague data that are unique to VSs are largely ignored. In this paper, we attempt to make a comparison between VSs and IFSs from various perspectives of algebraic properties, graphical representations and practical applications. We find that there are many interesting differences from a data modelling point of view. Incorporating the notion of VSs in relations, we describe Vague SQL (VSQL), which is an extension of SQL for the vague relational model, and show that VSQL combines the capabilities of a standard SQL with the power of manipulating vague relations. Although VSQL is a minimal extension to illustrate its usages, VSQL allows users to formulate a wide range of queries that occur in different modes of interaction between vague data and queries.