A Performance Analysis of Fuzzy, Vague, and Neutrosophic Relational Models in Processing Vague Queries

In the modern world, the data that arises from human thought and intellect are mostly uncertain, vague, or ambiguous. To deal with this uncertainty, Zadeh put forth the idea of fuzzy sets in 1965. In 1993, the conception of vague sets was conceived by Gau et al. as an abstraction of the fuzzy set. It segregates the positive and negative pieces of evidence for the presence of a set element and is designated by a truth as well as a false membership function. However, a fuzzy or vague set is not capable of handling inconsistent information that might appear in many physical applications of the real world. To overcome this drawback, the neutrosophic set theory was initiated by Smarandache in 1998. A neutrosophic set is based on the notion of three membership functions, namely, truthness, indeterminacy, and falsehood, and is a mathematical instrument that can deal with indeterminate, imprecise as well as inconsistent data. In the present work, a comparative analysis is presented on the usefulness and applicability of fuzzy, vague, and neutrosophic sets in processing vague queries. To determine the closeness between two uncertain data sets, different similarity measures have been put forth in the literature. In this analysis, an existing similarity measure put forth by Lu et al. for a vague set has been extended to the framework of neutrosophic sets. The execution of the proposed measure is validated with the well-known Hausdorff similarity measure. The study clearly shows that the neutrosophic data model can retrieve better decisions than the fuzzy or vague database model.