### Uncertain Query Processing using Vague Set or Fuzzy Set: Which One Is Better?

Jaydev Mishra, Sharmistha Ghosh
2014 International Journal of Computers Communications & Control
In this paper we attempt to make a theoretical comparison between fuzzy sets and vague sets in processing uncertain queries. We have designed an architecture to process uncertain i.e. fuzzy or vague queries. In the architecture we have presented an algorithm to find the membership value that generates the fuzzy or vague representation of the attributes with respect to the given uncertain query. Next, a similarity measure is used to get each tuples similarity value with the uncertain query for
more » ... th fuzzy and vague sets. Finally, a decision maker will supply a threshold or α-cut value based on which a corresponding SQL statement is generated for the given uncertain query. This SQL retrieves different result sets from the database for fuzzy or vague data. It has been shown with examples that vague sets give more accurate result in comparison with fuzzy sets for any uncertain query. In the real world, vaguely specified data values appear in many applications such as sensor information, expert systems, decision analysis, medical sciences, management and engineering problems and so on. Fuzzy set theory has been proposed to handle such vagueness by generalizing the notion of membership in a set. Essentially, in a fuzzy set each element is associated with a point-value selected from the unit interval [0, 1], which is termed as the grade of membership in the set. A vague set, which is conceived as a further generalization of fuzzy set, uses the idea of interval-based membership instead of point-based membership as in the case of fuzzy sets. The interval-based membership in vague sets is more expressive in capturing vagueness of data. Relational database systems have been extensively studied worldwide since Codd [1] had proposed the relational data model in 1970. Based on this model, several commercial relational database systems are available (see [2]-[4]). This data model usually takes care of precisely defined and unambiguous data. However, in the real world applications data are often partially known i.e., incomplete or imprecise. For example, instead of specifying that the height of David is 188 cm, one may say that the height of David is around 190 cm, or simply that David is tall. Other examples on uncertain data may be "Salaries of almost equally experienced employees are more or less the same" etc. All these are informative statements that may be useful in answering queries or making inferences. However, such type of data cannot be represented in the classical relational data model. In order to incorporate imprecise or uncertain data, the classical relational data model has been extended by several authors on the mathematical framework of fuzzy set theory which was initially introduced by Zadeh [5] in 1965. Based on this fuzzy set theory, various