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1 Computing, Multimedia and Intelligent Techniques

1 2007

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Fuzzy eqiu-join operator in type-1 and type-2 fuzzy relation databases

Saxena P. Ch., Tayal D. K.

Computing, Multimedia and Intelligent Techniques

2007

Vol. 3, nr 1

7-19

The classical databases were designed primarily for the efficient storage and convenient retrieval of large amount of precise data as they focus on describing precise information and take care of only well defined and unambiguous data. However in real world applications, the data are often partially known (incomplete) or imprecise. Also many times, the information, the user of the database is interested in may not be precise for e.g. a college senior may be interested in finding a university that has a "good graduate Engineering program and low living costs". The meaning of "good" and "low" is imprecise and is based on subjective judgments. Consequently the concept of fuzzy relational database was proposed as an extension to classical databases to handle this type of data. To capture the impreciseness in data in a better way, two particular types of fuzzy relational data models viz. type-1 and type-2 fuzzy relational databases have been described in the literature. These databases contain each tuple partially which is specified by a membership grade of each tuple. A type-1 fuzzy relational database may have the domain of an attribute as a fuzzy set while a type-2 fuzzy relational database may have the domain of an attribute as a set of fuzzy subsets. The objective of this paper is to define a fuzzy equi-join operator in both the type-1 and type-2 fuzzy relational databases with the help of fuzzy equality which is defined using the concept of fuzzy functions. The various cases which occur while joining the fuzzy attribute values like the joining attributes have crisp values, values as elements of a fuzzy set or a fuzzy set etc are discussed. A methodology has been proposed to derive the membership value of the new (joined tuple). The usefulness of fuzzy join operator defined is shown in computing the join of the decomposed fuzzy relation schemas.