In this model, the membership degree of tuples in a fuzzy relation is represented by fuzzy numbers on [0, 1], and fuzzy relational algebraic operations are defined by using the extension principle for computing minimum and maximum values of such fuzzy numbers. | Research and Development on Information and Communication Technology A Type-2 Fuzzy Relational Database Model Nguyen Hoa Saigon University, Ho Chi Minh City, Vietnam E-mail: nguyenhoa@ Communication: received 11 January 2017, revised 17 July 2017, accepted 31 July 2017 whereby the membership degree of tuples for the relation also is that for the fuzzy set. Abstract: This paper introduces a type-2 fuzzy relational database model (T-2FRDB) as an extension of type-1 fuzzy relational database models with a full set of basic fuzzy relational algebraic operations that can represent and query uncertain and imprecise information in real world applications. In this model, the membership degree of tuples in a fuzzy relation is represented by fuzzy numbers on [0, 1], and fuzzy relational algebraic operations are defined by using the extension principle for computing minimum and maximum values of such fuzzy numbers. Some properties of the type2 fuzzy relational algebraic operations in T-2FRDB are also formulated and proven as extensions of their counterpart in the type-1 fuzzy relational database models. Fuzzy relational database models that are built based on one of above approaches are extensions of the classical relational database model with fuzzy sets. They have different capabilities for expressing and dealing with uncertain and imprecise information. There are two types of the models based on the second approach, including the type-1 fuzzy relational database model (T-1FRDB), or the (ordinary) fuzzy relational database model, whereby the membership degree of tuples is assigned to a number in [0, 1], and the type-2 fuzzy relational database model (T-2FRDB), whereby the membership degree of tuples is expressed as a fuzzy number on [0, 1]. Many type-1 fuzzy relational database models have been proposed such as [3, 8–10, 17, 18]. However, since the membership degree of tuples is expressed as a number in [0, 1], these models were restricted in representing the
