A conceptual design methodology for fuzzy relational databases.(Research Note)(data modeling)

ABSTRACT

Computer applications in the nontraditional area have put requirements on conceptual data modeling. Some conceptual data models, being the tools of design databases, have been proposed. However, information in real-world applications is often vague or ambiguous. Currently, less research has been done in modeling imprecision and uncertainty in conceptual data models and design of databases. In this paper, based on fuzzy set and possibility distribution theory, different levels of fuzziness will be introduced into the IFO data model, and the corresponding graphical representations are given. IFO data model is then extended to the fuzzy IFO data model, denoted I[F.sub.2]O. In particular, we provide the approach to mapping an I[F.sub.2]O model to a fuzzy relational database schema.

Keywords: conceptual data modeling; database design; fuzzy data; fuzzy relational databases

INTRODUCTION

A major goal for database research has been the incorporation of additional semantics into data models. Databases have gone through the development from hierarchical and network databases to relational databases. As computer technologies move into nontransaction processing, such as CAD/CAM, knowledge-based systems, multimedia, and Internet systems, many feel the limitations of relational databases in these data-intensive applications. So, some nontraditional data models for databases, such as conceptual data models, for example, ER/EER (Chen, 1976), UML (Siau & Cao, 2001), and IFO (Abiteboul & Hull, 1987), object-oriented data model, and logic data model, have been proposed. Conceptual data models can capture and represent rich and complex semantics at a high abstract level (Chan, Wei & Siau, 1993; Fong, Karlapalem, Li & Kwam, 1999; Halpin, 2002; Shoval & Frumermann, 1994; Siau, 1999). Various conceptual data models have been used for conceptual design of databases. For example, the relational databases were designed by first developing a high-level conceptual data model, the ER model, and then the developed conceptual model was mapped to an actual implementation (Teorey, Yang & Fry, 1986). As to the IFO model, it was extended into a formal object model, IF[O.sub.2], and then the IF[O.sub.2] model was mapped into object-oriented databases in Poncelet, Tesseire, Cicchetti, and Lakhal (1993).

However, information is often imperfect in real-world applications. Therefore, different kinds of imperfect information have been extensively introduced into databases (Yazici & George, 1998). There have been some attempts to classify various possible kinds of imperfect information, although there are no unified points of view and definitions. But inconsistency, imprecision, vagueness, uncertainty, and ambiguity are viewed as the basic kinds of imperfect information in database systems (Bosc & Prade, 1993). Instead of giving the definitions of the imperfect information, we explain their meanings. Inconsistency is a kind of semantic conflict, meaning the same aspect of the real world is irreconcilably represented more than once in a database or in several different databases. For example, the age of George is stored as 34 and 37, simultaneously. Information inconsistency usually comes from information integration. Intuitively, the imprecision and vagueness are relevant to the content of an attribute value, and it means that a choice must be made from a given range (interval or set) of values, but we do not know exactly which one to choose at present. In general, vague information is represented by linguistic values. For example, the age of Michael is a set {18, 19, 20, 21}, a piece of imprecise information, and the age of John is a linguistic old, a piece of vague information. The uncertainty is related to the degree of truth of its attribute value, and it means that we can apportion some, but not all, of our belief to a given value or a group of values. For example, the possibility that the age of Chris is 35 right now should be 98%. The random uncertainty, described using probability theory, is not considered in this paper. The ambiguity means that some elements of the model lack complete semantics leading to several possible interpretations. Generally, several different kinds of imperfection can coexist with respect to the same piece of information. For example, the age of Michael is a set {18, 19, 20, 21}, and their possibilities are 70%, 95%, 98%, and 85%, respectively. Imprecision, uncertainty, and vagueness are three major types of imperfect information and can be modeled with possibility theory (Zadeh, 1978). Many of the existing approaches dealing with imprecision and uncertainty are based on the theory of fuzzy sets.

Fuzzy information has been extensively investigated in the context of the relational model (Buckles & Petry, 1982; Ma, Zhang & Ma, 1999; Ma & Mili, 2002; Prade & Testemale, 1984). Current efforts have been concentrated on fuzzy object-oriented databases and some related notions, such as class, superclass/subclass, inheritance, and so forth, are extended (Bordogna, Pasi & Lucarella, 1999; Cross, Caluwe & Vangyseghem, 1997; Dubois, Prade & Rossazza, 1991; George, Srikanth, Petry & Buckles, 1996; Gyseghem & Caluwe, 1998; Ma, 2005; Ma, Zhang & Ma, 2004). However, less research has been done in modeling fuzzy information in the conceptual datas model. It is particularly true in developing design methodologies for implementing fuzzy databases (Ma, Zhang, Ma & Chen, 2001). In Chaudhry, Moyne, and Rundensteiner (1999), the fuzzy relational databases were designed by using the fuzzy ER model proposed in Zvieli and Chen (1986). In this paper, fuzzy information is represented via the relational data bases and the IFO model. Here, the IFO model was proposed in Abiteboul and Hull (1987) as a formally defined conceptual database model that comprises a rich set of high-level primitives for database design. The reason why the IFO model is employed instead of the ER model for the conceptual modeling of fuzzy information might be because the IFO model subsumes the ER model and other semantic and functional data models as claimed in Abiteboul and Hull (1987). In addition, the IFO model hereby provides a formal representation of the main data structuring features found in previous semantics data models (Abiteboul & Hull, 1995; Hanna, 1995). In this paper, we extend the IFO model to handle fuzzy information. The fuzzy IFO model is called the I[F.sub.2]O model. A mapping process from the I[F.sub.2]O model to the fuzzy relational model is developed. It should be noticed that the IFO model has been extended for the conceptual modeling of fuzzy information in Vila, Cubero, Medina, and Pons (1996) and Yazici, Buckles, and Petty (1999). This paper differs from the research effort in Vila et al. (1996) in that the conceptual design of fuzzy databases was not provided there. In Yazici et al. (1999), based on similarity relations (Buckles & Petry, 1982), the IFO model was extended to the ExIFO (Extended IFO) model to ...