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Temporal databases offer a common framework to those database applications that need to store or handle different types of temporal data from a variety of sources. They allow the concept of time to be handled from the point of view of meaning, representation, and manipulation. Although at first sight the incorporation of time into a database might appear to be a direct and simple task, it is, however, quite complex: not only must new structures and specific operators be included, but the semantics of conventional DML sentences (insert, update, or delete) and queries must be appropriately changed. In addition, temporal information is not always as precise as desired since it might be affected by imprecision due to the use of natural language or to the nature of the information source. In this paper, we deal with the problem of the update (and, implicitly, insert and delete) and query operations when time is expressed by means of a fuzzy interval of dates.

Abstract. The client-server model is being used mostly in the actual DataBase Management Systems (DBMS). However, these DBMS do not allow either to make flexible queries to the database or to store vague information in it. We have developed a FSQL Server for a Fuzzy Relational Database (FRDB). The FSQL language (Fuzzy SQL) is an extension of the SQL language that allows us to write flexible conditions in our queries. This Server has been developed for Oracle, following the model GEFRED, a theoric model for FRDB that includes fuzzy attributes to store vague information in the tables. The FSQL Server allows us to make flexible queries about traditional (crisp) or fuzzy attributes and we can use linguistic labels defined on any attribute. KEYWORDS: Information Storage and Retrieval, Flexible and Fuzzy Queries, Fuzzy Relational Databases, Fuzzy SQL. IntroductionThe relational model was developed by E.F. Codd of IBM and published in 1970 in [6]. This model is the most used at present. In a theoric level, there exists many FRDB systems that, based on the relational model, they extend it in order to allow storing and/or treating vague and uncertain information. In [16], Tahani presented a system to carry out fuzzy queries in a classic relational database. More recently, this topic has been widely studied by P. Bosc et al. [1].Buckles and Perry presented in [2] their database model, in which they used similarity relations among a finite set of possible values for an attribute. This model was extended in [3] to store fuzzy numbers.In order to store possibility distributions (in Zadeh's sense [20]) Umano and Fukami published their model in [17,18], with a fuzzy relational algebra [19]. Later, other models appeared like the Prade-Testemale model [14,15] and the Zemankova-Kandel model [21].In [12,13], the GEFRED model was proposed for FRDB. The GEFRED model represents a synthesis among the different models which have appeared to deal with the problem of the representation and management of fuzzy information in relational databases. One of the main advantages of this model is that it consists of a general abstraction which allows us to deal with different approaches, even when these may seem disparate.

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The problem of the combination of imprecision and uncertainty combination from the approximate reasoning point of view is addressed. An imprecise and uncertain information can be represented as a fuzzy quantity together with a certainty value. In order to simplify the use of such information, it is necessary to combine the imprecision and uncertainty of the fuzzy number. In this paper we propose a method for combining them based on the use of information measures. The ®rst step consists in truncating the fuzzy number by the certainty value. Since non-normalized fuzzy numbers are dicult to use, we transform the truncated fuzzy number into a normalized fuzzy number which contains the same amount of information. To formalize this process, we develop a theoretical context for the information measures on fuzzy values. We study the fuzzy numbers transformation and its properties, and give an approximate reasoning interpretation to the approach. Ó 0888-613X/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 8 8 8 -6 1 3 X ( 9 9 ) 0 0 0 2 4 -9

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In real world, it is very common that some objects or concepts have properties with a time-variant or timerelated nature. Modelling this kind of objects or concepts in a (relational) database schema is possible, but time-variant and time-related attributes have an impact on the consistency of the entire database and must be appropriately managed. Therefore, temporal database models have been proposed to deal with this problem in the literature. Time can be affected by imprecision, vagueness and / or uncertainty, since existing time measuring devices are inherently imperfect. Additionally, human beings manage time using temporal indications and temporal notions, which may also be imprecise. However, the imperfection in human-used temporal indications is supported by human interpretation, whereas information systems need appropriate support in order to accomplish this task. Several proposals for dealing with such imperfections when modelling temporal data exist. Some of these proposals transform the temporal data into a compact representation but there is not a formal model for managing and handling uncertainty regarding temporal information. In this work we present a novel model to deal with imprecision in valid-time databases together with the definition and implementation of the data manipulation language, DML.

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