Evaluating aggregate functions on possibilistic data

The need for extending information management systems to handle the imprecision of information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature has dealt with queries involving a functional evaluation of a set of items, traditionally referred to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applications, and are thus being supported by traditional languages like SQL or QUEL. This paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. These extensions are based on fuzzy set-theoretical concepts such as the extension principle, the sigma-count operation, and the possibilistic expected value. The consistency and completeness of the proposed operations is shown

Representing fuzzy decision tables in a fuzzy relational database environment.

In this paper the representation of decision tables in a relational database environment is discussed. First, crisp decision tables are defined. Afterwards a technique to represent decision tables in a relational system is presented. Next, fuzzy extensions are made to crisp decision tables in order to deal with imprecision and uncertainty. As a result, with crisp decision tables as special cases fuzzy decision tables are defined which include fuzziness in the conditions as well as in the actions. Analogous to the crisp case, it is demonstrated how fuzzy decision tables can be stored in a fuzzy relational database environment. Furthermore, consultation of these tables is discussed using fuzzy queries.Decision making;

On nearness measures in fuzzy relational data models

AbstractIt has been widely recognized that the imprecision and incompleteness inherent in real-world data suggest a fuzzy extension for information management systems. Various attempts to enhance these systems by fuzzy extensions can be found in the literature. Varying approaches concerning the fuzzification of the concept of a relation are possible, two of which are referred to in this article as the generalized fuzzy approach and the fuzzy-set relation approach. In these enhanced models, items can no longer be retrieved by merely using equality-check operations between constants; instead, operations based on some kind of nearness measures have to be developed. In fact, these models require such a nearness measure to be established for each domain for the evaluation of queries made upon them. An investigation of proposed nearness measures, often fuzzy equivalences, is conducted. The unnaturalness and impracticality of these measures leads to the development of a new measure: the resemblance relation, which is defined to be a fuzzified version of a tolerance relation. Various aspects of this relation are analyzed and discussed. It is also shown how the resemblance relation can be used to reduce redundancy in fuzzy relational database systems

Querying Capability Enhancement in Database Using Fuzzy Logic

We already know that Structured Query Language (SQL) is a very powerful tool. It handles data, which is crisp and precise in nature.but it is unable to satisfy the needs for data which is uncertain, imprecise, inapplicable and vague in nature. The goal of this work is to use Fuzzy techniques i.e linguistic expressions and degrees of truth whose result are presented in this paper. For this purpose we have developed the fuzzy generalized logical condition for the WHERE part of SQL. In this way, fuzzy queries are accessing relational databases in the same way as with SQL. These queries with linguistic hedges are converted into Crisp Query, by deploying an application layer over the Structured Query Languag

Aspects of dealing with imperfect data in temporal databases

In reality, some objects or concepts have properties with a time-variant or time-related nature. Modelling these kinds 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. Therefore, temporal database models have been proposed to deal with this. Time itself can be at the source of imprecision, vagueness and uncertainty, since existing time measuring devices are inherently imperfect. Accordingly, human beings manage time using temporal indications and temporal notions, which may contain imprecision, vagueness and uncertainty. However, the imperfection in human-used temporal indications is supported by human interpretation, whereas information systems need extraordinary support for this. Several proposals for dealing with such imperfections when modelling temporal aspects exist. Some of these proposals consider the basis of the system to be the conversion of the specificity of temporal notions between used temporal expressions. Other proposals consider the temporal indications in the used temporal expressions to be the source of imperfection. In this chapter, an overview is given, concerning the basic concepts and issues related to the modelling of time as such or in (relational) database models and the imperfections that may arise during or as a result of this modelling. Next to this, a novel and currently researched technique for handling some of these imperfections is presented

A Relational Model for the Possibilistic Valid-time Approach

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.Junta de Andalucia P07-TIC-03175 BES-2009-013805 TIN2008-0206

Treatment of imprecision in data repositories with the aid of KNOLAP

Traditional data repositories introduced for the needs of business processing, typically focus on the storage and querying of crisp domains of data. As a result, current commercial data repositories have no facilities for either storing or querying imprecise/ approximate data. No significant attempt has been made for a generic and applicationindependent representation of value imprecision mainly as a property of axes of analysis and also as part of dynamic environment, where potential users may wish to define their “own” axes of analysis for querying either precise or imprecise facts. In such cases, measured values and facts are characterised by descriptive values drawn from a number of dimensions, whereas values of a dimension are organised as hierarchical levels. A solution named H-IFS is presented that allows the representation of flexible hierarchies as part of the dimension structures. An extended multidimensional model named IF-Cube is put forward, which allows the representation of imprecision in facts and dimensions and answering of queries based on imprecise hierarchical preferences. Based on the H-IFS and IF-Cube concepts, a post relational OLAP environment is delivered, the implementation of which is DBMS independent and its performance solely dependent on the underlying DBMS engine