The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

A B S T R A C T Soil compaction influences all stages of crop growth, but in many low yield sugarcane fields critical levels and effects of soil compaction are ignored. Therefore, identifying localization and intensity of compaction are very relevant for descompactation of soil. In this context, this study aimed to apply three criteria for delineating zones for soil compaction management: soil layer where first appear values of soil penetration resistance considered critical for sugarcane growth; cone index for 0-40 cm layer, and depth of occurrence of maximum soil penetration resistance. Sampling was carried out in a grid with 113 points spaced at 100 m, georeferenced by means of a Global Positioning System receiver. Soil penetration resistance in eight layers of 5 cm depth, cone index and depth of occurrence of maximum penetration resistance were determined from data gathered by an automatic measuring penetrometer. Estimative of non-sampled values were obtained by means of kriging interpolation, which allowed drawing of contour maps and the definition of four regions in the field for site specific subsoiling . Palavras-chave: Saccharum ssp. resistencia do solo a penetracao geoestatistica penetrometro

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Revista Brasileira de Engenharia Agrícola e Ambiental

Today large corporations are constructing enterprise data warehouses from disparate data sources in order to run enterprise-wide data analysis applications, including decision support systems, multidimensional online analytical applications, data mining, and customer relationship management systems. A major problem that is only beginning to be recognized is that the data in data sources are often “dirty”. Broadly, dirty data include missing data, wrong data, and non-standard representations of the same data. The results of analyzing a database/data warehouse of dirty data can be damaging and at best be unreliable. In this paper, a comprehensive classification of dirty data is developed for use as a framework for understanding how dirty data arise, manifest themselves, and may be cleansed to ensure proper construction of data warehouses and accurate data analysis. The impact of dirty data on data mining is also explored.

A Taxonomy of Dirty Data

Information technology is one of the most rapidly changing disciplines, especially with the fuzzy extension Fuzzy databases have been studied in many works and papers but, in general, these works study some particular area and many works are theoretical works, with very few real applications The Handbook of Research on Fuzzy Information Processing in Databases provides comprehensive coverage and definitions of the most important issues, concepts, trends, and technologies in fuzzy topics applied to databases, discussing current investigation into uncertainty and imprecision management by means of fuzzy sets and fuzzy logic in the field of databases and data mining This compendium of research offers researchers, students, and organizations a complete, practical, guide to fuzzy information processing in databases

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Handbook of Research on Fuzzy Information Processing in Databases

Fuzziness in database management systems

Sample of Contents: State of the Art in Fuzzy Database Modeling FuzzyEER Mapping FuzzyEER Model Concepts to Relations FSQL: A Fuzzy SQL for Fuzzy Databases.

Fuzzy Databases: Modeling, Design, and Implementation

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.

A Server for Fuzzy SQL Queries

While various articles about fuzzy entity relationship (ER) and enhanced entity relationship (EER) models have recently been published, not all examine how the constraints expressed in the model may be relaxed. In this paper, our aim is to relax the constraints which can be expressed in a conceptual model using the modeling tool, so that these constraints can be made more flexible. We will also study new constraints that are not considered in classic EER models. We use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and fuzzy query systems for databases. In addition, we shall examine the representation of these constraints in an EER model and their practical repercussions. The following constraints are studied: the fuzzy participation constraint, the fuzzy cardinality constraint, the fuzzy completeness constraint to represent classes and subclasses, the fuzzy cardinality constraint on overlapping specializations, fuzzy disjoint and fuzzy overlapping constraints on specializations, fuzzy attribute-defined specializations, fuzzy constraints in union types or categories and fuzzy constraints in shared subclasses. We shall also demonstrate how fuzzy (min, max) notation can substitute the fuzzy cardinality constraint but not the fuzzy participation constraint. All these fuzzy constraints have a new meaning, they offer greater expressiveness in conceptual design, and are included in the so-called fuzzy EER model.

Relaxing constraints in enhanced entity-relationship models using fuzzy quantifiers

The FSQL language is an extension of the SQL language which permits us to handle fuzzy information in fuzzy or crisp databases. The first version of FSQL was implemented for Oracle Databases in PL/SQL. This first version defined basic fuzzy (or flexible) queries for fuzzy or traditional databases. In this work we present some new characteristics for FSQL. These new definitions include four new fuzzy comparators, five new fuzzy attributes, six new fuzzy constant types, new characteristics in the fulfillment thresholds, dynamic change of functions in logic operations, fuzzy set operators, the ALTER FSQL statement, and some useful functions to handle fuzzy attributes and fuzzy values. Besides, we outline here the definition of some DDL statements of FSQL and eighteen fuzzy comparators for fuzzy time in FSQL. The advantages of these new characteristics are obvious: basically they allow a greater expressiveness.

http://www.wseas.us/e-library/conferences/2005salzburg/papers/492-268.pdf

José Galindo

Papers

Fuzzy Databases: Modeling, Design, and Implementation

Handbook of Research on Fuzzy Information Processing in Databases

A Server for Fuzzy SQL Queries

Relaxing constraints in enhanced entity-relationship models using fuzzy quantifiers

New characteristics in FSQL, a fuzzy SQL for fuzzy databases