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Fuzzy Database Query Languages and Their Relational Completeness Theorem
Abstract
Two fuzzy database query languages are proposed. They are used to query fuzzy databases that are enhanced from relational databases in such a way that fuzzy sets are allowed in both attribute values and truth values. A fuzzy calculus query language is constructed based on the relational calculus, and a fuzzy algebra query language is also constructed based on the relational algebra. In addition, a fuzzy relational completeness theorem such that the languages have equivalent expressive power is proved
... The main purpose of this model is to define imprecise answers based on precise data and on fuzzy conditions (which contain fuzzy predicates and fuzzy quantifiers). The Fuzzy Data model developed by Takahashi [14] assumes that some nonkey attributes may have values defined by fuzzy predicates (like "very reliable" in our case). All key attributes and some other attributes are assumed to have nonfuzzy values only. ...
... This approach treats a tuple as a set of attribute values, all having the same truth value. The case of different truth values associated with values of different attributes in the same tuple is not covered by the model of [14]. A similar idea of associating a single truth value (a weight) with each tuple is described by Petri in [13]. ...
... Since we have extended a regular relational database to a fuzzy relational database by adding fuzzy attributes expressing reliability degrees of nonfuzzy attributes, any operation of a fuzzy relational algebra (see [7][8], [14], [18]) can be applied to the extended database. In the application example, represented in the next section, we use two fuzzy relational operators, which seem to be particularly useful for filtering and analyzing partially reliable data: selection and aggregation. ...
A novel, fuzzy approach to deal with reliability of attribute values in a relational database is presented. The degree of reliability is defined as a fuzzy measure of certainty that the data is correct from user’s point of view. The relation scheme is partitioned into a subset of input (completely reliable) and a subset of target (partially reliable) attributes. An information theoretic connectionist network is constructed to evaluate the information content of links between input and target attributes. The network connection weights are used to calculate the reliability degrees of target attribute values. The method is applied to a real-world database, which includes partially reliable information. This work aims at improving reliability of data in a relational database by developing a framework for evaluating and representing reliability of attribute values in database tuples.
... That is, for any expression E A of our relational algebra there is an expression E D of our domain calculus such that for any state of any database d, the ranked tables E A (d) and E D (d), to which E A and E D evaluate, coincide and vice versa (and the same for the other cases). Remark 5. Previous approaches either consider only similarities (Buckles, Petry & Sachar, 1989) or only ranks (Takahashi, 1993) but not both. Most importantly, our approach provides more expressive power (including, e.g., top k ) and a firm connection to predicate fuzzy logic due to which both the relational algebra and calculi are open for further extensions (e.g., by other non-standard quantifiers, aggregation operators, etc.). ...
... Relational algebra for relational model with similarities on domains is a particular topic in this respect to which attention has been paid in the past. Papers on this topic include (Belohlavek & Vychodil, 2006c; Buckles, Petri, Sachar, 1989; Penzo, 2005; Prade & Testemale, 1984; Takahashi, 1993 ). However, the available results still need to be considered as preliminary attempts rather than a definite solution. ...
This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational model that consist of adding similarity relations to domains and consider functional dependencies in these extensions. We present a particular extension and functional dependencies in this extension that follow the principles of fuzzy logic in a narrow sense. We present selected features and results regarding this extension. Then, we use this extension as a reference model and compare it to several other extensions proposed in the literature. We argue that following the principles of fuzzy logic in a narrow sense, the same way we can follow the principles of classical logic in the case of the ordinary Codd relational model, helps achieve transparency, versatility, conceptual clarity, and theoretical and computational tractability of the extension. We outline several topics for future research.
... Thus, it is clear that information in image database is inherently both complex and uncertain, and managing uncertainty becomes a fundamental topic. The relational model has been extended in many ways, depending on " where " fuzziness is introduced and " what " one means with uncertainty [12, 13,171819. Specifically, the relational model of data has been extended to incorporate uncertainty either at the tuple level or at the attribute level. In the tuple-level approach, each tuple may have one or more uncertainty attributes; uncertainty attributes are usually real numbers, or intervals on real numbers. ...
... In this realm, most of the papers in the literature use the membership degree of a fuzzy domain as an attribute expressed by single numerical values or by an interval contained in [0, 1]. These values are calculated by using a possibility measure in query processing [11, 17]. In Chen et al. [2] fuzziness in attribute values and mutual relationships between domain elements are taken into account, and they are dealt with by using possibility distributions and closeness relations respectively. ...
In this paper we present a fuzzy approach for image databases. We exploit the concept of NF
2 relational model as a foundation for building image catalogues containing the semantic description of a given image database. New algebraic operators are defined in order to capture the fuzziness related to the semantic descriptors of an image. We compare our model to the First Normal Form annotated relation model, and show that in a number of interesting cases they can be considered equivalent, from the operational point of view, but in general NF
2 relational model is more powerful, and provides a more suitable framework for dealing with uncertainties in image databases.
... The Fuzzy Data model developed by Takahashi [29] assumes that some nonkey attributes may have values defined by fuzzy predicates (e.g., "very reliable"). All key attributes and some other attributes are assumed to have nonfuzzy values only. ...
... This approach treats a tuple as a set of attribute values, all having the same truth-value. The case of different truth-values associated with values of different attributes in the same tuple is not covered by the model of [29]. A similar idea of associating a single truth value (a weight) with each tuple is described by Petri [25]. ...
Most real-world databases contain some amount of inaccurate data. Reliability of critical attributes can be evaluated from the values of other attributes in the same data table. This paper presents a new fuzzy-based measure of data reliability in continuous attributes. We partition the relational schema of a database into a subset of input (predicting) and a subset of target (dependent) attributes. A data mining model, called information-theoretic connectionist network, is constructed for predicting the values of a continuous target attribute. The network calculates the degree of reliability of the actual target values in each record by using their distance from the predicted values. The approach is demonstrated on the voting data from the 2000 Presidential Elections in the US.
... The Fuzzy Relational Databases (FRDB) has been widely studied in a theoretic level [1,2,7,14,15]. However, few works have studied it from a practical point of view. ...
... This extension introduces fuzzy predicates under shapes of linguistic expressions that, at the time of a flexible querying, permits to have a range of answers (each with a member ship degree) in order to offer to the user all intermediate variations between the completely satisfactory answers and those completely dissatisfactory [1]. We can also say that a FRDB is defined as an enhanced relational database that allows fuzzy attribute values and fuzzy truth values; both of these are expressed as fuzzy sets [15]. The basic model of fuzzy relational databases is considered the simplest one, and it consists of adding a grade, normally in the [0,1] interval, to each instance (or tuple). ...
The Fuzzy Relational Databases (FRDB) has been extensively studied in a theoretical level. Unfortunately, the repercussions of these works on the practical level are negligible. Medina et al. have developed a server named FSQL, supporting flexible queries on FRDB. The FSQL Server is based on a fuzzy relational model named GEFRED. This server has been programmed in PL/SQL language under Oracle. Flexible queries in FSQL are expressed with an extension of the standard SQL, named FSQL (Fuzzy SQL). The FSQL server uses a Fuzzy Meta-knowledge Base (FMB) to model the different types of fuzzy attributes. Since Oracle doesn't recognize FSQL, consequently we must transform an FSQL script in a SQL script equivalent, which includes the necessary updates of the FMB. This hard task is supposed already made in the implementation of FSQL server by Medina et al. We propose in this paper an extension of FSQL server in order to remedy this serious limit especially in the case of voluminous DB. Our extension consists in transforming a FSQL script automatically in an SQL equivalent, including the necessary updates of the FMB. This extension has two enhancements to FSQL, while preserving all its possibilities: (1) a better extensibility notably in case of addition of new fuzzy types and (2) the possibility of definition and the manipulation of FRDB directly with the FSQL language. The enhanced server is operational under Oracle.
... Thus, it is clear that information in image database is inherently both complex and uncertain, and managing uncertainty becomes a fundamental topic. The relational model has been extended in many ways, depending on " where " fuzziness is introduced and " what " one means with uncertainty [12, 13,171819. Specifically, the relational model of data has been extended to incorporate uncertainty either at the tuple level or at the attribute level. In the tuple-level approach, each tuple may have one or more uncertainty attributes; uncertainty attributes are usually real numbers, or intervals on real numbers. ...
... In this realm, most of the papers in the literature use the membership degree of a fuzzy domain as an attribute expressed by single numerical values or by an interval contained in [0, 1]. These values are calculated by using a possibility measure in query processing [11, 17]. In Chen et al. [2] fuzziness in attribute values and mutual relationships between domain elements are taken into account, and they are dealt with by using possibility distributions and closeness relations respectively. ...
In this paper we present a fuzzy approach for image databases. We exploit the concept of NF 2 relational model as a foundation for building image catalogues containing the semantic description of a given image database. New algebraic operators are defined in order to capture the fuzziness related to the semantic descriptors of an image. We compare our model to the First Normal Form annotated relation model, and show that in a number of interesting cases they can be considered equivalent, from the operational point of view, but in general NF 2 relational model is more powerful, and provides a more suitable framework for dealing with uncertainties in image databases.
... The Fuzzy Data model developed by Takahashi [18] assumes that some nonkey attributes may have values deÿned by fuzzy predicates (like "very reliable" in our case). All key attributes and some other attributes are assumed to have nonfuzzy values only. ...
... This approach treats a tuple as a set of attribute values, all having the same truth value. The case of di erent truth values associated with values of di erent attributes in the same tuple is not covered by the model of [18]. ...
A novel, information-theoretic fuzzy approach to discovering unreliable data in a relational database is presented. A multilevel information-theoretic connectionist network is constructed to evaluate activation functions of partially reliable database values. The degree of value reliability is defined as a fuzzy measure of difference between the maximum attribute activation and the actual value activation. Unreliable values can be removed from the database or corrected to the values predicted by the network. The method is applied to a real-world relational database which is extended to a fuzzy relational database by adding fuzzy attributes representing reliability degrees of crisp attributes. The highest connection weights in the network are translated into meaningful if, then rules. This work aims at improving reliability of data in a relational database by developing a framework for discovering, accessing and correcting lowly reliable data.
... To extend the ability of dealing with vague and imprecise data, researchers expedite the development of fuzzy databases. In [25, 28, 33], researchers have pointed out that a fuzzy database can be defined as an enhanced relational database that stores fuzzy attribute values and fuzzy truth values [22] as shown inTable 1. We briefly explain these terms as follows. ...
... By further proposing more general and efficient structures for the dictionary, CD/MF, and CD/SRF for more flexible adaptation of our approach, we will implement a prototype system to valid our methodology. 2. Capture the semantics of natural language queries with fuzzy hedges: by combining present proposed fuzzy database frameworks, for example, Zadeh [31,32], Takahashi [22] and Bosc et al. [5], our work can be extended to process a natural language query involving a modifier like 'almost', 'very', or 'nearly'. This combination is served as a step toward analyzing the use of modifiers, which are fuzzy in natural, to communicate with fuzzy databases. ...
Database applications tend toward getting more versatile and broader to comply with the expansion of various organizations. However, naïve users usually suffer from accessing data arbitrarily by using formal query languages. Therefore, we believe that accessing databases using natural language constructs will become a popular interface in the future. The concept of object-oriented modeling makes the real world to be well represented or expressed in some kinds of logical form. Since the class diagram in UML is used to model the static relationships of databases, in this paper, we intend to study how to extend the UML class diagram representations to capture natural language queries with fuzzy semantics. By referring to the conceptual schema throughout the class diagram representation, we propose a methodology to map natural language constructs into the corresponding class diagram and employ Structured Object Model (SOM) methodology to transform the natural language queries into SQL statements for query executions. Moreover, our approach can handle queries containing vague terms specified in fuzzy modifiers, like ‘good’ or ‘bad’. By our approach, users obtain not only the query answers but also the corresponding degree of vagueness, which can be regarded as the same way we are thinking.
... In any case, the most basic issue in the use of any database structure lies in its ability to deal with information and questions precisely. A large portion of the creators have added to supply a hypothetical commitment to SQL for database models which based on Fuzzy logic [9][10][11][12]. In the new era, most of the researcher and scientist have been utilized the fuzzy based system in SQL query processing [11,12]. ...
As we know that in this new era, the availability of modern data sets is massive. It is very difficult to find the variation and appropriate class for a data set. So, this paper introduces a comparison between fuzzy and vague sets for handling Structured Query Language (SQL) processing problems. This paper proposed a new method to convert crisp set into vague set with help of Positive Ordered Transformation formula (POTF). Further, vague sets are converted into fuzzy sets with help of Transforming Vague Set into Fuzzy Set method proposed by Liu et al. (Trans Comput Sci II LNCS 5152:133–144, 2008). Further the similarity measures have been used to obtain similar tuple for classical fuzzy, vague and converted fuzzy sets based on SQL query processing. This proposed system diverse a resultant as a set based on supply limit/α-cut for fuzzy/vagueness/unclear information. After testing through many cases, this paper discussed a very good finding about proposed method for SQL query processing problems.
... So, dealing with marketing imprecise and uncertain information, fuzzy database is the appropriate choice for decision makers or marketing managers. According to [13] fuzzy relational database (FRDB) is an extension of relational database which allows fuzzy attributes values and fuzzy truth values, both of these are expressed as fuzzy sets. Generally, a fuzzy database can be defined as "A database that is able to serve imprecise information (Vague or uncertain) using fuzzy logic". ...
Marketing organizations use databases to locate potential customers and to generate sales lead. A number of software systems have been playing a key role in supporting the decision making activities in recent years but common problem in all that they cannot handle fuzzy data appropriately for "what-if" analysis. This paper proposes intelligent scenarios analysis system framework for marketing decision support which deals with crisp and fuzzy data like linguistic variable. Applying new approach "Hypothetical Database" for derived data that permits decision manager to manage views according to the need of organization and/or market environment. View in Hypothetical Database provides versatility in "What-If" analysis by using versions of "What-If" database and reduce data redundancy and data storage in updating. Using Fuzzy database will help to handle imprecise and uncertain information like "Linguistic variable" in a more human oriented process. Finally, the projected scenarios selected by decision manager will be aligned in a hierarchy according to the distance from "Ideal Vector" by using Fuzzy Multi-Criteria Decision Making method.
... First attempts to rank-based approaches can be found in [4,60,81,98,111]. Later works include [23,104,52,72,74,82,93,96]. There are also extensions in which the rank is assigned to every attribute value, e.g. in [70,38]. ...
Similarity search and related issues are current topic in databases. Over the last ten years more then 6500 papers dealing with similarity in databases were published according to Web of Science. The rising in the number of articles in the recent years shows that the research in this direction is still in its early stage. From the wide range of topics related with similarities in databases, one received a considerable attention already, namely functional dependencies which take similarities into account. Our main concern in this paper is to review and critically examine the existing work on this topic.
... The first fuzzy query language was presented by Takahashi in 1991 [17]. Two years later he published the full theory of two languages: calculus query language and fuzzy algebra query language [18]. In the eighties the problem of fuzzy database were investigated by: Zamenkowa [23], Chang Ke [7], Buckles and Petry [4], [5]. ...
Main assumptions of this work were two facts. First, that real data not representing random distribution (white noise), but have natural trend to granularity. The second one, that in everyday contacts we do not using strict defined conditions. The second feature lead us to use fuzzy logic which closer representing natural communication. First gives us opportunity to automatically construct functions defining membership to discrete
groups based only on data distribution.
The problem of extending database systems with natural language
expressions is a matter of many research centers. The basic idea of presented research is to extend an existing query language and make database systems able to satisfy user needs more closely. This paper deals mostly with gaining imprecise information from relational database systems. Presented concept is based on fuzzy sets and automatic clustering techniques that allow to build membership function and fuzzy queries. Thanks to applied solutions, the relational database system is more flexible, and similar to natural way of communication.
... Since for a human being the main communication is natural language, this causes it difficult to handle fuzzy, unambiguity and vagueness information etc. To handle such vague information several authors have been developed the theoretical foundation for the fuzzy query language of fuzzy database [3], [4], [5], [6], [7]. While developing the theory on fuzzy query testing several authors have defined different membership functions based on different fuzzy attributes for testing fuzzy equality of numbers [4], [7], [8], [9]. ...
In real world applications we often need to test the queries based on fuzzy data. For example, some one can specify as "find students' whose age is around 17 years old."; "find tall person". "find employee with high salary"; "find country with low population" etc. This fuzziness in measurement is captured in this paper. To test such fuzzy queries, we have developed an algorithm that is applicable universally to any type of database. In this paper first we have designed architecture to test fuzzy query. In the architecture we have defined an algorithm to find the membership value for each tuple of the relation based on the fuzzy attributes on which fuzzy query is made. Next Decision Maker (DM) will supply a threshold value or -cut based on which corresponding SQL of the given fuzzy query will be generated. This SQL will retrieve the resultant tuples from the database. Finally we have tested our algorithm with a real life example.
... Data space is to realize effective personal information management by integrating resources from various types of data sources that may be uncertain. Research also concerns fuzzy database query language [28], uncertain ontology modeling [30], probabilistic queries on probabilistic database and evaluation [9], [10], [25]. A system integrating research on data management, accuracy, and lineage is introduced in [32]. ...
Classification is the most basic method for organizing resources in the physical space, cyber space, socio space, and mental space. To create a unified model that can effectively manage resources in different spaces is a challenge. The Resource Space Model RSM is to manage versatile resources with a multidimensional classification space. It supports generalization and specialization on multidimensional classifications. This paper introduces the basic concepts of RSM, and proposes the Probabilistic Resource Space Model, P-RSM, to deal with uncertainty in managing various resources in different spaces of the cyber-physical society. P-RSM's normal forms, operations, and integrity constraints are developed to support effective management of the resource space. Characteristics of the P-RSM are analyzed through experiments. This model also enables various services to be described, discovered, and composed from multiple dimensions and abstraction levels with normal form and integrity guarantees. Some extensions and applications of the P-RSM are introduced.
... The research on querying in similarity relation based fuzzy databases has been summarized in Buckles and Petry (1985), Buckles et al. (1989), and Petry (1996) There are also a number of hybrid models proposed in the literature. Takahashi (1993) has proposed a model for a fuzzy relational database assuming possibility distributions as attribute values. Additionally, fuzzy sets are used as tuple truth-values. ...
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.
... The research in this direction includes extensions to SQL to facilitate vague queries on relational databases (Bosc et al., 1988;, functional dependencies in fuzzy relational data models (Raju and Majumdar, 1988), fuzzy extensions to relational calculus and relational algebra (Lee et al., 1993;Kim, 1993a, 1993b;Takahashi, 1993), and a logic based approach to the fuzzy relational databases to deal with various forms of fuzziness and a domain calculus based fuzzy query language (Villa et al.,1994). Gogolla and Hohenstein, (1991), while commenting on the appropriateness and the expressiveness of Chen's Entity-Relationship model (Chen, 1976), state "... it (ER model) captures most of the important phenomenon of the real world and expresses them in a natural and easily understandable way." ...
Most query languages are designed to retrieve information from databases containing precise and certain data using precisely specified commands. Application of fuzzy set theory to relational data models has been studied extensively in recent years. This paper presents a calculus for fuzzy queries on a fuzzy entity-relationship model. The paper, first, defines a fuzzy entity-relationship model capable of representing imprecision and uncertainty in entities, attributes, and relationships. Then, it describes a calculus for fuzzy queries along with operational semantics. Some of the key aspects of this calculus are the provision of multiple terms, aggregate functions, and various forms of quantification.
... This involves three challenges: 1) how to implement and process such Fuzzy-CQs, 2) how this affects the modules in the F-DSMS, such as the query optimizer, scheduler, load shedder and dissemination modules, and 3) a fuzzy-CQ language is needed. In traditional databases, two fuzzy database query languages were proposed based on fuzzy calculus and fuzzy algebra [14], as an extension to the relational calculus and algebra respectively. The fuzzy calculus and fuzzy algebra were proved to be relationally complete. ...
... s [14] which investigates how to implement a Fuzzy-SQL language on top of the commercial database system ORACLE. Most of the work in the area of fuzzy databases, however, do not support user weights. Furthermore, they rely on the two imprecise values necessity and possibility which do not conform to our intended scenario of multimedia applications. [22] sketches the design of a fuzzy calculus, fuzzy algebra and a mapping between them. However, this work suffers from an incomplete formalization. Most extensions of the relational model by imprecision were performed on the relational algebra, see e.g. [1, 6]. A very good work is [6] which introduced the same w similarity algebra. Our prop ...
Abstract Traditional database,query languages,are based on set theory and,crisp logic. Many applications, however, need similarity or retrieval-like queries producing results with truth values from the interval [0,1]. Such truth values can be regarded as continuous,membership,values of tuples expressing,how,strongly a query is matched.,Formulating,queries by applying,existing similarity relational algebras means,to express the user’s need,in a procedural,manner.,In order to support a declarative way of formulating queries, we generalize the classical relational domain,calculus by incorporating,fuzzy operations,and,user weights.,Besides defining syntax and semantics,we show,how to map,any calculus expression onto a corresponding similarity algebra expression. In this way, we present a theoretical foundation,for a declarative query language,combining,retrieval functionality and traditional relational databases.
... Based on various fuzzy relational database models, many studies have been done for data integrity constraints [6, 7, 26, 27]. Also there have been research studies on fuzzy query languages [5, 28] and fuzzy relational algebra [30, 21]. In [5], an existing query language, namely SQL, for fuzzy queries was extended and some fuzzy aggregation operators were developed. ...
A major goal for database research has been the incorporation of additional semantics into database models. It is recognized
that the relational database model has semantic and structured drawbacks when it comes to modeling some emerging applications
such as computer aided design (CAD), geographical information systems (GIS), and artificial intelligence. In response to this
problem, some attempts to relax the first normal form (1NF) limitation, which is the most fundamental normalization constraint
in the relational databases, are made and one kind of data model, called non-first normal (or nested) relational database
model, has been introduced. In common sense, the nested relational database model means that attribute values in the relational
instances are either atomic or set-valued and even relations themselves. In addition, the next generation of database models
takes the form of rich data models such as the object-oriented database model and the semantic (conceptual) data models.
... In this context, still the most important seem to be the relational databases due to their widespread use. The research on flexible querying of the relational databases started with the " fuzzification " of the classical retrieval means, i.e., the relational algebra and calculus (cf., e.g., Takahashi 1993). These are very promising research areas with a sound theoretical background within the relational data model: the classic set theory and logics. ...
Flexible querying of the relational databases is considered. The applicability of some non-standard, mainly linguistic quantifier
driven aggregation, and via Yager’s ordered weighted averaging (OWA) operators in particular, is shown. Their handling is
studied with a special emphasis on the selection and tuning of the OWA operator that is appropriate for the user needs. We
start with an OWA operator and intend to tune it to increase its ORness, but keeping the changes as limited as possible, or
to preserve consistency of the changes. These tasks are defined as optimization problems. The discussion is illustrated on
the example of the authors’ FQUERY for Access system.
... Namely, the idea of adding similarity to domains in the relational model appeared in several papers, but as a rule in an ad hoc manner, without proper logical foundations and comprehensive treatment, see e.g. [5,6,13,14,15] for selected papers. ...
Extensions of relational databases which aim at utilizing various aspects of similarity and imprecision in data processing
are widespread in the literature. A need for development of solid foundations for such extensions, sometimes called similarity-based
relational databases, has repeatedly been emphasized by leading database experts. This paper argues that, contrary to what
may be perceived from the literature, solid foundations for similarity-based databases can be developed in a conceptually
simple way. In this paper, we outline such foundations and develop in detail a part of the the facet related to similarity-based
queries and relational algebra. The foundations are close in principle to Codd’s foundations for relational databases, yet
they account for the main aspects of similarity-based data manipulation. A major implication of the paper is that similarity-based
data manipulation can be made an integral part of an extended, similarity-based, relational model of data, rather than glued
atop the classic relational model in an ad hoc manner.
... consider only similarities [9] or only ranks [29] but not both. Most importantly, our approach provides more expressive power (inclusing e.g. ...
We present an extension of Codd's relational model of data. Our extension is motivated by similarity-based querying. It consists in equipping each domain of attribute values with a similarity relation and in modifying the classical relational model in order to account for issues generated by adding similarities. As a counterpart to data tables over a set of domains of Codd's model, we introduce ranked data tables over domains with similarities. We present a relational algebra, and tuple and domain calculi for our model and prove their equivalence. An interesting point is that our relational algebra contains operations like top<sub>k</sub> (k best results matching a query). Then, we study functional dependencies extended by similarities, argue that they form a new type of data dependency not captured by the classical model, prove a completeness result w.r.t. Armstrong-like rules, describe non-redundant bases and provide an algorithm for computing the bases. In addition to that, we compare our model with other approaches and outline future research
Uncertainty extensively exists in data and knowledge intensive applications, in which fuzzy information processing plays a crucial role. Fuzzy sets have been extensively used to enhance various database models for managing fuzzy data or flexibly querying crisp data. This has resulted in numerous contributions in this research area. This paper pays attention to three crucial issues in fuzzy techniques for data management: modeling fuzzy data, querying fuzzy data, and fuzzy queries over crisp data, and provides a full up-to-date survey on the current state of the art in fuzzy data modeling and querying. The paper identifies fuzzy conceptual data models, fuzzy (relational and object-oriented) database models and fuzzy XML model as well as the relationships among these fuzzy data models. For each type of fuzzy data models, the paper summarizes its query processing. The paper also reviews fuzzy querying over classical data models. In addition to providing a generic overview of the approaches for fuzzy data modeling and querying, this survey paper serves for identifying possible research opportunities in the area of fuzzy data processing.
Imperfect information extensively exists in data and knowledge intensive applications, where fuzzy data play an import role in nature. Fuzzy set theory has been extensively applied to extend various database models and resulted in numerous contributions. The chapter concentrates on two main issues in fuzzy data management: fuzzy data models and fuzzy data querying based on the fuzzy data models. A full up-to-date overview of the current state of the art in fuzzy data modeling and querying is provided in the chapter. In addition, the relationships among various fuzzy data models are discussed in the chapter. The chapter serves as identifying possible research opportunities in the area of fuzzy data management in addition to providing a generic overview of the approaches to modeling and querying fuzzy data.
The authors present an object algebra for manipulating complex objects in fuzzy object-oriented database systems. Unlike in most of the existing query languages, the design of this object algebra is based on the type and set aspects of the class. A framework is presented for executing set-theoretic operations, namely union, intersection, and difference, on the class construct. The set operations on the membership of the corresponding class containing fuzzy objects are developed by using the truth-value of the object and object identity. The type description of the resulting class derived by a set operation is specified. The authors also discuss the inheritance property characteristic for the derived class with fuzzy objects.
A major goal for database research has been the corporation of additional semantics into the database model. Classical database models often suffer from their incapability of representing and manipulating imprecise and uncertain information that may occur in many real world applications. Since the early 1980's, Zadeh's fuzzy logic has been used to extend various database models. The purpose of introducing fuzzy logic in databases is to enhance the classical database models such that uncertain and imprecise information can be represented and manipulated. This resulted in numerous contributions, mainly with respect to the popular relational model or to some related form of it.
Nowadays database management systems are one of the most critical resources in every company. Despite advanced possibilities of SQL, relational database management systems do not support flexible query conditions. The problem of extending database systems with natural language expressions is a matter of many research centers. The basic idea of presented research is to extend an existing query language and make database systems able to satisfy user needs more closely. This paper mostly deals with gaining imprecise information from relational database systems. Presented concept is based on fuzzy sets and automatic clustering techniques that allow built membership function and fuzzy queries processing. Implementation of fuzzy logic on database systems extends traditional SQL language with new mechanisms and new features, so the existing relational database systems will be more flexible, queries more intelligent and similar to ordinary communication methods. © 2012 Division of Signal Processing and Electronic Systems, Poznan University of Technology.
This comprehensive, bird's view research note combines the state of the art, a brief presentation of the history and some original solutions, and position like views of some prospective future developments of one of the most relevant and interesting areas related to the use of fuzzy logic in database management systems, notably in its querying component, and – to some extent – in a broader issue of data and information management. We briefly summarize the roots of those new applications of fuzzy logic, more relevant proposals and development in the context of fuzzification of the basic relational database model, and then some of its further generalizations. We particularly focus on fuzzy querying as a human consistent and friendly way of retrieving information due to real human intentions and preferences expressed in natural language represented via fuzzy logic and possibility theory. We mention some extensions, notably fuzzy queries with linguistic quantifiers, and point their close relation to linguistic summaries. As for newer, prospective developments, we mainly focus on bipolar queries that can accomodate the users' intentions and preferences involving some sort of a required and desired, mandatory and optional, etc. conditions. We show various ways of handling such queries. We conclude with some brief position statements of our view on relevant and promising directions, and challenges.
In this paper we attempt to make a theoretical comparison between fuzzy sets and vague sets in processing uncertain queries. We have designed an architecture to process uncertain i.e. fuzzy or vague queries. In the architecture we have presented an algorithm to find the membership value that generates the fuzzy or vague representation of the attributes with respect to the given uncertain query. Next, a similarity measure is used to get each tuples similarity value with the uncertain query for both fuzzy and vague sets. Finally, a decision maker will supply a threshold or α-cut value based on which a corresponding SQL statement is generated for the given uncertain query. This SQL retrieves different result sets from the database for fuzzy or vague data. It has been shown with examples that vague sets give more accurate result in comparison with fuzzy sets for any uncertain query.
The authors present an object algebra for manipulating complex objects in fuzzy object-oriented database systems. Unlike in most of the existing query languages, the design of this object algebra is based on the type and set aspects of the class. A framework is presented for executing set-theoretic operations, namely union, intersection, and difference, on the class construct. The set operations on the membership of the corresponding class containing fuzzy objects are developed by using the truth-value of the object and object identity. The type description of the resulting class derived by a set operation is specified. The authors also discuss the inheritance property characteristic for the derived class with fuzzy objects.
Fuzzy databases have been introduced to deal with uncertain or incomplete information in many applications demonstrating the
efficiency of processing fuzzy queries. For these reasons, many organizations aim to integrate the fuzzy databases advantages
(flexible querying, handling imprecise data, fuzzy data mining, ...), minimizing the transformation costs. The best solution
is to offer a smoothly migration toward this technology. However, the migration of applications or databases in enterprises
arises from changes in business demands or technology challenges. The need for this migration is to improve operational efficiency
or to manage risk, data migration outage, as well as performance. This chapter is about the migration towards fuzzy databases.
We present our migration approach and we concentrate on their repercussions on programs.
This is an evolving bibliography of documents on uncertainty and imprecision in information systems. By uncertainty and imprecision, we mean the representation of and query support for information that is fuzzy, unknown, partially known, vague, uncertain, probabilistic, indefinite, disjunctive, possible, maybe, incomplete, approximate, erroneous, or imprecise. Currently, the bibliography concentrates almost exclusively on database and knowledge-base systems, with few bl]References on other kinds of information systems.
The object-oriented database management system has great promise as a future database technology because of its superior complex data structure manipulation, rich class structure, integration potential, and data reusability. An active database is another evolving technology which can generate new knowledge, execute commands, and maintain system integrity by means of triggers, constraints, and inference rules. Adding constraints and triggers into an object-oriented database creates an active object-oriented database which performs dynamic behaviors. However, both triggers and constraints may process data that arc qualitative, inexact, or uncertain. In this case, a fuzzy logic system may be utilized to improve performance by replacing fuzzy if-then rules as triggers or constraints. This study proposes adding a fuzzy class to the class library to solve fuzzy information problems.
Retrieving useful information from a specific database is a critical task in many application domains. Many research works today are devoted to finding better and more sophisticated functions that are better suited to information retrieval tasks. One of the important works in retrieving information is capturing the right perceptions of human communication. To this end, fuzzy logic is often used to provide a convenient tool for interfacing linguistic categories with numerical data and for expressing one user s preferences in a gradual and qualitative way. However, the human brain is very adept at finding patterns and meaning in random and fuzzy ways. To overcome such problems, we utilize an attribute relevance analysis method to make optimal weighted choices among different features and thus play an important role for the balance of the uncertainty and existed knowledge. Moreover, to demonstrate the effectiveness of our work, we develop a bird searching system which has the potentials of flexible querying for ecological databases. The experimental results show that our proposed method would be helpful in understanding the existed database and come up with a pretty good guess about the ambiguity.
Traditional database query languages are based on set theory and crisp logic. Many applications, however, need additionally retrieval-like queries returning the probability of a result object being relevant to a given query object. Traditionally, retrieval systems estimate relevance by exploiting hidden semantics whereas query processing in database systems relies mainly on term matching. Thus, completely different mechanisms were developed for database and information retrieval. As result, there is a lack of support for queries which involve both retrieval and database search terms. In this paper we develop basic concepts for a unifying framework based on quantum mechanics and quantum logic. Rijsbergen already discussed in his book the strong relation between quantum mechanics and information retrieval. The goal of this paper is to discuss the relation of database queries to quantum mechanics. Here, we develop the mapping of select operations as well as conjunction, disjunction, and negation as part of the relational calculus to quantum mechanics and quantum logic. i
Traditional database query languages are based on set theory and crisp first order logic. However, many applications require retrieval-like queries which return result objects associated with a degree value of being relevant to the query. Traditionally, retrieval systems estimate relevance by exploiting hidden object semantics whereas query processing in database systems relies on matching select-conditions with attribute values. Thus, different mechanisms were developed for database and information retrieval systems. In consequence, there is a lack of support for queries involving both retrieval and database search terms. In this work, we develop a unifying framework based on the mathematical formalism of quantum mechanics and quantum,logic. Van Rijsbergen already discussed the strong relation between the formalism of quantum,mechanics and information retrieval. The goal of this work is to interrelate concepts from database query processing to concepts from quantum mechanics and logic. As result, we obtain a common,theory which allows us to incorporate seamlessly retrieval search into traditional database query processing. Exploiting our theoretical results, we introduce the quantum query language QQL. In contrast to competing approaches, our formalism is based on quantum,logic. ii Contents
Fuzzy relational databases have been introduced to deal with uncertain or incomplete information
demonstrating the efficiency of processing fuzzy queries. For these reasons, many organizations aim
to integrate flexible querying to handle imprecise data or to use fuzzy data mining tools, minimizing
the transformation costs. The best solution is to offer a smooth migration towards this technology. This
chapter presents a migration approach from relational databases towards fuzzy relational databases.
This migration is divided into three strategies. The first one, named “partial migration,” is useful basically
to include fuzzy queries in classic databases without changing existing data. It needs some definitions
(fuzzy metaknowledge) in order to treat fuzzy queries written in FSQL language (Fuzzy SQL). The
second one, named “total migration”, offers in addition to the flexible querying, a real fuzzy database,
with the possibility to store imprecise data. This strategy requires a modification of schemas, data, and
eventually programs. The third strategy is a mixture of the previous strategies, generally as a temporary
step, easier and faster than the total migration.
Although the relational model for databases provides a great range of advantages over other data models, it lacks a comprehensive
way to handle imprecise and uncertain data. Vague set, as a generalized fuzzy set, has more powerful ability to process fuzzy
information than fuzzy set. In this paper, based on the vague set, a kind of vague relational model is proposed. Incorporating
the notion of vague sets in relations, we describe Vague SQL, which is an extension of SQL for the vague relational model,
and show that Vague SQL combines the capabilities of a standard SQL with the power of manipulating vague relations. Although
Vague SQL is a minimal extension to illustrate its usages, VSQL allows users to formulate a wide range of queries between
vague data and queries.
In this paper, through a developed software, crisp and fuzzy query were compared on a classical database. By means of this fuzzy query software tool, some fields (attribute) of a database table can be fuzzified and a supplementary database, which includes fuzzy values, is formed. Developed software tool is applied on a sample database including some fields about the students for the evaluation of scholarship application. It is concluded that, the fuzzy query method is more flexible and the results of such query are more predictive and satisfactory.
Infectious diseases are reemerging globally, many of them being
climate-related. The integration of remote sensing and disease outbreak
data along with GIS and artificial intelligence approaches provides the
tools for predicting future disease outbreaks. A fuzzy database
management system (FDBMS) has been constructed for this purpose, storing
disease outbreaks and a variety of parameters such as precipitation,
temperature, population density, elevation and other variables. The
FDBMS is able to search the database and provide disease risk
assessments based upon crisp and fuzzy conditions stated about spatial,
temporal, climatic and other parameters. The fuzzy search is generated
either by using a graphical user interface (GUI) or a fuzzy query
language (FQL). FQL is an extension to the well-known relational
structural query language (SQL), and it allows the user to make complex
queries. The FDBMS is able to display the locations of previous disease
outbreaks on a world map in the system GUI. Currently, nine years of
U.S. disease data from the Center for Disease Control (CDC) and from the
state of Texas are stored in the database. A major expansion to global
datasets is in progress, and international health agencies are asked to
contribute to this effort
In this paper, we present new Fuzzy Object Oriented Data model(F-model) and define an extended Fuzzy Association algebra(FA-algebra). F-model supports fuzzy classes and fuzzy associations between fuzzy objects. Several kinds of fuzzy attribute values are defined and expressed in databases. By the extended FA-algebra based on fuzzy association patterns, fuzzy queries with fuzzy values and linguistic hedges are processed.
The paper presents new developments in an extension of Codd’s relational model of data. The extension consists in equipping
domains of attribute values with a similarity relation and adding ranks to rows of a database table. This way, the concept
of a table over domains (i.e., relation over a relation scheme) of the classical Codd’s model extends to the concept of a
ranked table over domains with similarities. When all similarities are ordinary identity relations and all ranks are set to
1, our extension becomes the ordinary Codd’s model. The main contribution of our paper is twofold. First, we present an outline
of a relational algebra for our extension. Second, we deal with implementation issues of our extension. In addition to that,
we also comment on related approaches presented in the literature.
In this paper the Lie algebra analogues to groups with property E of Bechtell are investigated. Let X be the class of solvable Lie algebras with the following property: if H is a subalgebra of L, then (formula presented) where φ(L) denotes the Frattini subalgebra of L; that is, φ(L) is the intersection of all maximal subalgebras of L. Groups with the analogous property are called ingroups by Bechtell. The class X is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal N of L ∈X be the Frattini subalgebra of L. Only solvable Lie algebras of finite dimension are considered here.
Systematic Analysis of Gear Failures covers the modes, mechanisms, and appearances of gear failures and presents an orderly approach for determining how and why gears fail. It reviews the basics of gear design and operation and the factors that play a role in different types of failures. It explains how to examine and analyze failed gears and reconstruct initiating events. It describes the characteristics of fatigue, impact, wear, and stress rupture failures and contributing factors such as insufficient materials, design deficiencies, manufacturing defects, assembly and installation errors, improper lubrication, and overloading. It provides detailed case histories involving the failure of gears and related components and includes a chapter on documentation and reporting. For information on the print version, ISBN: 978-0-87170-200-5, follow this link.
The real world data may have two types of ambiguity, one is in a data value itself and the other in an association between values. For representing such data, we propose a possibility-distribution fuzzy-relational model. In this model, the former ambiguity is represented by a possibility distribution and the latter by a grade of membership. The relational algebra for such fuzzy data model is defined. The traditional operations, namely, the union, intersection, difference and extended Cartesian product are similarly defined as those in fuzzy set theory. And the special relational operations, namely, the projection, join, restriction and division, are newly defined for fuzzy databases.
Interactions between species cohabiting in an ecosystem have particular quadratic dynamical systems as mathematical models. We try to classify the low dimensional quadratic dynamical systems (n≤3), up to an affinity, then to separate among the obtained classes those that could characterize some trophic webs. This classification allows us to conclude that, in the case of two-species interactions, not more than four (among the ten) parameters are essential in their qualitative analysis, while, in the case of three-species interactions, not more than 12 (among the 27) parameters are essential. Both some biological reasons and some technical opportunities lead us to consider the particular case of those dynamical systems whose associated binary algebras have no nilpotent elements of index two.
We are concerned with three types of problems. (I) Existence and uniqueness of the solution u of the following boundary value problems: (1)p(t)u '' (t)+r(t)u ' (t)∈Au(t)+f(t),a·e·on[0,T],T>0, (2)u ' (0)∈α(u(0)-a),u ' (T)∈β(u(T)-b), (3)u '' (t)∈Au(u)+f(t),a·e·on[0,T], (4)u(0)=u(T),u ' (0)-u ' (T)∈γ(u(0)), (5)u '' (t)∈Au(t)+f(t),a·e·on[0,T], (6)u ' (0)=u ' (T),u(0)-u(T)∈δ(u ' (0))· Here, A,α,-β,γ,δ are maximal monotone (possibly multivalued) operators acting in a real Hilbert space H, a,b∈D(A), T>0 arbitrary, f∈L 2 ([0,T];H) (L 2 -with the weight function r ˜/p, where r ˜(t)=exp(∫ 0 t (r(s)/p(s))ds)), p,r:[0,T]→ℝ continuous with p(t)≥c>0∀t∈[0,T]· (II) Continuous dependence of u=u(t,a,b,f) on a,b and f. (III) In the case in which A, α and -β are subdifferentials of some lower semi-continuous convex (l.s.c.) proper functions, we prove the equivalence of (1)-(2) with a convex problem of Bolza.
The authors give a positive answer to the question “if Xα is г-distributed of order α, and Xβ of order β, with Xα and Xβ independent, is XαXβ infinitely divisible?”. This question, posed by Steutel in Ref. 1, has not been answered up to now, so far as they can find in the literature. In addition they show that the distribution of XαXβ is a generalized г-distribution.
In the present article the simple nonclassical Lie p-algebras Hn and Kn are shown to have n + 1 and 2n + 1 conjugacy classes of Cartan subalgebras, respectively.
Summary An exact solution of an eigenvalue problem arising in a thermal convection problem of Bénard type is given. Its numerical realisation gives the neutral curves at various values of an electrical dimensionless numberEl. Our results validate those obtained by Turnbull [1] by means of approximative Galerkin method.
Some ideas on bifurcation problems with several parameters are collected an different phenomena are illustrated on examples
of bifurcation problems which one can sole explicitely. The examples are dealing not only with differential equations but
also with other fields.
