Operators for Multidimensional Aggregate Data

2003 ◽  
pp. 116-165 ◽  
Author(s):  
Maurizio Rafanelli
Keyword(s):  
Aggregate Data ◽  
Basic Algebra ◽  
Relational Algebra ◽  
Relational Model ◽  
Statistical Databases ◽  
Formal Definitions ◽  
Relational Calculus

In this chapter the author proposes the different approaches for defining operators able to manipulate this multidimensional structure. In particular, he initially considers operators for multidimensional aggregate data which extend relational algebra and relational calculus (the so-called enlarged relational model). Then he discusses operators for multidimensional aggregate data defined in a tabular environment. In both the cases the author defines such data as statistical (aggregate) data. Subsequently he introduces the operators for OLAP applications, giving a terminology correspondence between the multidimensional aggregate (statistical) databases and OLAP areas. Then he defines the fundamental operators deduced from the previous ones, which form the basic algebra for the manipulation of multidimensional aggregate data, giving their formal definitions and some explanatory examples.

scholarly journals The Algebraic Operations and Their Implementation Based on a Two-Layer Cloud Data Model

2016 ◽  
Vol 16 (6) ◽  
pp. 5-26
Author(s):  
Ying Li ◽  
Baotian Dong
Keyword(s):  
Data Model ◽  
Relational Algebra ◽  
Cloud Data ◽  
Composite Object ◽  
Nested Data ◽  
Set Operations ◽  
Formal Definitions ◽  
Algebraic Operations ◽  
Query Operations ◽  
Layer Cloud

Abstract The existing cloud data models cannot meet the management requirements of structured data very well including a great deal of relational data, therefore a two-layer cloud data model is proposed. The composite object is defined to model the nested data in the representation layer, while a 4-tuple is defined to model the non-nested data in the storage layer. Referring the relational algebra, the concept of SNO (Simple Nested Object) is defined as basic operational unit of the algebraic operations; the formal definitions of the algebraic operations consisting of the set operations and the query operations on the representation layer are proposed. The algorithm of extracting all SNOs from a CAO (Component-Attribute-Object) set of a composite object is proposed firstly as the foundation, and then as the idea; the pseudo code implementation of algorithms of the algebraic operations on the storage layer are proposed. Logic proof and example proof indicate that the definition and the algorithms of the algebraic operations are correct.

Extending relational algebra with similarities

2012 ◽  
Vol 22 (4) ◽  
pp. 686-718 ◽  
Author(s):  
MELITA HAJDINJAK ◽  
GAVIN BIERMAN
Keyword(s):  
Real World ◽  
Worked Examples ◽  
Relational Algebra ◽  
Relational Model ◽  
Attribute Level ◽  
Similarity Queries ◽  
Relation Model

In this paper we propose various extensions to the relational model to support similarity-based querying. We build upon the -relation model, where tuples are assigned values from an arbitrary semiring , and its associated positive relational algebra $\text{RA}^{+}_{\mathcal{K}}$. We consider a recently proposed extension to $\text{RA}^{+}_{\mathcal{K}}$ using a monus operation on the semiring to support negative queries, and show how, surprisingly, it fails for important ‘fuzzy’ semirings. Instead, we suggest using a negation operator. We also consider the identities satisfied by the relational algebra $\text{RA}^{+}_{\mathcal{K}}$. We show that moving from a semiring to a particular form of lattice (a De Morgan frame) yields a relational algebra that satisfies all the classical (positive) relational algebra identities. We claim that to support real-world similarity queries realistically, one must move from tuple-level annotations to attribute-level annotations. We show in detail how our De Morgan frame-based model can be extended to support attribute-level annotations and give worked examples of similarity queries in this setting.

scholarly journals Application of semantic models and criteria equivalence of data to increase efficiency func-tioning of economic systems

2021 ◽  
pp. 41-46
Author(s):  
Ganna Pliekhova ◽  
Olena Alisejko ◽  
Zoia Kochuieva
Keyword(s):  
Modern Society ◽  
Subject Area ◽  
Relational Algebra ◽  
Relational Model ◽  
Practical Significance ◽  
Model Parameters ◽  
Mathematical Methods ◽  
Semantic Equivalence ◽  
Subject Areas ◽  
Modern Information

Problem. In modern society, the role of modeling as a way of cognizing objects with complex structures is growing. The problem of development of models and criteria of semantic equivalence of data under the condition of their lexical ambiguity in relation to relational databases is considered. This is due to the impossibility or undesirability of conducting an experiment on real objects. Modeling was initially applied in "well" studied subject areas (for which the basic laws of object interaction were already known. This knowledge made it possible to set a priori the class of used models of the subject area and reduce the task to setting the model parameters according to the available experimental data. A fundamental change in the modeling scheme occurred during the transition to the development of modeling systems for "weakly" formalized subject areas, where the structure itself and the class of applicable models must be refined in the course of research. The widespread use of relational DB and their use in a wide variety of applications shows that the relational data model is sufficient for modeling domains. Results. The purpose of developing criteria is to prevent relational algebra operations on attributes with lexical and semantic ambiguity. Methods of developing methods and criteria are based on the use of mathematical methods and the use of modern information technology. The scientific novelty is to solve the problem of semantic comparability of relational relations attributes by means of relational model, which allows to effectively solve problems of prevention of relational algebra operations, which lead to data destruction due to ambiguity of lexical and semantic meanings of attribute names. The practical significance lies in the development of methods for organizing access to data in large subject areas, which together with the degree of efficiency of their processing serve as the foundation of the modern information industry and normalizes the vocabulary of subject area description and coordination of management tasks within a single approach.

A Semantic-Ambiguity-Free Relational Model for Handling Imperfect Information1

1999 ◽  
Vol 3 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Michinori Nakata ◽  
Keyword(s):  
Query Processing ◽  
Fuzzy Sets ◽  
Imperfect Information ◽  
Cartesian Product ◽  
Relational Algebra ◽  
Integrity Constraints ◽  
Relational Model ◽  
Semantic Ambiguity ◽  
Model Features ◽  
Attribute Value

An extended relational model without semantic ambiguity, called a semantic-ambiguity-free relational model, is proposed using fuzzy sets and the theory of possibility. The model features every attribute having a membership attribute whose value consists of a pair of values based on necessity and possibility measures. The membership attribute value of an attribute in a base relation is the degree to which the attribute value is compatible with integrity constraints imposed on the base relation. This clarifies the source of the membership attribute value. The model has no semantic ambiguity for interpreting membership attribute values, unlike models consisting of relations with membership attribute values attached to tuple values. We show the formulation of 8 operations - union, intersection, difference, Cartesian product, projection, join, selection, and quotient - consisting of relational algebra proposed by Codd for query processing. This approach shows how to prevent users from misinterpreting tuples in databases allowing imperfect information.

scholarly journals A Simpler and Semantic Multidimensional Database Query Language to Facilitate Access to Information in Decision-making

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Fredi Edgardo Palominos ◽  
Felisa Córdova ◽  
Claudia Durán ◽  
Bryan Nuñez
Keyword(s):  
Decision Making ◽  
Query Language ◽  
Database Systems ◽  
Relational Algebra ◽  
Multidimensional Database ◽  
Management Indicators ◽  
Relational Calculus ◽  
Database Technology ◽  
Sql Language ◽  
Relational Database Systems

OLAP and multidimensional database technology have contributed significantly to speed up and build confidence in the effectiveness of methodologies based on the use of management indicators in decision-making, industry, production, and services. Although there are a wide variety of tools related to the OLAP approach, many implementations are performed in relational database systems (R-OLAP). So, all interrogation actions are performed through queries that must be reinterpreted in the SQL language. This translation has several consequences because SQL language is based on a mixture of relational algebra and tuple relational calculus, which conceptually responds to the logic of the relational data model, very different from the needs of the multidimensional databases. This paper presents a multidimensional query language that allows expressing multidimensional queries directly over ROLAP databases. The implementation of the multidimensional query language will be done through a middleware that is responsible for mapping the queries, hiding the translation to a layer of software not noticeable to the end-user. Currently, progress has been made in the definition of a language where through a key statement, called aggregate, it is possible to execute the typical multidimensional operators which represent an important part of the most frequent operations in this type of database.

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