Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data

1994 ◽  
Vol 3 (1) ◽  
pp. 7-27 ◽  
Author(s):  
Motohide Umano ◽  
Satoru Fukami
Keyword(s):  
Relational Algebra ◽  
Relational Model ◽  
Fuzzy Data ◽  
Possibility Distribution

scholarly journals Generalizing Possibility-Based Fuzzy Relational Models

2006 ◽  
Vol 10 (5) ◽  
pp. 633-646 ◽  
Author(s):  
Michinori Nakata ◽  
Keyword(s):  
Data Model ◽  
Relational Algebra ◽  
Relational Model ◽  
Imprecise Data ◽  
Semantic Ambiguity ◽  
Possibility Distribution ◽  
Relational Models ◽  
Data Value ◽  
Attribute Value

The generalized possibility-based fuzzy relational model we propose frees possibility-based fuzzy relational models from the semantic ambiguity and the indistinguishability of membership attribute values. We demonstrate extended relational algebra in this data model. To prevent the semantic ambiguity, a membership attribute is attached to every attribute. This clarifies where each membership attribute value comes from. What each membership attribute value means depends on the property of that attribute. To prevent the indistinguishability of membership attribute values, the value is expressed in a possibility distribution in interval [0,1]. This clarifies what effects the imprecise data value allowed for an attribute has on the membership attribute value. No semantic ambiguity and no indistinguishability of membership attribute values therefore exists in the generalized possibility-based fuzzy relational model.

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.

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.

A Fully Precise Null Extended Nested Relational Algebra

1993 ◽  
Vol 19 (3-4) ◽  
pp. 303-342
Author(s):  
Mark Levene ◽  
George Loizou
Keyword(s):  
Normal Form ◽  
General Class ◽  
Relational Algebra ◽  
Relational Model ◽  
Detailed Structure ◽  
Complex Objects ◽  
Nested Relations ◽  
Null Values

The nested relational model extends the fiat relational model by relaxing the first normal form assumption in order to allow the modelling of complex objects. Recently many extended algebras have been suggested for the nested relational model, but only few have incorporated null values into the attribute domains. Furthermore, some of the previously defined extended algebras are defined only over a subclass of nested relations, and all of them are difficult to use, since the user must know the detailed structure of the nested relations being queried. Herein, we define an extended algebra for nested relations, which may contain null values, called the null extended algebra. The null extended algebra is defined over the general class of nested relations with null values and, in addition, allows queries to be formulated without the user having to know the detailed structure of the nested relations being queried. In this sense, our null extended join operator of the null extended algebra is unique in the literature, since it joins two nested relations by taking into account all their common attributes at all levels of their structure, whilst operating directly on the two nested relations. All the operators of the null extended algebra are proved to be faithful and precise. The null extended algebra is a complete extended algebra in the context of nested relations, and, in addition, it includes the null extended powerset operator, which provides recursion and iteration facilities.

Application of Functional Approach to Lists for Development of Relational Model Databases and Petri Net Analysis

2014 ◽  
pp. 407-444
Author(s):  
Sasanko Sekhar Gantayat ◽  
B. K. Tripathy
Keyword(s):  
Characteristic Function ◽  
Query Processing ◽  
Data Structures ◽  
Petri Net ◽  
Relational Databases ◽  
Functional Approach ◽  
Relational Algebra ◽  
Relational Model ◽  
Algebraic Operations ◽  
Definition Of

The concept of list is very important in functional programming and data structures in computer science. The classical definition of lists was redefined by Jena, Tripathy, and Ghosh (2001) by using the notion of position functions, which is an extension of the concept of count function of multisets and of characteristic function of sets. Several concepts related to lists have been defined from this new angle and properties are proved further in subsequent articles. In this chapter, the authors focus on crisp lists and present all the concepts and properties developed so far. Recently, the functional approach to realization of relational databases and realization of operations on them has been proposed. In this chapter, a list theory-based relational database model using position function approach is designed to illustrate how query processing can be realized for some of the relational algebraic operations. The authors also develop a list theoretic relational algebra (LRA) and realize analysis of Petri nets using this LRA.

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