Fuzzy relations and fuzzy relational databases

Recently, new applications have emerged that require database management systems with uncertainty capabilities. Many of the existing approaches to modeling uncertainty in database management systems are based on the theory of fuzzy sets. This paper introduces basic parallelism in fuzzy relational databases and its queries. Article describes basic characteristics of fuzzy relational databases and their properties, compares fuzzy logic with Boolean one in connection with fuzzy relational databases. Deal with data classification and form of storage fuzzy data in database systems. Paper describes fuzzy queries and parallelism in queries from view of today's systems and their connection to SQL language and its extension fuzzy SQL. Discuss about pipeline parallelism of query operators and its benefits.

Extending the fuzzy database with fuzzy numbers

In this paper we argue that fuzzy sets and rough sets aim to different purposes and that it is more natural to try to combine the two models of uncertainty (vagueness for fuzzy sets and coarseness for rough sets) in order to get a more accurate account of imperfect information. First, the upper and lower approximations of a fuzzy set are defined, when the universe of discourse of a fuzzy sets is coarsened by means of an equivalence relation. We then come close to Caianiello’s C-calculus. Shafer’s concept of coarsened belief functions also belongs to the same line of thought and is reviewed here. Another idea is to turn the equivalence relation relation into a fuzzy similarity relation, for a more expressive modeling of coarseness. New results on the representation of similarity relations by means of a fuzzy partition of fuzzy clusters of more or less indiscernible points are surveyed. The properties of upper and lower approximations of fuzzy sets by similarity relations are thoroughly studied. Lastly the potential usefulness of the fuzzy rough set notions for logical inference in the presence of both fuzzy predicates and graded indiscernibility is indicated. Especially fuzzy rough sets may provide a nice semantic background for modal logic involving fuzzy modalities and/or fuzzy sentences.

Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation if and if is a fuzzy congruence relations on fuzzy group and a fuzzy relation defined of is a fuzzy congruence relations on fuzzy factor group.

Fuzzy set theory was introduced by L.A. Zadeh in 1965. Immediately, it has many applications in practice and in building databases, one of which is the construction of a fuzzy relational database based on similar relationship. The study of cases of fuzzy relations in different environments will help us understand its applications. In this paper, the rough fuzzy relation on Cartesian product of two universe sets is defined, and then the algebraic properties of them, such as the max, min, and composition of two rough fuzzy relations are examined. Finally, reflexive, αreflexive, symmetric and transitive rough fuzzy relations on two universe sets are also defined.

Linguistic modelling based on semantic similarity relation among linguistic labels

The Extensible Markup Language (XML) is emerging as the dominant data format for data exchange between applications. Many translation techniques have been devised to publish large amounts of existing conventional relational data in XML format. There also exists a need to be able to represent imprecise data in both relational databases and XML. This paper describes a fuzzy XML schema model for representing a fuzzy relational database in XML format. It also outlines a translation algorithm to include fuzzy relations and similarity matrices with their associated conventional relations. We also describe how the proposed fuzzy XML schema and the conversion process from fuzzy relational data into fuzzy XML have been integrated into VIREX, which is a prototype with powerful visual tool for transforming relational data into XML.KeywordsFuzzy XMLFuzzy Relational DatabaseSchema ConversionVisual Interface

The one central problem in global forecasting area is to minimize the forecasting error and to have a simple model. This paper focuses on the fuzzy time series (FTS) forecasting which is one branch of fuzzy set (FS). Numerous FTS models have been proposed in literature during the past decades and the number of new models is still growing especially in stock markets and student enrolment problems. Some of the FTS models found in literature do not explain the fuzzy logical relationship strength between Ai and Aj which are the left-hand side (LHS) and right-hand side (RHS) of the fuzzy logical relationship respectively. This paper proposed Weighted Subsethood Fuzzy Time Series (WeSuFTS) to build fuzzy reasoning based to address the drawback in forecasting enrolment of students. In this paper, we create the weighted subsethood fuzzy rules to explain the fuzzy relationship between Ai and Aj . The simple centre mid-point defuzzification technique was introduced in defuzzification step. The results show that WeSuFTS method gives promising results where the average error forecasting is 2.31% which is smaller than the one presented by Song and Chissom in 1993 and Chen in 1996, the pioneer of FTS. The proposed method has an advantage since it can give a new interpretation of FTS model. Furthermore, this method able to present the degree of importance of LHS to RHS in explaining the fuzzy logical relationship in FTS.

An often raised objection to fuzzy logic can be articulated as follows. Fuzzy sets are intended to represent vague collections of objects. On the one hand, boundaries of such collections are inherently imprecise. On the other hand, fuzzy sets are defined by membership degrees which are precise. There is, therefore, an obvious discrepancy between the imprecision of a collection and the precision of a fuzzy set representing the collection. The objection leads to a question posed in the title of this paper: do exact shapes of fuzzy sets matter? That is, do the exact values of membership degrees of fuzzy sets matter? This is a fundamental question, particularly when fuzzy sets are supplied as an input to further processing. This paper presents a particular answer to this question. We focus on the case when the fuzzy sets in question are part of the input I from which the output O is produced in a way which can be described by logical formulas. This case covers several widely used fuzzy logical models including extension principle, products of fuzzy relations, Zadeh's compositional rule of inference, fuzzy automata, and properties of fuzzy relations. We present formulas which say how similar is the original output O to a new output O′ when the original input I is replaced by a new input I′. The presented formulas provide us with an analytical tool which enables us to answer the question of whether (and to what extent) the exact shapes of fuzzy sets in a particular fuzzy logical model matter. We present application of our formulas to selected topics including the above-mentioned extension principle, fuzzy relational products, Zadeh's compositional rule of inference, fuzzy automata, and properties of fuzzy relations. Based on the analysis, we argue that in several applications of fuzzy logic, the exact shapes of fuzzy sets do not really matter.

The study of joins in fuzzy relational databases

Construction is a highly dynamic environment with numerous interacting factors that affect construction processes and decisions. Uncertainty is inherent in most aspects of construction engineering and management, and traditionally, it has been treated as a random phenomenon. However, there are many types of uncertainty that are not naturally modelled by probability theory, such as subjectivity, ambiguity and vagueness. Fuzzy logic provides an approach for handling such uncertainties. However, fuzzy logic alone has some limitations, including its inability to learn from data and its extensive reliance on expert knowledge. To address these limitations, fuzzy logic has been combined with other techniques to create fuzzy hybrid techniques, which have helped solve complex problems in construction. In this chapter, a background on fuzzy logic in the context of construction engineering and management applications is presented. The chapter provides an introduction to uncertainty in construction and illustrates how fuzzy logic can improve construction modelling and decision-making. The role of fuzzy logic in representing uncertainty is contrasted with that of probability theory. Introductory material is presented on key definitions, properties and methods of fuzzy logic, including the definition and representation of fuzzy sets and membership functions, basic operations on fuzzy sets, fuzzy relations and compositions, defuzzification methods, entropy for fuzzy sets, fuzzy numbers, methods for the specification of membership functions and fuzzy rule-based systems. Finally, a discussion on the need for fuzzy hybrid modelling in construction applications is presented, and future research directions are proposed.

By normalizing the values of its pixels with respect to the length of the used scale, a gray image can be interpreted as a fuzzy relation R which is divided in submatrices (possibly square) called blocks. Every block R B is compressed to a block G B , which in turn is decompressed to a block D B (unsigned) ?R B . Both G B and D B are obtained via fuzzy relation equations with continuous triangular norms in which fuzzy sets with Gaussian membership functions are used as coders. The blocks D B are recomposed in order to give a fuzzy relation D. We use the Lukasiewicz t-norm and a watermark (matrix) is embedded in every G B with the LSBM (Least Significant Bit Modification) algorithm by obtaining a block [InlineMediaObject not available: see fulltext.], decompressed to a block [InlineMediaObject not available: see fulltext.] (signed). Both [InlineMediaObject not available: see fulltext.] and [InlineMediaObject not available: see fulltext.] are obtained by using the same fuzzy relation equations. The blocks [InlineMediaObject not available: see fulltext.] are recomposed by obtaining the fuzzy relation [InlineMediaObject not available: see fulltext.] (signed). By evaluating the quality of the reconstructed images via the PSNR (Peak Signal to Noise Ratio) with respect to the original image R, we show that the signed image [InlineMediaObject not available: see fulltext.] is very similar to the unsigned image D for low values of the compression rate.

Attribute reduction based on neighborhood constrained fuzzy rough sets

Many flexible approaches allow users to query the relational database with vague or imprecise terms similar to natural language; most of these proposals are based on the fuzzy set theory which provides an environment for working with the uncertainty described by the linguistic terms. This paper presents an overview of the most important proposals, to highlight important models concerning fuzzy query databases we consider two classifications: the first classification deals with flexible queries in crisp relational databases and the second deals with flexible queries in fuzzy relational databases. This paper aims to help researchers understand these approaches for further research in this area.

On fuzzy implication relations