scholarly journals Optimal Codes in the Enomoto-Katona Space

2014 ◽  
Vol 24 (2) ◽  
pp. 382-406 ◽  
Author(s):  
YEOW MENG CHEE ◽  
HAN MAO KIAH ◽  
HUI ZHANG ◽  
XIANDE ZHANG
Keyword(s):  
Metric Space ◽  
Relational Databases ◽  
Central Problem ◽  
Optimal Code ◽  
Optimal Codes ◽  
Functional Dependencies ◽  
Complete Solutions ◽  
Congruence Classes

Coding in a new metric space, called the Enomoto-Katona space, has recently been considered in connection with the study of implication structures of functional dependencies and their generalizations in relational databases. The central problem is the determination ofC(n,k,d), the size of an optimal code of lengthn, weightk, and distancedin the Enomoto-Katona space. The value ofC(n,k,d) was known only for some congruence classes ofnwhen (k,d) ∈ {(2,3),(3,5)}. In this paper, we obtain new infinite families of optimal codes in the Enomoto-Katona space and verify a conjecture of Brightwell and Katona in certain instances. In particular,C(n,k, 2k− 1) is determined for all sufficiently largensatisfying eithern≡ 1 modkandn(n− 1) ≡ 0 mod 2k2, orn≡ 0 modk. We also give complete solutions fork= 2 and determineC(n,3,5) for certain congruence classes ofnwith finite exceptions.

Comparison of Linguistic Summaries and Fuzzy Functional Dependencies Related to Data Mining

2014 ◽  
pp. 174-203 ◽  
Author(s):  
Miroslav Hudec ◽  
Miljan Vučetić ◽  
Mirko Vujošević
Keyword(s):  
Data Mining ◽  
Fuzzy Logic ◽  
Relational Databases ◽  
Missing Values ◽  
Expert Knowledge ◽  
Real Data ◽  
Research Area ◽  
Functional Dependencies ◽  
Useful Knowledge ◽  
Important Research Area

Data mining methods based on fuzzy logic have been developed recently and have become an increasingly important research area. In this chapter, the authors examine possibilities for discovering potentially useful knowledge from relational database by integrating fuzzy functional dependencies and linguistic summaries. Both methods use fuzzy logic tools for data analysis, acquiring, and representation of expert knowledge. Fuzzy functional dependencies could detect whether dependency between two examined attributes in the whole database exists. If dependency exists only between parts of examined attributes' domains, fuzzy functional dependencies cannot detect its characters. Linguistic summaries are a convenient method for revealing this kind of dependency. Using fuzzy functional dependencies and linguistic summaries in a complementary way could mine valuable information from relational databases. Mining intensities of dependencies between database attributes could support decision making, reduce the number of attributes in databases, and estimate missing values. The proposed approach is evaluated with case studies using real data from the official statistics. Strengths and weaknesses of the described methods are discussed. At the end of the chapter, topics for further research activities are outlined.

Incremental Discovery of Fuzzy Functional Dependencies

2011 ◽  
pp. 615-633 ◽  
Author(s):  
Shyue-Liang Wang ◽  
Ju-Wen Shen ◽  
Tuzng-Pei Hong
Keyword(s):  
Data Mining ◽  
Relational Databases ◽  
Search Algorithm ◽  
Current Data ◽  
Research Interest ◽  
Functional Dependencies ◽  
Incremental Search ◽  
Data Mining Techniques ◽  
Analysis Technique ◽  
Mining Algorithms

Mining functional dependencies (FDs) from databases has been identified as an important database analysis technique. It has received considerable research interest in recent years. However, most current data mining techniques for determining functional dependencies deal only with crisp databases. Although various forms of fuzzy functional dependencies (FFDs) have been proposed for fuzzy databases, they emphasized conceptual viewpoints and only a few mining algorithms are given. In this research, we propose methods to validate and incrementally search for FFDs from similarity-based fuzzy relational databases. For a given pair of attributes, the validation of FFDs is based on fuzzy projection and fuzzy selection operations. In addition, the property that FFDs are monotonic in the sense that r1 ? r2 implies FDa(r1) ? FDa(r2) is shown. An incremental search algorithm for FFDs based on this property is then presented. Experimental results showing the behavior of the search algorithm are discussed.

scholarly journals A Method for Normalization of Relation Schema Based on Data to Abide by the Third Normal Form

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Normal Form ◽  
Relational Databases ◽  
Normal Forms ◽  
Applied Mathematics ◽  
Database Management System ◽  
Functional Dependencies ◽  
Full Understanding ◽  
Data Bases ◽  
The Third ◽  
Relation Schema

Data bases play an important role in applied Mathematics. Normalization for relational databases is very important to avoid anomalies of relations which may not be in normalized forms of the third normal forms. But, normalization may be a difficult task, since the designers of the databases may not fully understand the domain of each attribute that are contained in the relation schema or they may not have full understanding about the concept of normalization. In this paper an efficient method that checks the possibility of the need of further normalization using stored data in relations is presented based on possible functional dependencies between attributes in the relations. By checking possible functional dependencies, the database designers can determine the need of further normalization, and may improve the structure of the relation schemas. Experiments were performed for an example of relational database that can be found in the organization of tutorial of MySQL which is a representational database management system, and the experiments showed good results.

Multivalued Dependencies in Fuzzy Multivalued Relational Databases Using Fuzzy Functions

2015 ◽  
Vol 23 (04) ◽  
pp. 589-626 ◽  
Author(s):  
Devendra K. Tayal ◽  
P. C. Saxena
Keyword(s):  
Real World ◽  
Data Model ◽  
Relational Databases ◽  
Relational Model ◽  
Relational Data ◽  
Inference Rules ◽  
Functional Dependencies ◽  
Technical Institute ◽  
Relational Schema ◽  
Relational Data Model

In this paper we discuss an important integrity constraint called multivalued dependency (mvd), which occurs as a result of the first normal form, in the framework of a newly proposed model called fuzzy multivalued relational data model. The fuzzy multivalued relational data model proposed in this paper accommodates a wider class of ambiguities by representing the domain of attributes as a “set of fuzzy subsets”. We show that our model is able to represent multiple types of impreciseness occurring in the real world. To compute the equality of two fuzzy sets/values (which occur as tuple-values), we use the concept of fuzzy functions. So the main objective of this paper is to extend the mvds in context of fuzzy multivalued relational model so that a wider class of impreciseness can be captured. Since the mvds may not exist in isolation, a complete axiomatization for a set of fuzzy functional dependencies (ffds) and mvds in fuzzy multivalued relational schema is provided and the role of fmvds in obtaining the lossless join decomposition is discussed. We also provide a set of sound Inference Rules for the fmvds and derive the conditions for these Inference Rules to be complete. We also derive the conditions for obtaining the lossless join decomposition of a fuzzy multivalued relational schema in the presence of the fmvds. Finally we extend the ABU's Algorithm to find the lossless join decomposition in context of fuzzy multivalued relational databases. We apply all of the concepts of fmvds developed by us to a real world application of “Technical Institute” and demonstrate that how the concepts fit well to capture the multiple types of impreciseness.

scholarly journals Representation of functional dependencies in relational databases using linear graphs

1983 ◽  
Vol 24 (2) ◽  
pp. 143-159 ◽  
Author(s):  
K.K. Nambiar ◽  
T. Radhakrishnan ◽  
V.G. Tikekar
Keyword(s):  
Relational Databases ◽  
Functional Dependencies ◽  
Linear Graphs

scholarly journals Thuật toán xác định bao đóng và khóa theo tiếp cận hợp giải trong lớp các phụ thuộc logic

2016 ◽  
pp. 50
Author(s):  
Trương Thị Thu Hà ◽  
Nguyễn Thị Vân ◽  
Nguyễn Xuân Huy
Keyword(s):  
Relational Databases ◽  
Knowledge Bases ◽  
New Technique ◽  
Functional Dependencies ◽  
A New Technique

The algorithms for closures and keys in relation schemas with functional dependencies are well-known in theory of relational databases. However, the problems of closures and keys in relation schemas with positive Boolean dependencies are still opened. This paper proposes a solution to these problems. The results are presented by unification method which is a new technique to construct the basic algorithms for logic dependencies in data and knowledge bases.  

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