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 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.

An Extended Relational Model & SQL for Fuzzy Multidatabases

2011 ◽  
pp. 185-219
Author(s):  
Awadhesh Kumar Sharma ◽  
A. Goswami ◽  
D.K. Gupta
Keyword(s):  
Query Processing ◽  
Fuzzy Sets ◽  
Real World ◽  
Relational Model ◽  
Ambiguous Information ◽  
Fuzzy Query ◽  
Algebraic Properties ◽  
Recent Trends ◽  
Real World Problems

Many real world problems involve imprecise and ambiguous information rather than crisp information. Recent trends in the database paradigm are to incorporate fuzzy sets to tackle imprecise and ambiguous information of real world problems. Fuzzy query processing in multidatabases have been extensively studied, however, the same has rarely been addressed for fuzzy multidatabases. This chapter attempts to extend the SQL to formulate a global fuzzy query on a fuzzy multidatabase under FTS relational model discussed earlier. The chapter provides architecture for distributed fuzzy query processing with a strategy for fuzzy query decomposition and optimization. Proofs of consistent global fuzzy operations and some of algebraic properties of FTS Relational Model are also supplemented.

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.

scholarly journals Multidimensional Space Structure for Adaptable Data Model

2019 ◽  
Vol 8 (3) ◽  
pp. 7753-7758
Keyword(s):  
Data Model ◽  
Cartesian Product ◽  
Data Representation ◽  
Space Structure ◽  
Automated System ◽  
Relational Model ◽  
Multidimensional Data ◽  
Multidimensional Space ◽  
Model Based ◽  
Five Axes

The article presents an adaptable data model based on multidimensional space. The main difference between a multidimensional data representation and a table representation used in relational Database Management Systems (DBMSs) is that it is possible to add new elements to sets defining the axes of multidimensional space at any time. This changes the data model. The tabular representation of the relational model does not allow you to change the model itself during the operation of an automated system. Three levels of multidimensional data presentation space are considered. There are axis of multidimensional space, the Cartesian product of the sets of axis values and the values of space points. The five axes of multidimensional space defined in the article (entities, attributes, identifiers, time, modifiers) are basic for the design of an adaptable automated system. It is shown that it is possible to use additional axes for greater granularity of the stored data. The multidimensional space structure defined in the article for an adaptable data model is a flexible set for storing a relational domain model. Two types of operations in multidimensional information space are defined. Relations of the relational model are formed dynamically depending on the conditions imposed on the coordinates of the points. Thus, an adaptable data representation model based on multidimensional space can be used to create flexible dynamic automated information systems.

Pre-Processing Highly Sparse and Frequently Evolving Standardized Electronic Health Records for Mining

2021 ◽  
pp. 8-21
Author(s):  
Shivani Batra ◽  
Shelly Sachdeva
Keyword(s):  
Electronic Health Records ◽  
Data Model ◽  
Semantic Interoperability ◽  
Relational Model ◽  
Health Records ◽  
Related Information ◽  
Health Related ◽  
Electronic Health ◽  
Mining Tools ◽  
Attribute Value

EHRs aid in maintaining longitudinal (lifelong) health records constituting a multitude of representations in order to make health related information accessible. However, storing EHRs data is non-trivial due to the issues of semantic interoperability, sparseness, and frequent evolution. Standard-based EHRs are recommended to attain semantic interoperability. However, standard-based EHRs possess challenges (in terms of sparseness and frequent evolution) that need to be handled through a suitable data model. The traditional RDBMS is not well-suited for standardized EHRs (due to sparseness and frequent evolution). Thus, modifications to the existing relational model is required. One such widely adopted data model for EHRs is entity attribute value (EAV) model. However, EAV representation is not compatible with mining tools available in the market. To style the representation of EAV, as per the requirement of mining tools, pivoting is required. The chapter explains the architecture to organize EAV for the purpose of preparing the dataset for use by existing mining tools.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

2020 ◽  
pp. 244-274
Author(s):  
Prakasam Muralikrishna ◽  
Tapan Senapati ◽  
Perumal Hemavathi
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Algebraic Structures ◽  
Interval Valued

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

scholarly journals ANALISA OPTIMALISASI BAHASA SQL BERDASARKAN RELATIONAL ALGEBRA PADA KASUS REKAPITULASI MAHASISWA LAYAK WISUDA

2015 ◽  
Vol 6 (2) ◽  
pp. 405
Author(s):  
Eko Darmanto
Keyword(s):  
Cartesian Product ◽  
Relational Algebra ◽  
Query Tree

ABSTRAK Aljabar relasional sangat membantu adanya kemungkinan penggunaan sintaks bahasa SQL yang berlainan dalam masalah yang sama. Masalah yang digunakan sebagai eksperimen adalah kasus rekapitulasi data mahasiswa layak wisuda pada suatu perguruan tinggi. Penggunaan sintaks bahasa SQL yang optimal dapat dianalisa menggunakan teknik query tree untuk mendapatkan hal utama dalam pemrosesan basis data yaitu kecepatan dan ketepatan komputasi yang berhubungan dengan pemuatan data ke dalam memori komputer. Hasil dari penelitian menunjukkan bahwa pemuatan data ke dalam memori komputer lebih optimal jika menggunakan join dibandingankan dengan Cartesian product. Dimungkinkan gabungan keduanya menjadi lebih cepat jika aturan penggunaan seleksi kemudian proyeksi didahulukan ketimbang penggabungan menggunakan Join atau Cartesian product terlebih dulu, hal ini bertujuan untuk mengurangi pemuatan baris dan kolom data yang berlebih. Ditinjau dari kecepatan komputasi untuk operasi himpunan yang melibatkan lebih dari satu tabel, Cartesian product dengan didahului proyeksi dan seleksi lebih cepat dibandingkan dengan Join untuk kasus yang sama. Kata kunci: optimalisasi sintaks SQL, aljabar relasional, query-tree.

Complex bipolar fuzzy sets: An application in a transport’s company

2020 ◽  
pp. 1-17
Author(s):  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Cartesian Product ◽  
Real Numbers ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Bipolar Fuzzy Sets ◽  
Range Of Values

Zadeh’s fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and complex fuzzy set with wide range of values by adding positive membership function and negative membership function to unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets. Thus this paper leads us towards a new direction of research, which has many applications in different directions. We develop the notions of union, intersection, complement, Cartesian product and De-Morgan’s Laws of complex bipolar fuzzy sets. Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the algorithm.

scholarly journals Type-2 Multi-Fuzzy Sets and Their Applications in Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 170 ◽  
Author(s):  
Mohuya B. Kar ◽  
Bikashkoli Roy ◽  
Samarjit Kar ◽  
Saibal Majumder ◽  
and Dragan Pamucar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imperfect Information ◽  
Real Life ◽  
Distance Measures ◽  
Expert Assessment ◽  
Decision Making Problem ◽  
Medical Diagnosis System

In a real-life scenario, it is undoable and unmanageable to solve a decision-making problem with the single stand-alone decision-aid method, expert assessment methodology or deterministic approaches. Such problems are often based on the suggestions or feedback of several experts. Usually, the feedback of these experts are heterogeneous imperfect information collected from various more or less reliable sources. In this paper, we introduce the concept of multi-sets over type-2 fuzzy sets. We have tried to propose an extension of type-1 multi-fuzzy sets into a type-2 multi-fuzzy set (T2MFS). After defining T2MFS, we discuss the algebraic properties of these sets including set-theoretic operations such as complement, union, intersection, and others with examples. Subsequently, we define two distance measures over these sets and illustrate a decision-making problem which uses the idea of type-2 multi-fuzzy sets. Furthermore, an application of a medical diagnosis system based on multi-criteria decision making of T2MFS is illustrated with a real-life case study.

Sign in / Sign up

Export Citation Format

Share Document