Object-Oriented Publish/Subscribe for Modeling and Processing Imperfect Information

2011 ◽  
pp. 301-332
Author(s):  
Haifeng Liu ◽  
Hans Arno Jacobsen
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Imperfect Information ◽  
Information Dissemination ◽  
Object Oriented ◽  
Possibility Theory ◽  
Matching Problem ◽  
Fuzzy Measures ◽  
Information Providers ◽  
Selective Information

In the publish/subscribe paradigm, information providers disseminate publications to all consumers who expressed interest by registering subscriptions with the publish/subscribe system. This paradigm has found widespread applications, ranging from selective information dissemination to network management. In all existing publish/subscribe systems, neither subscriptions nor publications can capture uncertainty inherent to the information underlying the application domain. However, in many situations, knowledge of either specific subscriptions or publications is not available. To address this problem, this chapter proposes a new object-oriented publish/subscribe model based on possibility theory and fuzzy set theory to process imperfect information for expressing subscriptions, publications, or both combined. Furthermore, the approximate publish/subscribe matching problem based on fuzzy measures is defined, and the real-world A-ToPSS™ system is described.

UNCERTAIN AND FUZZY OBJECT BASES: A DATA MODEL AND ALGEBRAIC OPERATIONS

2011 ◽  
Vol 19 (02) ◽  
pp. 275-305 ◽  
Author(s):  
TRU H. CAO ◽  
HOA NGUYEN
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Object Oriented ◽  
Possibility Theory ◽  
Object Properties ◽  
Common Framework ◽  
Formal Basis ◽  
Object Oriented Systems ◽  
Is Value

Fuzzy set theory and probability theory are complementary for soft computing, in particular object-oriented systems with imprecise and uncertain object properties. However, current fuzzy object-oriented data models are mainly based on fuzzy set theory or possibility theory, and lack of a rigorous algebra for querying and managing uncertain and fuzzy object bases. In this paper, we develop an object base model that incorporates both fuzzy set values and probability degrees to handle imprecision and uncertainty. A probabilistic interpretation of relations on fuzzy sets is introduced as a formal basis to coherently unify the two types of measures into a common framework. The model accommodates both class attributes, representing declarative object properties, and class methods, representing procedural object properties. Two levels of property uncertainty are taken into account, one of which is value uncertainty of a definite property and the other is applicability uncertainty of the property itself. The syntax and semantics of the selection and other main data operations on the proposed object base model are formally defined as a full-fledged algebra.

Fundamental Concepts

2019 ◽  
pp. 27-77
Keyword(s):  
Decision Making ◽  
Probability Theory ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Probability Distributions ◽  
Possibility Theory ◽  
Multi Objective ◽  
Basic Ideas ◽  
Fuzzy Stochastic Programming

In this chapter, the authors discuss some basic concepts of probability theory and possibility theory that are useful when reading the subsequent chapters of this book. The multi-objective fuzzy stochastic programming models developed in this book are based on the concepts of advanced topics in fuzzy set theory and fuzzy random variables (FRVs). Therefore, for better understanding of these advanced areas, the authors at first presented some basic ideas of probability theory and probability density functions of different continuous probability distributions. Afterwards, the necessity of the introduction of the concept of fuzzy set theory, some important terms related to fuzzy set theory are discussed. Different defuzzification methodologies of fuzzy numbers (FNs) that are useful in solving the mathematical models in imprecisely defined decision-making environments are explored. The concept of using FRVs in decision-making contexts is defined. Finally, the development of different forms of fuzzy goal programming (FGP) techniques for solving multi-objective decision-making (MODM) problems is underlined.

Modeling and Querying Fuzzy Data

2018 ◽  
pp. 2245-2273
Author(s):  
Li Yan ◽  
Z. M. Ma
Keyword(s):  
Data Management ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Imperfect Information ◽  
Data Models ◽  
Fuzzy Data ◽  
Current State ◽  
Data Querying ◽  
Database Models ◽  
Knowledge Intensive

Imperfect information extensively exists in data and knowledge intensive applications, where fuzzy data play an import role in nature. Fuzzy set theory has been extensively applied to extend various database models and resulted in numerous contributions. The chapter concentrates on two main issues in fuzzy data management: fuzzy data models and fuzzy data querying based on the fuzzy data models. A full up-to-date overview of the current state of the art in fuzzy data modeling and querying is provided in the chapter. In addition, the relationships among various fuzzy data models are discussed in the chapter. The chapter serves as identifying possible research opportunities in the area of fuzzy data management in addition to providing a generic overview of the approaches to modeling and querying fuzzy data.

Modeling and Querying Fuzzy Data

2015 ◽  
pp. 129-157
Author(s):  
Li Yan ◽  
Z. M. Ma
Keyword(s):  
Data Management ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Imperfect Information ◽  
Data Models ◽  
Fuzzy Data ◽  
Current State ◽  
Data Querying ◽  
Database Models ◽  
Knowledge Intensive

Imperfect information extensively exists in data and knowledge intensive applications, where fuzzy data play an import role in nature. Fuzzy set theory has been extensively applied to extend various database models and resulted in numerous contributions. The chapter concentrates on two main issues in fuzzy data management: fuzzy data models and fuzzy data querying based on the fuzzy data models. A full up-to-date overview of the current state of the art in fuzzy data modeling and querying is provided in the chapter. In addition, the relationships among various fuzzy data models are discussed in the chapter. The chapter serves as identifying possible research opportunities in the area of fuzzy data management in addition to providing a generic overview of the approaches to modeling and querying fuzzy data.

scholarly journals Fuzzy Epidemiology: Measures for Observational Epidemiological Studies

2020 ◽  
Author(s):  
Ana Cláudia Oliveira Melo ◽  
Laisa Ribeiro de Sá ◽  
Rodrigo Pinheiro de Toledo Vianna ◽  
Ronei Marcos de Moraes
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Observational Studies ◽  
Risk Measures ◽  
Possibility Theory ◽  
Epidemiological Studies ◽  
Case Control ◽  
Case Scenario ◽  
Fuzzy Measures ◽  
Study Population

Abstract Background Epidemiological studies bring forth classic epidemiological measures calculation that are based on resulting quantities of dichotomic categorization of individuals, such as in events: diseased, non-diseased, exposed or unexposed. Dichotomic categorizations discard inherent uncertainties and subjectivities from the illness process the exposure which generate information losses on the measures. The fuzzy set theory categorizes each individual, allowing the soft transit amongst the events and considering the uncertainties and subjectivities. For the calculation of these measures, the fuzzy possibility theory is useful. Although there is already the proposition of making use of this methodology to the calculation of association and risk measures, there are no additional studies, in the literature, that characterize or apply the measures in epidemiological studies. Neither there are proposed calculations of other epidemiological measures or studies explaining the contribution of the resulting epidemiological measure of this methodology. This paper aims to increase the epidemiological measures sets to observational studies, using fuzzy set and possibility theories in the calculation of the denominated fuzzy epidemiological measures, featuring them in an original way.Methodology The proposed fuzzy measures were based in classic epidemiological measures. An observational study was simulated on a case-control type and fuzzy theories on the categorization of the individuals and for the calculation of fuzzy measures were applied. The simulations and calculations were performed by the software R.Results It was graphically observed the incorporation of uncertainties and subjectivities in the study population categorization. Comparing the classic to the fuzzy measures, it was observed that the contribution of the embedded uncertainties and subjectivities on the fuzzy measure presented a more complete final information about the illness process and exposure of the individuals. The graphic behavior of the proposed measures and of the already existent ones were characterized.Conclusion The fuzzy set epidemiological measures changes the paradigm of measures restricted to one numerical value. The information of the new fuzzy measures is seen as more trustworthy and helpful to decision making health managers, regarding which policies must be considered in accordance to the susceptible of harm and exposure in every population of each case scenario.

Uncertainty Modeling Using Expert’s Knowledge as Evidence

2014 ◽  
pp. 39-53 ◽  
Author(s):  
D. Datta
Keyword(s):  
Probability Theory ◽  
Monte Carlo ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Input Data ◽  
Evidence Theory ◽  
Uncertainty Modeling ◽  
Data Set ◽  
Mathematical Structures ◽  
Fuzzy Measures

In this paper we discuss the uncertainty modeling using evidence theory. In practice, very often availability of data is incomplete in the sense that sufficient amount of data which is required may not be possible to collect. Therefore, uncertainty modeling in that case with this incomplete data set is not possible to carry out using probability theory or Monte Carlo method. Fuzzy set theory or any other imprecision based theory is applicable in this case. With a view to this expert’s knowledge is represented as the input data set. Belief and plausibility are the two bounds (lower and upper) of the uncertainty of this imprecision based system. The fundamental definitions and the mathematical structures of the belief and plausibility fuzzy measures are discussed in this chapter. Uncertainty modeling using this technique is illustrated with a simple example of contaminant transport through groundwater.

An Overview of Fuzzy Approaches to Flexible Database Querying

2009 ◽  
pp. 135-156 ◽  
Author(s):  
Slawomir Zadrozny ◽  
Guy de Tré ◽  
Rita de Caluwe ◽  
Janusz Kacprzyk
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Object Oriented ◽  
Database Systems ◽  
Database Modeling ◽  
Database Querying ◽  
Object Oriented Database ◽  
Flexible Querying ◽  
Natural Way

In reality, a lot of information is available only in an imperfect form. This might be due to imprecision, vagueness, uncertainty, incompleteness, or ambiguities. Traditional database systems can only adequately cope with perfect data. Among others, fuzzy set theory has been applied to deal with imperfections of data in a more natural way and to enhance the accessibility of databases. In this chapter, we give an overview of main trends in the research on flexible querying techniques that are based on fuzzy set theory. Both querying techniques for traditional databases as well as querying techniques for fuzzy databases are described. The discussion comprises both the relational and the object-oriented database modeling approaches.

An Overview of Fuzzy Approaches to Flexible Database Querying

2011 ◽  
pp. 34-54 ◽  
Author(s):  
Slawomir Zadrozny ◽  
Guy de Tré ◽  
Rita de Caluwe ◽  
Janusz Kacprzyk
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Object Oriented ◽  
Database Systems ◽  
Database Modeling ◽  
Database Querying ◽  
Object Oriented Database ◽  
Flexible Querying ◽  
Natural Way

In reality, a lot of information is available only in an imperfect form. This might be due to imprecision, vagueness, uncertainty, incompleteness, or ambiguities. Traditional database systems can only adequately cope with perfect data. Among others, fuzzy set theory has been applied to deal with imperfections of data in a more natural way and to enhance the accessibility of databases. In this chapter, we give an overview of main trends in the research on flexible querying techniques that are based on fuzzy set theory. Both querying techniques for traditional databases as well as querying techniques for fuzzy databases are described. The discussion comprises both the relational and the object-oriented database modeling approaches.

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