Application of Uncertain Variables to Knowledge-Based Resource Distribution

Application of Uncertain Variables to Knowledge-Based Resource Distribution

Donat Orski (Wroclaw University of Technology, Poland)
Copyright: © 2009 |Pages: 22
DOI: 10.4018/978-1-59904-576-4.ch004
OnDemand PDF Download:


The chapter concerns a class of systems composed of operations performed with the use of resources allocated to them. In such operation systems, each operation is characterized by its execution time depending on the amount of a resource allocated to the operation. The decision problem consists in distributing a limited amount of a resource among operations in an optimal way, that is, in finding an optimal resource allocation. Classical mathematical models of operation systems are widely used in computer supported projects or production management, allowing optimal decision making in deterministic, well-investigated environments. In the knowledge-based approach considered in this chapter, the execution time of each operation is described in a nondeterministic way, by an inequality containing an unknown parameter, and all the unknown parameters are assumed to be values of uncertain variables characterized by experts. Mathematical models comprising such two-level uncertainty are useful in designing knowledge-based decision support systems for uncertain environments. The purpose of this chapter is to present a review of problems and algorithms developed in recent years, and to show new results, possible extensions and challenges, thus providing a description of a state-of-the-art in the field of resource distribution based on the uncertain variables.
Chapter Preview


Among many theories of uncertainty (Klir, 2006) developed for different applications the uncertain variables introduced by Bubnicki (2001a, 2001b) may be considered as a useful tool for modeling expert’s knowledge in knowledge-based decision systems. In the definition of the uncertain variable we consider two soft properties: “” which means “ is approximately equal to ” or “ is the approximate value of ,” and “” which means “ approximately belongs to the set ” or “the approximate value of belongs to .” The uncertain variable is defined by a set of values (real number vector space), the function (i.e., the certainty index that , given by an expert) and the following definitions for :


The function is called a certainty distribution. Let us consider a plant with the input vector and the output vector , described by a relation (relational knowledge representation) where the vector of unknown parameters is assumed to be a value of an uncertain variable described by the certainty distribution given by an expert. If the relation is not a function, then the value determines a set of possible outputs . For the requirement given by a user, we can formulate the following decision problem: For the given , and one should find the decision maximizing the certainty index that the set of possible outputs approximately belongs to (i.e., belongs to for an approximate value of ). Then

where . It is easy to see that maximizes where is a set of all such that the implication is satisfied. The uncertain variables are dedicated to analysis and decision problems (Bubnicki, 2002, 2004a) in a class of systems containing a decision plant described by a relational knowledge representation with unknown parameter characterized by an expert.

Complete Chapter List

Search this Book:
Table of Contents
Dariusz Król, Ngoc Thanh Nguyen
Chapter 1
Juliusz L. Kulikowski
In this chapter, a concept of using incomplete or fuzzy ontologies in decision making is presented. A definition of ontology and of ontological... Sample PDF
Logical Inference Based on Incomplete and/or Fuzzy Ontologies
Chapter 2
Amelia Badica, Costin Badica, Elvira Popescu
The Web is designed as a major information provider for the human consumer. However, information published on the Web is difficult to understand and... Sample PDF
Using Logic Programming and XML Technologies for Data Extraction from Web Pages
Chapter 3
Andreas Jacobsson, Paul Davidsson
This chapter introduces a formal model of virtual enterprises, as well as an analysis of their creation and operation. It is argued that virtual... Sample PDF
A Formal Analysis of Virtual Enterprise Creation and Operation
Chapter 4
Donat Orski
The chapter concerns a class of systems composed of operations performed with the use of resources allocated to them. In such operation systems... Sample PDF
Application of Uncertain Variables to Knowledge-Based Resource Distribution
Chapter 5
Clive Fencott
This chapter undertakes a methodological study of virtual environments (VEs), a specific subset of interactive systems. It takes as a central theme... Sample PDF
A Methodology of Design for Virtual Environments
Chapter 6
Salvador Sanchez-Alonso, Dirk Frosch-Wilke
In current organizations, the models of knowledge creation include specific processes and elements that drive the production of knowledge aimed at... Sample PDF
An Ontological Representation of Competencies as Codified Knowledge
Chapter 7
Marcos De Oliveira, Martin Purvis
In the distributed multi-agent systems discussed in this chapter, heterogeneous autonomous agents interoperate in order to achieve their goals. In... Sample PDF
Aspects of Openness in Multi-Agent Systems: Coordinating the Autonomy in Agent Societies
Chapter 8
Kostas Kolomvatsos, Stathes Hadjiefthymiades
The field of Multi-agent systems (MAS) has been an active area for many years due to the importance that agents have to many disciplines of research... Sample PDF
How Can We Trust Agents in Multi-Agent Environments? Techniques and Challenges
Chapter 9
Mariusz Nowostawski
The concept of autonomy is one of the central concepts in distributed computational systems, and in multi-agent systems in particular. With diverse... Sample PDF
The Concept of Autonomy in Distributed Computation and Multi-Agent Systems
Chapter 10
Maryam Purvis, Toktam Ebadi, Bastin Tony Roy Savarimuthu
The objective of this research is to describe a mechanism to provide an improved library management system using RFID and agent technologies. One of... Sample PDF
An Agent-Based Library Management System Using RFID Technology
Chapter 11
Sharmila Savarimuthu, Martin Purvis, Maryam Purvis, Mariusz Nowostawski
Societies are made of different kinds of agents, some cooperative and uncooperative. Uncooperative agents tend to reduce the overall performance of... Sample PDF
Mechanisms to Restrict Exploitation and Improve Societal Performance in Multi-Agent Systems
Chapter 12
Bastin Tony Roy Savarimuthu, Maryam Purvis, Stephen Cranefield
Norms are shared expectations of behaviours that exist in human societies. Norms help societies by increasing the predictability of individual... Sample PDF
Norm Emergence in Multi-Agent Societies
Chapter 13
Scott A. DeLoach, Madhukar Kumar
This chapter provides an overview of the Multi-agent Systems Engineering (MaSE) methodology for analyzing and designing multi-agent systems. MaSE... Sample PDF
Multi-Agent Systems Engineering: An Overview and Case Study
Chapter 14
František Capkovic
An alternative approach to modeling and analysis of agents’ behaviour is presented in this chapter. The agents and agent systems are understood here... Sample PDF
Modeling, Analysing, and Control of Agents Behaviour
Chapter 15
Martin Tabakov
This chapter presents a methodology for an image enhancement process of computed tomography perfusion images by means of partition generated with... Sample PDF
Using Fuzzy Segmentation for Colour Image Enhancement of Computed Tomography Perfusion Images
Chapter 16
Giovanni Vincenti, Goran Trajkovski
This chapter presents an innovative approach to the field of information fusion. Fuzzy mediation differentiates itself from other algorithms, as... Sample PDF
Fuzzy Mediation in Shared Control and Online Learning
Chapter 17
Adam Jatowt, Yukiko Kawai, Katsumi Tanaka
The Web is a useful data source for knowledge extraction, as it provides diverse content virtually on any possible topic. Hence, a lot of research... Sample PDF
Utilizing Past Web for Knowledge Discovery
Chapter 18
Dariusz Król
In this chapter, we propose a generic framework in C# to distribute and compute tasks defined by users. Unlike the more popular models such as... Sample PDF
Example-Based Framework for Propagation of Tasks in Distributed Environments
Chapter 19
Xia Xie, Jin Huang, Song Wu, Hai Jin, Melvin Koh, Jie Song, Simon See
In this chapter, we present a survey on some of the commercial players in the Grid industry, existing research done in the area of market-based Grid... Sample PDF
Survey on the Application of Economic and Market Theory for Grid Computing
About the Contributors