Uncertainty and Vagueness in Knowledge Based Systems: Numerical Methods


The primary aim of this monograph is to provide a formal framework for the representation and management of uncertainty and vagueness in the field of artificial intelligence. Particular emphasis is put on a thorough analysis of these phenomena and on the development of sound mathematical modeling approaches. The scope of the book also includes implementational aspects and a valuation of existing models and systems. The fundamental claim of the book is that vagueness and uncertainty can be handled adequately by ...
See more details below
Paperback (Softcover reprint of the original 1st ed. 1991)
BN.com price
Other sellers (Paperback)
  • All (8) from $95.61   
  • New (7) from $95.61   
  • Used (1) from $156.38   
Sending request ...


The primary aim of this monograph is to provide a formal framework for the representation and management of uncertainty and vagueness in the field of artificial intelligence. Particular emphasis is put on a thorough analysis of these phenomena and on the development of sound mathematical modeling approaches. The scope of the book also includes implementational aspects and a valuation of existing models and systems. The fundamental claim of the book is that vagueness and uncertainty can be handled adequately by using measure-theoretic methods. The presentation of applicable knowledge representation formalisms and reasoning algorithms shows that efficiency requirements do not necessarily require renunciation of an uncompromising mathematical modeling approach. The results are used to evaluate systems based on probabilistic methods as well as on non-standard concepts such as certainty factors, fuzzy sets, and belief functions. The book is self-contained and addresses researchers and practitioners in the field of knowledge based sys- tems and decision support systems. It is suitable as a textbook for graduate-level students in AI, operations research, and applied probability.
Read More Show Less

Product Details

  • ISBN-13: 9783642767043
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/21/2011
  • Series: Artificial Intelligence Series
  • Edition description: Softcover reprint of the original 1st ed. 1991
  • Edition number: 1
  • Pages: 491
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.03 (d)

Table of Contents

1. General Considerations of Uncertainty and Vagueness.- 1.1 Artificial Intelligence.- 1.2 Modeling Ignorance.- 1.3 The Scope of the Book.- 2. Introduction.- 2.1 Basic Notations.- 2.2 A Simple Example.- 2.3 Vagueness and Uncertainty.- 2.3.1 Modeling Vague Data.- 2.3.2 Modeling Partial Belief.- 3. Vague Data.- 3.1 Basic Concepts.- 3.2 On the Origin of Vague Data.- 3.3 Uncertainty Handling by Means of Layered Contexts.- 3.3.1 Possibility and Necessity.- 3.3.2 Operations with Vague Data.- 3.3.3 On the Interpretation of Vague Data.- 3.4 The General Case.- 3.5 Concluding Remarks.- 4. Probability Theory.- 4.1 Basic Concepts.- 4.1.1 Axiomatic Probability Theory.- 4.1.2 On the Interpretation of a Probability.- 4.1.3 Practical Aspects.- 4.2 Probabilities on Different Sample Spaces.- 4.3 Bayesian Inference.- 4.4 Classes of Probabilities.- 4.5 Decision Making Aspects.- 4.6 Aggregating Probability Distributions.- 4.7 Concluding Remarks.- 5. Random Sets.- 5.1 Random Variables.- 5.2 The Notion of a Random Set.- 5.2.1 Weighted Sets versus Random Sets.- 5.2.2 On the Updating of Random Sets.- 5.3 Decision Making in the Context of Vague Data.- 5.4 The Notion of an Information Source.- 5.4.1 Updating Information Sources.- 5.4.2 The Combination of Information Sources.- 5.5 Concluding Remarks.- 6. Mass Distributions.- 6.1 Basic Concepts.- 6.1.1 Condensed Representations of Random Sets.- 6.1.2 Belief Functions.- 6.2 Different Frames of Discernment.- 6.2.1 Specializations.- 6.2.2 Strict Specializations.- 6.2.3 Orthogonal Extensions.- 6.2.4 Conjunctive and Disjunctive Extensions.- 6.3 Measures for Possibility/Necessity.- 6.4 Generalized Mass Distributions.- 6.5 Decision Making with Mass Distributions.- 6.6 Knowledge Representation with Mass Distributions.- 6.6.1 Encoding Knowledge by Mass Distributions.- 6.6.2 Integration of Different Pieces of Knowledge.- 6.7 Simplifying Assumptions.- 6.8 Concluding Remarks.- 7. On Graphical Representations.- 7.1 Graphs and Trees.- 7.1.1 Undirected Graphs.- 7.1.2 Trees.- 7.2 Hypergraphs and Hypertrees.- 7.2.1 Hypertrees.- 7.2.2 Simple Hypertrees.- 7.3 Analysis of Simple Hypertrees.- 7.3.1 Markov Trees.- 7.3.2 Knowledge Representation with Hypergraphs.- 7.4 Dependency Networks.- 7.5 Triangulated Graphs.- 7.6 Directed Acyclic Graphs.- 7.7 Concluding Remarks.- 8. Modeling Aspects.- 8.1 Rule Based Approaches.- 8.2 Model Based Representations.- 8.2.1 Requirements on Models.- 8.2.2 On the Structure of Models.- 8.2.3 On the Choice of Mathematical Models.- 8.2.4 Selected Problems with Mathematical Models.- 8.3 Dependency Network Based Systems.- 9. Heuristic Models.- 9.1 MYCIN — The Certainty Factor Approach.- 9.1.1 The Mathematical Model.- 9.1.2 Uncertainty Representation in MYCIN.- 9.1.3 Related Models and Proposals.- 9.1.4 Conclusions.- 9.2 RUM — Triangular Norms and Conorms.- 9.2.1 Families of Uncertainty Calculi — Triangular Norms and Conorms.- 9.2.2 RUM.- 9.2.3 Final Remarks.- 9.3 INFERNO — A Bounds Propagation Architecture.- 9.4 Other Heuristic Models.- 10. Fuzzy Set Based Models.- 10.1 Fuzzy Sets.- 10.2 Possibility Distributions.- 10.3 Approximate Reasoning.- 10.4 Reasoning with Fuzzy Truth Value.- 10.5 Conclusions.- 11. Reasoning with L-Sets.- 11.1 Knowledge Representation with L-Sets.- 11.2 On the Interpretation of Vague Rules.- 11.3 L-Sets on Product Spaces.- 11.4 Local Computation of Marginal ¿-Sets.- 11.5 The Propagation Algorithm.- 11.6 Aspects of Implementation.- 12. Probability Based Models.- 12.1 The Interpretation of Rules.- 12.2 The Straightforward Use of Probabilities.- 12.2.1 The Model of Ishizuka et al.- 12.2.2 The Model of Adams.- 12.2.3 Discussions.- 12.3 PROSPECTOR — Inference Networks.- 12.3.1 The Inference Network Model.- 12.3.2 PROSPECTOR.- 12.3.3 Discussion and Related Work.- 12.4 Decomposable Graphical Models.- 12.4.1 The Model of Pearl.- 12.4.2 MUNIN — An Application.- 12.4.3 HUGIN — A Professional Tool.- 12.5 Propagation Based on Dependency Networks.- 12.5.1 Knowledge Representation.- 12.5.2 Graph Structure and Conditional Independence.- 12.5.3 Local Computation of Marginal Probability Distributions...- 12.5.4 The Propagation Algorithm.- 12.5.5 Aspects of Implementation.- 12.5.6 Numerical Example.- 12.6 Concluding Remarks.- 13. Models Based on the Dempster-Shafer Theory of Evidence.- 13.1 The Mathematical Theory of Evidence.- 13.2 Knowledge Representation Aspects.- 13.2.1 Representing Pieces of Knowledge.- 13.2.2 Integration of Pieces of Evidence.- 13.3 The Straightforward Use of Belief Functions.- 13.3.1 The Model of Ishizuka et al.- 13.3.2 The Model of Ginsberg.- 13.3.3 Discussion, Related Work.- 13.4 Belief Functions in Hierarchical Hypothesis Spaces.- 13.4.1 Gordon and Shortliffe’s Extension to MYCIN.- 13.4.2 The Model of Yen — A Quasi-Probabilistic Approach.- 13.5 MacEvidence — Belief Propagation in Markov Trees.- 13.5.1 Belief Propagation in Markov Trees.- 13.5.2 MacEvidence.- 13.5.3 Discussion.- 13.6 Conclusions.- 14. Reasoning with Mass Distributions.- 14.1 Matrix Notation for Specializations.- 14.1.1 Specialization Matrices.- 14.1.2 Composition of Specialization Matrices.- 14.1.3 Properties of Specialization Matrices.- 14.2 Specializations in Product Spaces.- 14.3 Knowledge Representation with Mass Distributions.- 14.4 Local Computations with Mass Distributions.- 14.5 The Propagation Algorithm.- 14.6 Aspects of Implementation.- 15. Related Research.- 15.1 Nonstandard Logics.- 15.2 Integrating Uncertainty Calculi and Logics.- 15.3 Symbolic Methods.- 15.4 Conclusions.- References.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)