Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems

Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems

Copyright: © 2014 |Pages: 441

ISBN13: 9781466649910|ISBN10: 1466649917|EISBN13: 9781466649927

DOI: 10.4018/978-1-4666-4991-0

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Chakraverty, S., editor. Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems. IGI Global, 2014. https://doi.org/10.4018/978-1-4666-4991-0

APA

Chakraverty, S. (Ed.). (2014). Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems. IGI Global. https://doi.org/10.4018/978-1-4666-4991-0

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Chakraverty, S., ed. Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems. Hershey, PA: IGI Global, 2014. https://doi.org/10.4018/978-1-4666-4991-0

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For various scientific and engineering problems, how to deal with variables and parameters of uncertain value is an important issue. Full analysis of the specific errors in measurement, observations, experiments, and applications are vital in dealing with the parameters taken to simplify the problem.

Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems aims to provide the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications. This book is an essential reference work for students, scholars, practitioners and researchers in the assorted fields of engineering and applied mathematics interested in a model for uncertain physical problems.

Table of Contents

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Front Materials

Title Page

Copyright Page

Advances in Computational Intelligence and Robotics (ACIR) Book Series

Editorial Advisory Board and List of Reviewers

Preface

Acknowledgment

Chapters

Chapter 1

Interval Mathematics as a Potential Weapon against Uncertainty (pages 1-38)

Hend Dawood

This chapter is devoted to introducing the theories of interval algebra to people who are interested in applying the interval methods to uncertainty analysis in science and engineering. In view of this purpose, we shall introduce the...

Chapter 2

Uncertainty Modeling Using Expert’s Knowledge as Evidence (pages 39-53)

D. Datta

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....

Chapter 3

Evidence-Based Uncertainty Modeling (pages 54-74)

Tazid Ali

Evidence is the essence of any decision making process. However in any situation the evidences that we come across are usually not complete. Absence of complete evidence results in uncertainty, and uncertainty leads to belief. The...

Chapter 4

Hybrid Set Structures for Soft Computing (pages 75-94)

Sunil Jacob John, Babitha KV

A Major problem in achieving an effective computational systems is the presence of inherent uncertainty in the computational problem itself. Among various techniques proposed to address this, the technique of soft computing is of...

Chapter 5

Source and m-Source Distances of Fuzzy Numbers and their Properties (pages 95-108)

Majid Amirfakhrian

In many applications of fuzzy logic and fuzzy mathematics we need (or it is better) to work with the same fuzzy numbers. In this chapter we present source distance and source distance between two fuzzy numbers. Also some properties...

Chapter 6

Construction of Normal Fuzzy Numbers using the Mathematics of Partial Presence (pages 109-126)

Hemanta K. Baruah

Every normal law of fuzziness can be expressed in terms of two laws of randomness defined in the measure theoretic sense. Indeed, two probability measures are necessary and sufficient to define a normal law of fuzziness. Hence, the...

Chapter 7

Numerical Solution of Fuzzy Differential Equations and its Applications (pages 127-149)

S. Chakraverty, Smita Tapaswini

Theory of fuzzy differential equations is the important new developments to model various science and engineering problems of uncertain nature because this theory represents a natural way to model dynamical systems under uncertainty....

Chapter 8

Modeling with Stochastic Fuzzy Differential Equations (pages 150-172)

Marek T. Malinowski

In the chapter, the author considers an approach used in the studies of stochastic fuzzy differential equations. These equations are new mathematical tools for modeling uncertain dynamical systems. Some qualitative properties of...

Chapter 9

Mathematics of Probabilistic Uncertainty Modeling (pages 173-204)

D. Datta

This chapter presents the uncertainty modeling using probabilistic methods. Probabilistic method of uncertainty analysis is due to randomness of the parameters of a model. Randomness of parameters is characterized by specified...

Chapter 10

Reaction-Diffusion Problems with Stochastic Parameters Using the Generalized Stochastic Finite Difference Method (pages 205-216)

Marcin Kamiński, Rafał Leszek Ossowski

The main aim of this work is to demonstrate the new stochastic discrete computational methodology consisting of the generalized stochastic perturbation technique and of the classical Finite Difference Method for the regular grids to...

Chapter 11

MV-Partitions and MV-Powers (pages 217-238)

C. Drossos, P. L. Theodoropoulos

In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-partitions together with a notion of refinement is tantamount a construction of an MV-power, analogous to Boolean power construction...

Chapter 12

An Algebraic Study of the Notion of Independence of Frames (pages 239-267)

Fabio Cuzzolin

The theory of belief functions or “theory of evidence” allows the mathematical representation of uncertain pieces of evidence on which decisions can be based. Frequently, different pieces of evidence belong to distinct, albeit...

Chapter 13

Pricing and Lot-Sizing Decisions in Retail Industry: A Fuzzy Chance Constraint Approach (pages 268-289)

R. Ghasemy Yaghin, S. M. T. Fatemi Ghomi, S. A. Torabi

Analysis of inventory systems involving market-oriented pricing decisions has recently become an interesting topic in the field of inventory control. Price and marketing expenditure are considered as important elements when selling...

Chapter 14

A New Approach for Suggesting Takeover Targets Based on Computational Intelligence and Information Retrieval Methods: A Case Study from the Indian Software Industry (pages 290-308)

Satyakama Paul, Andreas Janecek, Fernando Buarque de Lima Neto, Tshilidzi Marwala

In recent years researchers in financial management have shown considerable interest in predicting future takeover target companies in merger and acquisition (M&A) scenarios. However, most of these predictions are based upon multiple...

Chapter 15

Fuzzy Finite Element Method in Diffusion Problems (pages 309-328)

S. Chakraverty, S. Nayak

Diffusion is an important phenomenon in various fields of science and engineering. It may arise in a variety of problems viz. in heat transfer, fluid flow problem and atomic reactors etc. As such these diffusion equations are being...

Chapter 16

Uncertainty Quantification of Aeroelastic Stability (pages 329-356)

Georgia Georgiou, Hamed Haddad Khodaparast, Jonathan E. Cooper

The application of uncertainty analysis for the prediction of aeroelastic stability, using probabilistic and non-probabilistic methodologies, is considered in this chapter. Initially, a background to aeroelasticity and possible...

Chapter 17

Uncertain Static and Dynamic Analysis of Imprecisely Defined Structural Systems (pages 357-382)

S. Chakraverty, Diptiranjan Behera

This chapter presents the static and dynamic analysis of structures with uncertain parameters using fuzzy finite element method. Uncertainties presents in the parameters are modelled through convex normalised fuzzy sets. Fuzzy finite...

Back Materials

Compilation of References

About the Contributors

Index

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