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The signed distance measure in fuzzy statistical analysis : theoretical, empirical and programming advances / Rédina Berkachy.

Berkachy, Rédina, author.
2021
QA276.5 .B47 2021
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Title
The signed distance measure in fuzzy statistical analysis : theoretical, empirical and programming advances / Rédina Berkachy.
Author
Berkachy, Rédina, author.
ISBN
9783030769161 (electronic bk.)
303076916X (electronic bk.)
9783030769154
3030769151
DOI
https://doi.org/10.1007/978-3-030-76916-1
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations (some color).
Item Number
10.1007/978-3-030-76916-1 doi
Call Number
QA276.5 .B47 2021
Dewey Decimal Classification
519.5
Summary
The main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called FuzzySTs which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 12, 2021).
Series
Fuzzy management methods.
Available in Other Form
Print version: 9783030769154
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Intro
Foreword
Preface
Acknowledgements
Contents
List of Figures
List of Tables
1 Introduction
References
Part I Theoretical Part
2 Fundamental Concepts on Fuzzy Sets
2.1 Fuzzy Sets and Fuzzy Numbers
2.2 Common Fuzzy Numbers
2.3 Vector of Fuzzy Numbers and Fuzzy Vector
2.4 Logical Operations on Fuzzy Sets
2.5 Extension Principle
2.6 Arithmetic Operations on Fuzzy Sets
References
3 Fuzzy Rule-Based Systems
3.1 Fuzzification
3.2 Inference Rules
3.3 Defuzzification
References
4 Distances Between Fuzzy Sets

5.3.1 The Kwakernaak-Kruse and Meyer Approach
5.3.2 The Féron-Puri and Ralescu Approach
5.3.3 Synthesis
5.4 Expectation and Variance
5.4.1 The Kwakernaak-Kruse and Meyer Approach
5.4.2 The Féron-Puri and Ralescu Approach
5.4.3 Synthesis
5.5 Estimators of the Fuzzy Distributions Parameters
5.5.1 The Mean
5.5.2 The Sample Moments
5.6 Simulation
References
6 Fuzzy Statistical Inference
6.1 Testing Hypotheses by the Classical Approach
6.2 Fuzzy Hypotheses
6.3 Fuzzy Confidence Intervals
6.3.1 Fuzzy Confidence Intervals for Pre-defined Parameter

6.3.2 Fuzzy Confidence Intervals with the Likelihood Function
Procedure
6.3.3 Bootstrap Technique for the Approximation of the Likelihood Ratio
6.3.4 Simulation Study
6.3.5 Numerical Example
6.4 Fuzzy Hypotheses Testing
6.4.1 Fuzzy Hypotheses Testing Using Fuzzy Confidence Intervals
6.4.2 Defuzzification of the Fuzzy Decisions
6.4.3 Fuzzy p-Values
6.4.4 Defuzzification of the Fuzzy p-Value
6.5 Applications: Finanzplatz
6.5.1 Application 1
6.5.2 Application 2
6.5.3 Classical Versus Fuzzy Hypotheses Testing
References
Conclusion Part I

Part II Applications
7 Evaluation of Linguistic Questionnaire
7.1 Questionnaire in Fuzzy Terms
7.2 Readjustement of Weights
7.3 Global and Individual Evaluations
7.4 Indicators of Information Rate of a Data Base
7.5 Application: Finanzplatz
7.6 Analyses by Simulations on the Individual Evaluations
7.7 Conclusion
Appendix
B Description of the Finanzplatz Data Base
C Results of the Applications of Chap. 7
References
8 Fuzzy Analysis of Variance
8.1 Classical Multi-Ways Analysis of Variance
8.2 Introduction to Fuzzy Regression
8.3 Fuzzy Multi-Ways Analysis of Variance.

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