The Signed Distance Measure in Fuzzy Statistical Analysis

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.

Provides a didactical approach to advanced fuzzy statistical methods, together with examples and illustrations Compares fuzzy statistical approaches with standard classical approaches Addresses theoretical advances, applications and programming tools

Autorentext

Dr. Re dina Berkachy is a Senior Researcher at the Applied Statistics and Modelling (ASAM) group at the Department of Informatics, Faculty of Management, Economics and Social Sciences of the University of Fribourg, and a Senior Lecturer at the School of Engineering and Architecture of Fribourg of the University of Applied Sciences and Arts Western Switzerland. She holds a BSc in Mathematics from the Lebanese University (Lebanon), a MSc in Numerical Analysis and Mathematical Modelling from the Saint-Joseph University of Beirut (Lebanon), and a PhD in Statistics from the University of Fribourg (Switzerland). Her main research interests are fuzzy statistics and their applications, fuzzy decision making and mathematical and statistical modelling. She is also an R developer and the author of FuzzySTs package available on CRAN.

Inhalt

• 1. Introduction. - Part I Theoretical Part. - 2. Fundamental Concepts on Fuzzy Sets. - 3. Fuzzy Rule-Based Systems. - 4. Distances Between Fuzzy Sets. - 5. Fuzzy Random Variables and Fuzzy Distributions. - 6. Fuzzy Statistical Inference. - Conclusion Part I. - Part II Applications. - 7. Evaluation of Linguistic Questionnaire. - 8. Fuzzy Analysis of Variance. - Part III An R Package for Fuzzy Statistical Analysis: A Detailed
     Description. - 9. FuzzySTs: Fuzzy Statistical Tools: A Detailed Description. - Conclusion.