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Statistical Methods for Fuzzy Data
About this book
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively.
Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information.
Key Features:
- Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data.
- Describes methods of increasing importance with applications in areas such as environmental statistics and social science.
- Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples.
- Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data.
This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Statistical Methods for Fuzzy Data by Reinhard Viertl in PDF and/or ePUB format, as well as other popular books in Matemáticas & Probabilidad y estadística. We have over one million books available in our catalogue for you to explore.
Information
Part I
FUZZY INFORMATION
Fuzzy information is a special kind of information and information is an omnipresent word in our society. But in general there is no precise definition of information.
However, in the context of statistics which is connected to uncertainty, a possible definition of information is the following: Information is everything which has influence on the assessment of uncertainty by an analyst. This uncertainty can be of different types: data uncertainty, nondeterministic quantities, model uncertainty, and uncertainty of a priori information.
Measurement results and observational data are special forms of information. Such data are frequently not precise numbers but more or less nonprecise, also called fuzzy. Such data will be considered in the first chapter.
Another kind of information is probabilities. Standard probability theory is considering probabilities to be numbers. Often this is not realistic, and in a more general approach probabilities are considered to be so-called fuzzy numbers.
The idea of generalized sets was originally published in Menger (1951) and the term ‘fuzzy set’ was coined in Zadeh (1965).
1
Fuzzy data
All kinds of data which cannot be presented as precise numbers or cannot be precisely classified are called nonprecise or fuzzy. Examples are data in the form of linguistic descriptions like high temperature, low flexibility and high blood pressure. Also, precision measurement results of continuous variables are not precise numbers but always more or less fuzzy.
1.1 One-dimensional fuzzy data
Measurement results of one-dimensional continuous quantities are frequently idealized to be numbers times a measurement unit. However, real measurement results of continuous quantities are never precise numbers but always connected with uncertaint...
Table of contents
- Cover
- Title Page
- Copyright
- Preface
- Part I: Fuzzy Information
- Part II: Descriptive Statistics for Fuzzy Data
- Part III: Foundations of Statistical Inference With Fuzzy Data
- Part IV: Classical Statistical Inference for Fuzzy Data
- Part V: Bayesian Inference and Fuzzy Information
- Part VI: Regression Analysis and Fuzzy Information
- Part VII: Fuzzy time series
- Part VIII: Appendices
- References
- Index