Ebook: Fundamentals of Statistics with Fuzzy Data

This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general.

HUNG T. NGUYEN is a professor of Mathematical Sciences at New Mexico State University, USA.

BERLIN WU is a professor of Mathematical Sciences at National Chengchi University, Taipei, Taiwan.

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This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general.

HUNG T. NGUYEN is a professor of Mathematical Sciences at New Mexico State University, USA.

BERLIN WU is a professor of Mathematical Sciences at National Chengchi University, Taipei, Taiwan.

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This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general.

HUNG T. NGUYEN is a professor of Mathematical Sciences at New Mexico State University, USA.

BERLIN WU is a professor of Mathematical Sciences at National Chengchi University, Taipei, Taiwan.

Content:
Front Matter....Pages -
Introduction....Pages 1-4
Set-valued Data....Pages 5-12
Modeling of Fuzzy Data....Pages 13-34
Random Fuzzy Sets....Pages 35-43
Aspects of Statistical Inference....Pages 45-70
Convergence of Random Fuzzy Sets....Pages 71-108
Fuzzy Statistical Analysis and Estimation....Pages 109-128
Tests of Hypothesis: Means....Pages 129-144
Fuzzy Time Series Analysis and Forecasting....Pages 145-182
Back Matter....Pages -

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This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general.

HUNG T. NGUYEN is a professor of Mathematical Sciences at New Mexico State University, USA.

BERLIN WU is a professor of Mathematical Sciences at National Chengchi University, Taipei, Taiwan.

Content:
Front Matter....Pages -
Introduction....Pages 1-4
Set-valued Data....Pages 5-12
Modeling of Fuzzy Data....Pages 13-34
Random Fuzzy Sets....Pages 35-43
Aspects of Statistical Inference....Pages 45-70
Convergence of Random Fuzzy Sets....Pages 71-108
Fuzzy Statistical Analysis and Estimation....Pages 109-128
Tests of Hypothesis: Means....Pages 129-144
Fuzzy Time Series Analysis and Forecasting....Pages 145-182
Back Matter....Pages -
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