Statistics with Imprecise Data
نویسندگان
چکیده
Article Outline Glossary I. Definition of the Subject and Its Importance II. Introduction III. Mathematical modeling of imprecise data IV. Fuzzy random variables V. Statistical analysis of random fuzzy perceptions VI.1 Fuzzy estimators and fuzzy confidence intervals VI.2 Fuzzy statistical tests VII. Statistical analysis of random fuzzy variables VIII. Future directions Bibliography Glossary Fuzzy estimators Estimators of 'parameters' of probability distributions, or other characteristics, of random variables/fuzzy random variables (such as e.g. the expected value/the fuzzy expected value) when statistical data are imprecise and are described by means of fuzzy sets. Fuzzy random variable Random element whose observed values are described by fuzzy sets. Fuzzy set Generalization of a classical notion of a set. In contrast to the case of a classical set, each element x of a fuzzy set may belong to it to a degree described by the so-called membership function µ(x). Thus, the fuzzy set may be defined as a set of ordered pairs (x, µ(x)), where x belongs to a set X called the universe of discourse or
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