Fuzzy Statistics

Fuzzy Statistics - James J. Buckley

Fuzzy set theory and probability theory are used to handle two different types of uncertainty. We use probability to study random phenomena. Each event itself has distinct meaning and not uncertain. However, due to the lack of sufficient condition the outcome for certain event to occur during a process cannot be determined.

In fuzzy set theory, concept or event itself does not have a clear definition. For example, "tall mean", how tall they are is not defined. Here, whether certain phenomena belong to this concept is difficult to determine. We call it fuzziness the uncertainty involved in a classification due to the imprecise concept definition. The root for fuzziness is that there exists transitions between two phenomena. Such transitions make it possible for us to label phenomena into either this or that class. Fuzzy set theory is the base for us to study membership relationships from the fuzziness of phenomena.

Fuzzy set theory and probability theory are used to handle two different types of uncertainty. We use probability to study random phenomena. Each event itself has distinct meaning and not uncertain. However, due to the lack of sufficient condition the outcome for certain event to occur during a process cannot be determined.

In fuzzy set theory, concept or event itself does not have a clear definition. For example, "tall mean", how tall they are is not defined. Here, whether certain phenomena belong to this concept is difficult to determine. We call it fuzziness the uncertainty involved in a classification due to the imprecise concept definition. The root for fuzziness is that there exists transitions between two phenomena. Such transitions make it possible for us to label phenomena into either this or that class. Fuzzy set theory is the base for us to study membership relationships from the fuzziness of phenomena.