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Fuzzy Sets and Their Operations

Authors: Shu-Jen Chen; Ching-Lai Hwang;

Fuzzy Sets and Their Operations

Abstract

Fuzzy set theory is developed for solving problems in which descriptions of activities and observations are imprecise, vague, and uncertain. The term “fuzzy” refers to the situation in which there are no well-defined boundaries of the set of activities or observations to which the descriptions apply. For example, one can easily assign a person seven feet tall to the “class of tall men”. But it would be difficult to justify the inclusion or exclusion of a six-foot tall person to that class, because the term “tall” does not constitute a well-defined boundary. This notion of fuzziness exists almost everywhere in our daily life, such as the “class of red flowers,” the “class of good kickers,” the “class of expensive cars,” or “numbers close to 10,” etc. These classes of objects cannot be well represented by classical set theory. In classical set theory, an object is either in a set or not in a set. An object cannot partially belong to a set.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Average
Average
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