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# What is Fuzzy Sets

Fuzzy sets are sets whose members have a degree of membership. They were introduced to be an extension of the classical sets, whose elements’ membership was assessed by binary numbers.
Published in Chapter:
Fuzzy Logic Estimator for Variant SNR Environments
Rosa Maria Alsina Pagès (Universitat Ramon Llull, Spain), Clàudia Mateo Segura (Universitat Ramon Llull, Spain), and Joan-Claudi Socoró Carrié (Universitat Ramon Llull, Spain)
DOI: 10.4018/978-1-59904-849-9.ch107
Abstract
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Fuzzy sets are a set theory approach in which set membership is less precise than having objects strictly in or out of the set.
A set which is a collection of object with graded membership function.
are an extension of classical set theory and are used in fuzzy logic. In classical set theory, the membership of elements in relation to a set is assessed in binary terms according to a crisp condition: An element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in relation to a set (Klir & Yuan, 1995).
It is a set of elements that have no strict boundaries. Examples of such sets are sets of “young people”, “expensive cars”, “successful companies”, etc.
These are capable of describing the vagueness and ambiguity inherent in real world data by assigning degrees of containment to the elements of the constituent sets in the universe of discourses.
A set which is a collection of object with graded membership function.
This type of sets contains a degree of fuzziness, where each of its elements as they are closer to 1 belongs more to this set, and as they get closer to 0 belong less to the set. As it is implied the elements in this set have values in the interval [0,1].
Mathematical means of representing vagueness and imprecise information.
Fuzzy sets is a set theory approach in which set membership is less precise than having objects strictly in or out of the set.
In a fuzzy set , elements can have degrees of membership. The concept of a fuzzy set was developed by Lotfi A. Zadeh.
In a fuzzy set, elements can have degrees of membership. The concept of a fuzzy set was developed by Lotfi A. Zadeh.
Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced by Lotfi A. Zadeh and Dieter Klaua in 1965 as an extension of the classical notion of set. Fuzzy relations, which are used now in different areas, such as linguistics decision-making and clustering, are special cases of L -relations when L is the unit interval [0, 1].
In 1965, Lotfi A. Zadeh introduced fuzzy sets. Fuzzy sets are those sets whose elements have a degree of membership i.e., every fuzzy set is characterized by a membership function.
It is a set of elements which have no strict boundaries. Examples of such sets are sets of “young people”, “expensive cars”, “successful companies”, etc.
Let U be a set of objects so called universe of discourse. A fuzzy set F in U is characterized by a function of inclusion µF taking values in the interval [0,1], i.e. µF: U ?[0,1]; where µF(u) represents the degree in which u ? U belongs to fuzzy set F.
A generalization of ordinary sets by allowing a degree of membership for their elements. This theory was proposed by Lofti Zadeh in 1965. Fuzzy sets are the base of fuzzy logic.