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What is Fuzzy Set

A set of ordered pairs composed of the elements and corresponding degrees of membership to this set.
Published in Chapter:
Hybrid Multi-Criteria Models: Joint Health and Safety Unit Selection on Hybrid Multi-Criteria Decision Making
Ömer Faruk Efe (Afyon Kocatepe University, Turkey)
DOI: 10.4018/978-1-7998-2216-5.ch004
Abstract
JHSUs should have occupational safety specialists, workplace physicians, and other health personnel to establish and provide services. To provide occupational safety services in the most effective operating environment, it is necessary to select the most appropriate JHSU. This chapter provides a hybrid model to assist the JHSU selection process. Using fuzzy logic linguistic variables makes an important contribution to decision making in uncertain environment. The hybrid model using Fuzzy AHP (Analytical Hierarchy Process) and Fuzzy TOPSIS (Technique for Similarity Sorting Preference for Ideal Solution) approaches were used in JHSU selection. The most important criterion was found to be the references of JHSU. Candidate JHSUs were evaluated on the basis of criteria with fuzzy TOPSIS. Five alternative JHSU were evaluated. Alternative 2 was found to be the most appropriate choice. A numerical example is presented to demonstrate the effectiveness of the proposed hybrid model.
More Results
Fuzzy set is expressed as a function and the elements of the set are mapped into their degree of membership. A set with the fuzzy boundaries are “hot,” “medium,” or “cold” for temperature.
A generalization of the definition of the classical set. A fuzzy set is characterized by a membership function, which maps the members of the universe into the unit interval, thus assigning to elements of the universe degrees of belongingness with respect to a set.
An extension of a classical notion of a set whose elements have degrees of membership.
Contrary to the classical sets, the approach that reveals that in fuzzy sets, the membership degrees of the elements can vary infinitely in the range [0, 1].
The ambiguity, vagueness and uncertainty in real world knowledge bases can be determined by this soft computing technique.
One of the earliest uncertainty based models proposed by L.A.Zadeh in 1965 that assigns graded memberships to elements instead of binary membership provided by Crisp sets.
Any set that allows its members to have different grades of membership (membership function) in the interval [0,1]. A numerical value between 0 and 1 that represents the degree to which an element belongs to a particular set, also referred to as membership value.
Fuzzy sets are an extension of the classical notion of sets whose elements have degrees of membership.
A set whose elements have degrees of membership, as opposed to a classical set.
A fuzzy set on a classical set ? is defined as follows: The MF µA(x) quantifies the grade of membership of the elements x to the fundamental set ?.
A set, which each element is accompanied by the degree of membership.
A fuzzy set is any set that allows its members to have different grades of membership (membership function) in the interval [0,1]. A numerical value between 0 and 1 that represents the degree to which an element belongs to a particular set, also referred to as membership value.
This is yet another imprecise model introduced by L.A. Zadeh in 1965, where the concept of membership function was introduced. Unlike crisp sets here the belongingness of elements to a fuzzy set are graded in the sense that these values can lie in the interval [0, 1].
A set whose elements have degrees of membership rather than full membership or non-membership as in conventional crisp set. A fuzzy set has no sharp boundary.
A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership.
A set of ordered pairs composed of the elements and corresponding degrees of membership to this set.
A class of objects with a continuum of grades of membership ranging between 0 and 1. Differ from Boolean or crisp sets which are limited to only values of 1 or 0.
A fuzzy set F of U is defined by the mapping F : U ? I = [0, 1].
In mathematics, fuzzy sets (a.k.a. uncertain sets) are somewhat like sets whose elements have membership grades. The fuzzy set generalizes classical set, since the characteristic function of classical set is a special case of the membership function of fuzzy set, if the latter only take values 0 or 1. These sets can be used in a wide range of domains in which information is imprecise or incomplete.
Extended set where the belonging of an element is given by a membership function whose range is the [0, 1] interval.
Fuzzy set is expressed as a function and the elements of the set are mapped into their degree of membership. A set with the fuzzy boundaries are “hot,” “medium,” or “cold” for temperature.
An extension of classical set theory. Fuzzy set theory used in Fuzzy Logic, permits the gradual assessment of the membership of elements in relation to a set
A set that can have elements with different crisp membership degrees between 0 and 1 interval.
A set in which the belongingness of elements to the set are given by membership functions providing values lying between 0 and 1.
A set of elements with a real-valued membership function describing their grades.
It is one of the most popular models of uncertainty introduced by Zadeh in 1965 where each element has a grade of belongingness to the set instead of the dichotomous belongingness in case of crisp sets.
A soft computing technique to determine the ambiguity, vagueness and uncertainty in real world knowledge bases.
A generalization of the definition of the classical set. A fuzzy set is characterized by a membership function, which maps the member of the universe into the unit interval, thus assigning to elements of the universe degrees of belongingness with respect to a set.
An extension of the classical set whose memberships have degrees of membership.
A fuzzy set is a generalization of an ordinary (crisp) set. A fuzzy set S allows an element to have partial degree (between zero and one) of membership in S.
Fuzzy set was introduced by Zadeh (1965). Fuzzy set is the extension of crisp set. In fuzzy, each and every element has the degrees of membership value which lies between [0, 1]. A fuzzy set is the pair ( S , µ) where S is a set and µ : S ? [0,1].
Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set.
It is an extension of the concept of fuzzy set, introduced by Atanassov in 1986. It is more general than fuzzy set. In fuzzy set the non-membership of an element in a set is one’s complement of its membership. However, this may not be the same in many real life situations because of the hesitation component. In order to model this in intuitionistic fuzzy sets the sum of membership and non-membership values of an element is not restricted to be one.
Set of elements with membership values between 0 and 1 for each of the clusters to which it belongs according to fuzzy set theory by Zadeh.
A mapping from a universe of discourse—definition domain of the fuzzy set—into the interval [0,1]. The concept of fuzzy set extends the notion of Boolean membership to a set to the notion of degree of membership.
Fuzzy set is expressed as a function and the elements of the set are mapped into their degree of membership. A set with the fuzzy boundaries are ‘hot’, ’medium’, or ‘cold’ for temperature.
A set whose elements have degrees of membership, rather than crisp membership or non-membership in classical sets.
A generalization of the concept of a crisp set introduced by Zadeh in 1965. It is characterized by a membership function defined on the universal set U and taking values in the interval [0, 1], thus assigning a membership degree to each element of U with respect to the fuzzy set. It covers the real situations where certain definitions have no clear boundaries (e.g. the high mountains of a country).
Fuzzy set is expressed as a function and the elements of the set are mapped into their degree of membership. A set with the fuzzy boundaries are “hot,” “medium,” or “cold” for temperature.