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What is Fuzzy Set

Multi-Criteria Decision Analysis in Management
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)
Copyright: © 2020 |Pages: 23
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.
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Adaptive Neuro-Fuzzy Inference System in Agriculture
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.
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Intuitionistic Fuzzy Image Processing
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.
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Rough Approximations on Hesitant Fuzzy Sets
An extension of a classical notion of a set whose elements have degrees of membership.
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Application of Fuzzy Analytic Hierarchy Process for Evaluation of Ankara-Izmir High-Speed Train Project
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].
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Multilevel and Color Image Segmentation by NSGA II Based OptiMUSIG Activation Function
The ambiguity, vagueness and uncertainty in real world knowledge bases can be determined by this soft computing technique.
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On Theory of Multisets and Applications
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.
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A Hybrid GA-GSA Algorithm for Optimizing the Performance of an Industrial System by Utilizing Uncertain Data
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.
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Application of Soft Set in Game Theory
Fuzzy sets are an extension of the classical notion of sets whose elements have degrees of membership.
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Fuzzy System Dynamics of Manpower Systems
A set whose elements have degrees of membership, as opposed to a classical set.
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Introduction to Fuzzy Logic and Fuzzy Linear Programming
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 ?.
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Predicting Uncertain Behavior and Performance Analysis of the Pulping System in a Paper Industry using PSO and Fuzzy Methodology
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.
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Application of Rough Set Based Models in Medical Diagnosis
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].
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Fuzzy System Dynamics: An Application to Supply Chain Management
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.
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Enhanced Fuzzy Assessment Methodology to Find Overlapping in Membership Function Using K Ratio to Find the Yield of Rice
A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership.
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Evaluation of Hotel Web Pages According to User Suitability
A set of ordered pairs composed of the elements and corresponding degrees of membership to this set.
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Fuzzy Set Qualitative Comparative Analysis: Application of Fuzzy Sets in the Social Sciences
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.
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Some Hybrid Soft Sets and Their Application in Decision Making
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Tanimoto Similarity Coefficients Measuring Bipolar q-Rung Picture Fuzzy Information and Their Applications
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.
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Processing of Queries with Fuzzy Similarity Domains
Extended set where the belonging of an element is given by a membership function whose range is the [0, 1] interval.
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Fuzzy Expert System in Agriculture Domain
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.
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Handling Fuzzy Similarity for Data Classification
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
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Interval Type II Fuzzy Number Generation From Data Set Applied to Sedation Stage Classification
A set that can have elements with different crisp membership degrees between 0 and 1 interval.
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An Uncertainty-Based Model for Optimized Multi-Label Classification
A set in which the belongingness of elements to the set are given by membership functions providing values lying between 0 and 1.
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Fuzzy Control Systems: An Introduction
A set of elements with a real-valued membership function describing their grades.
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Application of Uncertainty Models in Bioinformatics
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.
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Multilevel Image Segmentation by a Multiobjective Genetic Algorithm Based OptiMUSIG Activation Function
A soft computing technique to determine the ambiguity, vagueness and uncertainty in real world knowledge bases.
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Fuzzy Graphs and Fuzzy Hypergraphs
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.
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Cost-Sensitive Classification for Medical Diagnosis
An extension of the classical set whose memberships have degrees of membership.
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Fabric Database and Fuzzy Logic Models for Evaluating Fabric Performance
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.
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Soft Sets and Its Applications
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].
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Probabilistic Ranking Method of XML Fuzzy Query Results
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.
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Application of Uncertainty Models in Bioinformatics
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.
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Remote Sensing Image Classification Using Fuzzy-PSO Hybrid Approach
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.
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Hierarchical Fuzzy Sets to Query Possibilistic Databases
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.
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Risk Factor in Agricultural Sector: Prioritizing Indian Agricultural Risk Factor by MAUT Method
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.
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A Fuzzy Simulated Evolution Algorithm for Hard Problems
A set whose elements have degrees of membership, rather than crisp membership or non-membership in classical sets.
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Triangular and Trapezoidal Fuzzy Assessment Models
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).
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Agricultural Health and Safety Measures by Fuzzy ahp and Prediction by Fuzzy Expert System: Agricultural Risk Factor
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.
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An Overview of Tourism Supply Chains Management and Optimization Models (TSCM – OM)
Provide a scheme for handling a variety of problems considering several rules not only true or false. It is a good approach to model the entropy in systems.
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