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What is Fuzzy Set Theory

Handbook of Research on Smart Computing for Renewable Energy and Agro-Engineering
Is a branch of applied mathematics devoted to methods of analysis of uncertain data, in which the description of uncertainties of real phenomena and processes is carried out using the concept of sets that do not have clear boundaries.
Published in Chapter:
Multi-Criteria Evaluation of Reconstruction Strategies for Distribution Power Networks Designed for Rural Power Supply
Tamara Leshchinskaya (Russian State Agrarian University – Moscow Timiryazev Agricultural Academy, Russia), Pavel Podobedov (Federal State Budgetary Scientific Institution, Federal Scientific Agroengineering Center VIM, Russia), Pavel Maslennikov (Federal State Budgetary Scientific Institution, Federal Scientific Agroengineering Center VIM, Russia), Anton Nekrasov (Federal State Budgetary Scientific Institution, Federal Scientific Agroengineering Center VIM, Russia), and Alexey Nekrasov (Federal State Budgetary Scientific Institution, Federal Scientific Agroengineering Center VIM, Russia)
DOI: 10.4018/978-1-7998-1216-6.ch013
Abstract
The rural distribution network has deteriorated. This is due to the high failure rate of electrical equipment, high maintenance costs, reduced power quality, and the increased duration of power outages in agricultural production. This leads to a short supply of electricity, downtime of processing equipment, loss of production or production of low-grade products, as well as excessive energy losses during transmission. The important issue is the development of advanced methods for assessing the feasibility and effectiveness for component replacement of power transmission equipment with newer and more modern, reducing electrical energy loss in the distribution network. To solve these problems, various strategies have been developed and studied to improve the reliability of 10 kV overhead power lines by using modern insulators, wires, and supports.
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Integrated Fuzzy AHP-TOPSIS Model for Optimization of National Defense Management Based on Inclusive Growth Drivers Using SWOT Analysis
In mathematics, 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. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics, economics, logistics, supply chain management, etc.
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Evaluation of a Scenario-Based Socratic Style of Teaching and Learning Practice
In mathematics, fuzzy sets are somewhat like sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotif A. Zadeh and Dieter Klaua in 1965 as an extension of the classical notion of set.
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Data Hierarchies for Generalization of Imprecise Data
The concept of fuzzy sets was introduced by Lotfi Zadeh. In ordinary sets a data values either belongs or does not belong to the set. However fuzzy set theory allows a gradual assessment of the membership of data values in a set described by of a membership function Where elements can either belong or not belong to a regular set, with fuzzy sets elements can belong to the set to a certain degree with zero indicating not an element, one indicating complete membership, and values between zero and one indicating partial or uncertain membership in the set. Fuzzy set theory has been used in a wide range of applications in which information is incomplete or imprecise.
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Integration of Fuzzy Logic Techniques into DSS for Profitability Quantification in a Manufacturing Environment
Set membership that handles the concept of partial truth where the truth values fall between completely true and completely false
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Granular Computing
Fuzzy set theory was introduced by Zahed in 1965. The central idea of fuzzy set theory is that an object belongs to more than one sets simultaneously. the closeness of the object to a set is indicated by membership degrees.
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Uncertainty and Vagueness Concepts in Decision Making
Fuzzy set theory was introduced by Zadeh in 1965. The central idea of fuzzy set theory is that an object belongs to more than one set simultaneously. The closeness of the object to a set is indicated by membership degrees.
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Quality Control Using Agent Based Framework
A Fuzzy Set (FS) approach is used due to the following reasons: First, the FS method enables fast and easy synthesis and modification of the control rule base; Second, the FS method can be integrated into the quality controller to compensate for process variations. The FS application includes Type 1 and Type 2 FS. Different types of FS express different strengths to handle heterogeneous factors as well as variables in the process.
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