Research on Fuzzy Fault Diagnosis of the Equipments

2013 ◽  
Vol 411-414 ◽  
pp. 1484-1487
Author(s):  
Ji Yang Qi ◽  
Li Na Ren ◽  
Shan Ping Ning ◽  
Yu Fu
Keyword(s):  
Fault Diagnosis ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Comparison Matrix ◽  
Fuzzy Diagnosis ◽  
The Given ◽  
Pair Wise Comparison ◽  
Pair Wise Comparison Matrix

The paper introduces a method of fault diagnosis using fuzzy set theory. In the paper, the principle that a fault symptom either exists or doesnt exist is abandoned. A crisp number between 0 and 1 is used to denote the degree of fault symptom, by which the fault symptom vector is constructed. For every kind of fault symptom, a fuzzy pair-wise comparison matrix is constructed. The elements of the pair-wise comparison matrix are triangular fuzzy numbers which denote the qualitative comparisons between the membership values of the given fault symptom with the reference to a pair of possible faults respectively. The least logarithm squares method is applied to determine the membership of the fault symptom with respect to each fault, and then the fuzzy diagnosis matrix is constructed. A simple weighted addition is used to calculate the fault vector based on the fuzzy diagnosis matrix and the fault symptom vector. Center of area is used to determine the best non-fuzzy performance value of the fuzzy number, according to which the fuzzy numbers can be ranked. The ordering of all the possible faults based on the fault symptoms is determined. At the end of the paper, an example is used to demonstrate the procedure of fuzzy fault diagnosis.

scholarly journals Reliability Analysis in Planning of Traction Substation Reconstruction Based on Fuzzy Set Theory

2020 ◽  
pp. 52-62
Author(s):  
Vladislav G. Belov ◽  
Vladimir A. Tremyasov
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Probabilistic Method ◽  
Reliability Assessment ◽  
Electrical Equipment ◽  
Triangular Fuzzy Numbers ◽  
Traction Substation ◽  
Reliability Indicators

The study proposes a probabilistic method using triangular fuzzy numbers to analyze the reliability of the traction substation. With this approach, the reliability assessment of the traction substation can be performed considering changes in the values of reliability indicators of electrical equipment, determined on the basis of the fuzzy set theory

A FUZZY COMPROMISE SOLUTION FOR MULTICRITERIA PROBLEMS

2007 ◽  
Vol 15 (03) ◽  
pp. 363-380 ◽  
Author(s):  
SERAFIM OPRICOVIC
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Multicriteria Decision Making ◽  
Compromise Solution ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Environment ◽  
Multicriteria Problem ◽  
Multicriteria Problems ◽  
The Ideal

The VIKOR-F method has been developed to solve fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. It determines the compromise solution that is the "closest" to the ideal. Imprecision in multicriteria decision making can be modelled using fuzzy set theory to define criteria and the importance of criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. It is based on the aggregating fuzzy merit that represents distance of an alternative to the ideal solution. The fuzzy operations and procedures for ranking fuzzy numbers are used in developing the VIKOR-F algorithm. A numerical example illustrates an application of the VIKOR-F method.

Evaluation of Quantified Statements Using Gradual Numbers

2011 ◽  
pp. 246-269 ◽  
Author(s):  
Ludovic Liétard ◽  
Daniel Rocacher
Keyword(s):  
Decision Making ◽  
Expert Systems ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Relational Databases ◽  
Fuzzy Numbers ◽  
Theoretical Background ◽  
Definition Of ◽  
Flexible Querying

This chapter is devoted to the evaluation of quantified statements which can be found in many applications as decision making, expert systems, or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type “Q X are A” and “Q B X are A.” In this context, quantified statements are interpreted using an arithmetic on gradual numbers from Nf, Zf, and Qf. It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches.

scholarly journals Fuzzy Insurance

1990 ◽  
Vol 20 (1) ◽  
pp. 33-55 ◽  
Author(s):  
Jean Lemaire
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Life Insurance ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Basic Concepts ◽  
Definition Of

AbstractFuzzy set theory is a recently developed field of mathematics, that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained in a given set, in fuzzy set theory the transition between membership and non-membership is gradual. The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or ill-defined to be analysed by conventional methods. This paper aims at presenting the basic concepts of the theory in an insurance framework. First the basic definitions of fuzzy logic are presented, and applied to provide a flexible definition of a “preferred policyholder” in life insurance. Next, fuzzy decision-making procedures are illustrated by a reinsurance application, and the theory of fuzzy numbers is extended to define fuzzy insurance premiums.

scholarly journals Some properties of integration of real-valued function over a fuzzy interval

2021 ◽  
Vol 8 (12) ◽  
pp. 9-13
Author(s):  
M. A. Shakhatreh ◽  
◽  
A. M. Al-Shorman ◽  
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Interval Analysis ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
Mathematical Concepts ◽  
Fuzzy Distance ◽  
Real Algebra ◽  
Fuzzy Interval

One of the most fundamental concepts in fuzzy set theory is the extension principle. It gives a generic way of dealing with fuzzy quantities by extending non-fuzzy mathematical concepts. There are a few examples, including the concept of fuzzy distance between fuzzy sets. The extension approach is then methodically applied to real algebra, with considerable development of fuzzy number operations. These operations are computationally appealing and generalized interval analysis. Although the set of real fuzzy numbers with extended addition or multiplication is no longer a group, it retains many structural qualities. The extension concept is demonstrated to be particularly beneficial for defining set-theoretic operations for higher fuzzy sets. We need some definitions related to our properties before we can create the properties of integration of a crisp real-valued function over a fuzzy interval. It is our goal in this article to develop and demonstrate certain characteristics of a real-valued function over a fuzzy interval in order to broaden the scope of the notion of integration of a real-valued function over a fuzzy interval. Some of these characteristics are linked to the operations of extended addition and extended subtraction, while others are not.

Interval Methods and Fuzzy Optimization

1997 ◽  
Vol 05 (03) ◽  
pp. 239-249 ◽  
Author(s):  
Weldon A. Lodwick ◽  
K. David Jamison
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Interval Analysis ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Interval Methods

In this paper, we describe interval-based methods for solving constrained fuzzy optimization problems. The class of fuzzy functions we consider for the optimization problems is the set of real-valued functions where one or more parameters/coefficients are fuzzy numbers. The focus of this research is to explore some relationships between fuzzy set theory and interval analysis as it relates to optimization problems.

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