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

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.

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.

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.

Reliability Assessment of Mechanical Components Using Fuzzy-Set Theory

1998 ◽  
Vol 120 (3) ◽  
pp. 270-275 ◽  
Author(s):  
J. Tang
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Reliability Assessment ◽  
Pressure Vessels ◽  
Reliability Model ◽  
Flexible Form ◽  
Failure Event ◽  
Mechanical Components ◽  
Fuzzy Random

An approach to assessing the reliability of mechanical components, especially for pressure vessels and piping, is proposed in which the vagueness and fuzziness in variables have been considered. In this method, a fuzzy-random reliability model is developed by using a fuzzy-set theory. This particular theory can be described as a generalization of the classical set theory. Using a fuzzy-set theory, a failure event is defined in a more flexible form than usual. In particular, the concept of nonfuzzy probability of fuzzy events is used to derive a reliability approach which includes the subjectivity of human judgement. Meanwhile, a constructive way for generating a membership function of a fuzzy set is also provided in the paper.

scholarly journals FUZZY SET THEORY---------- SOME USEFUL DISCUSSIONS AND INVESTIGATIONS

2021 ◽  
Vol 9 (8) ◽  
pp. 125-149
Author(s):  
Surajit Bhattacharyya
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers

In this paper I have discussed some basic but very important theories of fuzzy set theory with numerous examples. I have investigated α-sets, operations of fuzzy numbers, on interval fuzzy sets and also on fuzzy mappings. I have introduced S.Bs. class of fuzzy complements with its increasing and decreasing generators .

Quantitative HAZOP Risk Analysis for Oil Tanks Using the Fuzzy Set Theory

2012 ◽  
Author(s):  
Tao Cao ◽  
Huabing Zhang ◽  
Honglong Zheng ◽  
Yufeng Yang ◽  
Xin Wang
Keyword(s):  
Quantitative Analysis ◽  
Risk Analysis ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Storage Tanks ◽  
Worst Case ◽  
Quantitative Calculation ◽  
Oil Storage

Oil storage tanks are identified as the major hazard installations because of the hazard of huge fire & explosion. Evaluating the risk and controlling the danger is the advancement of accident prevention and the compulsory requirement of laws. HAZOP (Hazard and Operability Analysis), is a simple but intensive, systematic, qualitative risk analytical method, is an important technique for the identification of hidden hazards in operation of tank facility. It can only qualitatively account for potential risks, but cannot quantify their possibility and severity. Thus, research involving HAZOP quantitative analysis has become an area of focus. Due to uncertainty of deviation probability in the traditional HAZOP analysis, this paper discusses a new approach of HAZOP quantitative analysis, combining HAZOP with fuzzy set theory to calculate the possibilities of deviation and consequence quantitatively. The evaluation process and technique route of risk analysis is also brought forward in this paper. Based on the traditional HAZOP analysis, the typical outputs of a HAZOP analysis can be achieved, including identification of possible deviation states, identification of the possible causes for deviations and probable worst case consequence. Next, according to fuzzy evaluation of some HAZOP experts on deviation by means of their knowledge, the triangular fuzzy-number is introduced in this paper to conduct quantitative calculation. Based on the fuzzy set theory, combining Delphi method and judging matrix method, the linguistic values are transformed into triangular fuzzy numbers. The probability of deviation is evaluated by fuzzy cut and raking method of fuzzy numbers. Finally, the probability of consequence caused by deviation is evaluated. A complete quantitative risk analysis example for oil tank is conducted, the probabilities of deviations and incident consequence are computed, the quantitative risk is determined and reasonable mitigations of the storage tanks are given. It is shown that the proposed approach is advanced and practicable to make a quantitative assessment on the risk of existing deviation, which is helpful for risk managers to bring forward the suggested measure and regulate the hidden hazards.

scholarly journals The basic arithmetic operations on fuzzy numbers and new approaches to the theory of fuzzy numbers under the classification of space images

2020 ◽  
Vol 3 ◽  
pp. 49-59
Author(s):  
S.I. Alpert ◽  
Keyword(s):  
Remote Sensing ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Mathematical Tool ◽  
Classification Problems ◽  
Arithmetic Operations

Classification in remote sensing is a very difficult procedure, because it involves a lot of steps and data preprocessing. Fuzzy Set Theory plays a very important role in classification problems, because the fuzzy approach can capture the structure of the image. Most concepts are fuzzy in nature. Fuzzy sets allow to deal with uncertain and imprecise data. Many classification problems are formalized by using fuzzy concepts, because crisp classes represent an oversimplification of reality, leading to wrong results of classification. Fuzzy Set Theory is an important mathematical tool to process complex and fuzzy da-ta. This theory is suitable for high resolution remote sensing image classification. Fuzzy sets and fuzzy numbers are used to determine basic probability assignment. Fuzzy numbers are used for detection of the optimal number of clusters in Fuzzy Clustering Methods. Image is modeled as a fuzzy graph, when we represent the dissimilitude between pixels in some classification tasks. Fuzzy sets are also applied in different tasks of processing digital optical images. It was noted, that fuzzy sets play an important role in analysis of results of classification, when different agreement measures between the reference data and final classification are considered. In this work arithmetic operations of fuzzy numbers using alpha-cut method were considered. Addition, subtraction, multiplication, division of fuzzy numbers and square root of fuzzy number were described in this paper. Moreover, it was illustrated examples with different arithmetic operations of fuzzy numbers. Fuzzy Set Theory and fuzzy numbers can be applied for analysis and classification of hyperspectral satellite images, solving ecological tasks, vegetation clas-sification, in remote searching for minerals.

scholarly journals The development of fmea based on the use of fuzzy set theory.

2014 ◽  
Vol 2014 (4) ◽  
pp. 153-163
Author(s):  
Николай Борбаць ◽  
Nikolay Borbats ◽  
Вячеслав Мирошников ◽  
Vyacheslav Miroshnikov ◽  
Олег Горленко ◽  
...  
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Mathematical Operations

Considered the analysis of the types and effects of potential defects on the basis of application of fuzzy set theory.Proposed baths relevant linguistic variables.The example of calculation priority number of risk on the basis of mathematical operations with fuzzy numbers.

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