Fuzzy Reliability of an Imprecise Failure to Start of an Automobile Using Pseudo-Parabolic Fuzzy Numbers

2018 ◽  
Vol 14 (03) ◽  
pp. 323-341 ◽  
Author(s):  
F. Abbasi
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Fuzzy Reliability ◽  
Fuzzy Environment ◽  
Distributed Components ◽  
Proposed Model ◽  
New Type ◽  
The Membership Function

In this paper, we propose the notion of pseudo-parabolic fuzzy numbers and the component failure probabilities are considered as a new type of fuzzy number as pseudo-parabolic to incorporate the uncertainties in the parameter, due to a more realistic estimate of them. Then, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components, and using the new operations of TA [F. Abbasi et al., Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861], due to the smaller results support, easier calculations and special properties than fuzzy arithmetic operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). We provide a more realistic fuzzy reliability analysis. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as pseudo-parabolic fuzzy numbers.

Estimation of Failure Using Fault Tree Analysis Based on New Operations on LR-Type Flat Fuzzy Numbers

2020 ◽  
pp. 1-22
Author(s):  
F. Abbasi ◽  
T. Allahviranloo
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Fault Tree Analysis ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
General Shape ◽  
Fuzzy Environment ◽  
Distributed Components ◽  
Proposed Model ◽  
Arithmetic Operator

In this paper, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components using the new operations of TA [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861.] due to the smaller results support, easier calculations and special properties than operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). we propose the new fuzzy arithmetic operations based on transmission average(TA) on LR type flat fuzzy numbers. In the proposed formulae, LR type flat fuzzy numbers are not restricted to have the same [Formula: see text] and [Formula: see text] shape functions. This allows arithmetic operator for arithmetic involving LR type flat fuzzy numbers of different and general shape. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as LR type flat fuzzy numbers.

Conception and Implementation of a New Data-Driven Fuzzy Method for Reliability and Safety Analysis

2020 ◽  
Vol 16 (03) ◽  
pp. 517-539
Author(s):  
F. Abbasi ◽  
T. Allahviranloo
Keyword(s):  
System Reliability ◽  
Fuzzy Number ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Accurate Estimate ◽  
Data Driven ◽  
Proposed Model ◽  
Parameters Uncertainty ◽  
New Type

In this paper, the probability of failure of the components is introduced as a new type of fuzzy numbers called Gaussian patchy fuzzy number to insert parameters’ uncertainty. The reason for the use of such fuzzy numbers is also due to their realistic estimation. Hence, in order to obtain a more accurate estimate of each failure occurrence and overall system reliability analysis, we assume that the fundamental events of fault tree are in the form of Gaussian patchy fuzzy number on [0, 1], and then, by applying the fuzzy transmission average (TA) [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems, 29 (2015) 851-861], we will model the reliability of the fuzzy system (especially the series and the parallel). Applying such fuzzy operations and numbers will lead to a more realistic analysis of the reliability of the fuzzy system. Finally, the proposed model has been used for the lack of satisfaction of the University’s administrative and financial assistant.

Conception and Implementation of a New Data-Driven Fuzzy Method for Reliability and Safety Analysis

2020 ◽  
Vol 16 (02) ◽  
pp. 339-361
Author(s):  
F. Abbasi ◽  
T. Allahviranloo
Keyword(s):  
System Reliability ◽  
Fuzzy Number ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Accurate Estimate ◽  
Data Driven ◽  
Proposed Model ◽  
Parameters Uncertainty ◽  
New Type

In this paper, the probability of failure of the components is introduced as a new type of fuzzy number called Gaussian patchy fuzzy number to insert parameters’ uncertainty. The reason for the use of such fuzzy numbers is also due to their realistic estimation. Hence, in order to obtain a more accurate estimate of each failure occurrence and overall system reliability analysis, we assume that the fundamental events of fault tree are in the form of Gaussian patchy fuzzy number on [0, 1], and then, by applying the fuzzy transmission average (TA) [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861.], we will model the reliability of the fuzzy system (especially the series and the parallel). Applying such fuzzy operations and numbers will lead to a more realistic analysis of the reliability of the fuzzy system. Finally, the proposed model has been used for the lack of satisfaction of the University’s administrative and financial assistant.

scholarly journals Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1272
Author(s):  
Bogdana Stanojević ◽  
Milan Stanojević ◽  
Sorin Nădăban
Keyword(s):  
Mathematical Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Advantages And Disadvantages ◽  
Fuzzy Environment ◽  
Basic Ideas ◽  
Mathematical Programming Problems

Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

scholarly journals Fuzzy Number Addition with the Application of Horizontal Membership Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Andrzej Piegat ◽  
Marcin Pluciński
Keyword(s):  
Interval Arithmetic ◽  
Fuzzy Numbers ◽  
Order Relation ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Multidimensional Approach ◽  
Membership Functions ◽  
Multidimensional Information ◽  
Rdm Arithmetic ◽  
Horizontal Membership Functions

The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods useα-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.

scholarly journals On a Flow-Shop Scheduling Problem with Fuzzy Pentagonal Processing Time

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Majed G. Alharbi ◽  
Hamiden Abd El-Wahed Khalifa
Keyword(s):  
Processing Time ◽  
Fuzzy Numbers ◽  
Flow Shop ◽  
Simple Approach ◽  
Flow Shop Scheduling ◽  
Fuzzy Arithmetic ◽  
Scheduling Problem ◽  
Numerical Illustration ◽  
Fuzzy Environment ◽  
Ranking Technique

Scheduling involves planning and arranging jobs across a coordinated set of events to satisfy the customer’s demands. In this article, we present a simple approach for the flow-shop (FS) scheduling problem under fuzzy environment in which processing time of jobs are represented by pentagonal fuzzy numbers. This study is intended to reduce the rental cost of the machine in compliance with the rental policy. The fuzzy FS scheduling problem is solved without converting the processing time into its equivalent crisp numbers using a robust ranking technique and a fuzzy arithmetic pentagonal fuzzy numbers. A numerical illustration indicates that the approach is workable, accurate, and relevant.

A NOVEL DEFUZZIFYING APPROACH TO CAR EVALUATION AND SELECTION UNDER FUZZY ENVIRONMENT

2002 ◽  
Vol 10 (03) ◽  
pp. 309-326 ◽  
Author(s):  
TA-CHUNG CHU ◽  
CHUNG-TSEN TSAO
Keyword(s):  
Fuzzy Numbers ◽  
Ranking Method ◽  
New Method ◽  
Multiple Level ◽  
Numerical Example ◽  
Fuzzy Environment ◽  
Proposed Model

This paper proposes a new method for ranking fuzzy numbers by difference between relative areas. Comparative examples illustrate the advantage of the proposed method. The ranking method is further applied to help establish a defuzzified multiple level FMADM model, which avoids the complicatied aggregation of fuzzy numbers so that the multiple level FMADM problem can be efficiently solved. A numerical example of car evaluation and selection illustrates the feasibility of the proposed model.

scholarly journals Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

2021 ◽  
Vol 26 (4) ◽  
pp. 357-364
Author(s):  
Hanumantha Rao Sama ◽  
Vasanta Kumar Vemuri ◽  
Venkata Siva Nageswara Hari Prasad Boppana
Keyword(s):  
Nonlinear Programming ◽  
Performance Measures ◽  
Fuzzy Numbers ◽  
Upper And Lower Bounds ◽  
Service Rate ◽  
Extension Principle ◽  
Single Server ◽  
Two Phase ◽  
Expected Cost ◽  
Fuzzy Environment

The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estimates for some performance measures of a controllable two-phase service single server Markovian gated queue with server startups and breakdowns under N-policy in which the queue parameters viz. arrival rate, startup rate, batch service rate, individual service rate, repair rate and cost elements are all defined as fuzzy numbers. Based on Zadeh’s extension principle and the α-cuts, a set of parametric nonlinear programming problems are developed to find the upper and lower bounds of the minimum total expected cost per unit time at the possibility level α. As the analytical solutions of the nonlinear programming problems developed for the proposed model are tedious, considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical results for the lower and upper bounds of the optimal threshold N* and the minimum total expected cost per unit time are computed using the nonlinear programming solver available in MATLAB.

Intuitionistic Fuzzy Measures of Correlation Coefficient of Intuitionistic Fuzzy Numbers Under Weakest Triangular Norm

2019 ◽  
Vol 8 (1) ◽  
pp. 48-64 ◽  
Author(s):  
Mohit Kumar
Keyword(s):  
Correlation Coefficient ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Triangular Norm ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Technology Level

The correlation coefficient of variables has wide applications in statistics and is often calculated in crisp or fuzzy environment. This article extends the application of correlation coefficient to intuitionistic fuzzy environment. In this article, a new method is proposed to measure the correlation coefficient of intuitionistic fuzzy numbers using weakest triangular norm based intuitionistic fuzzy arithmetic operations. Different from previous studies, the correlation coefficient computed in this article is an intuitionistic fuzzy number rather than a crisp or fuzzy number. It is well known that the weakest t-norm arithmetic operations effectively reduce fuzzy spreads (fuzzy intervals) and provide more exact results. Therefore, a simplified, effective and exact method based on weakest t-norm arithmetic operations is presented to compute the correlation coefficient of intuitionistic fuzzy numbers. To illustrate the proposed method, the correlation coefficient between the technology level and management achievement from a sample of 15 machinery firms in Taiwan is calculated using proposed approach.

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