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The purpose of this paper is to investigate the performance of a turbine structure of the oil and gas Egyptian company in terms of reliability, mean time to failure (MTTF), mean time to repair (MTTR) and mean time between failures (MTBF) under fuzzy environment and working criteria. This paper examines the impact of the failure of various components on the complete turbine structure of the oil and gas system.

To overcome the problem of uncertain behavior of available data for various components, the right triangular generalized fuzzy number (RTrGFN) is proposed to be taken into the account to express the uncertainty which attains some tolerance in data. Furthermore, reliability indices are calculated with the help of the Lambda Tau method and the arithmetic operations on right generalized triangular fuzzy numbers (RTrGFN).

This paper explores the reliability of a repairable 3 out of 4 structure of turbines and along with the other parameters namely MTTF, MTTR and MTBF; under a fuzzy environment. Failure rates and repair times are expected to be exponential. The ranking of components of the structure is being found to decide the priority for maintenance.

This paper investigates the performance of the system with different spread/tolerance like 15%, 25% and 50% of crisp data. It helps to predict realistic results in the range value. To enhance the system's performance, the most important item of the system requires greater attention. For this, the authors find the sensitive part by ranking. For ranking, an extended approach has been developed to find the sensitive unit of the system by using the right triangular generalized fuzzy number. This paper explores the most and least sensitive component of the system, which helps the maintenance department to plan the maintenance action.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

As the functions of environmental regulations cannot be quantified while assessing their environmental efficiency, there has been no comprehensive evaluation of environmental efficiency. The purpose of this paper is to evaluate environmental regulations based on triangular and trapezoidal fuzzy numbers.

This paper uses L-R fuzzy numbers to transform the evaluation language into triangular fuzzy numbers, and adopts an α-level flexible slacks-based measurement model to evaluate the performance of these regulations. Trapezoidal fuzzy numbers are combined with a data envelopment analysis model, and an α-slack-based measurement (SBM) model is used to evaluate the environmental efficiency. The α-SBM model is confirmed to be stable and sustainable.

Relevant index data from 16,375 enterprises were collected to test the proposed model, and models corresponding to triangular fuzzy numbers and trapezoidal fuzzy numbers were used to evaluate their environmental efficiency. Comparative results showed that the proposed model is feasible and stable.

The main contributions of this study are twofold. First, this paper provides a valuable evaluation method for environmental regulation. Second, our research improves the practical performance of trapezoidal fuzzy data envelopment analysis and enhances its feasibility and stability.

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

The purpose of this paper is to analyze the fuzzy reliability of the compressor house unit (CHU) system in a coal fired thermal power plant under vague environment by reducing the accumulating phenomenon of fuzziness and accelerating the computation process. This paper uses different fuzzy membership functions to quantify uncertainty and access the system reliability in terms of different fuzzy reliability indices having symmetric shapes.

This study analyses the fuzzy reliability of the CHU system in a coal fired thermal power plant using T_ω-based generalized fuzzy Lambda-Tau (TBGFLT) technique. This approach applies fault tree, Lambda-Tau method, different fuzzy membership functions and α-cut coupled T_ω-based approximate arithmetic operations to compute various reliability parameters (such as failure rate, repair time, mean time between failures, expected number of failures, availability and reliability) of the system. The effectiveness of TBGFLT technique has been demonstrated by comparing the results with results obtained from four different existing techniques. Moreover, this paper applies the extended Tanaka et al. (1983) approach to rank the critical components of the system when different membership functions are used.

The adopted TBGFLT technique in the present study improves the shortcomings of the existing approaches by reducing the accumulating phenomenon of fuzziness, accelerating the computation process and getting symmetric shapes for computed reliability parameters when different membership functions are used to quantify data uncertainty.

In existing fuzzy reliability techniques which are developed for repairable systems either triangular fuzzy numbers, triangle vague sets or triangle intuitionistic fuzzy sets have been used for quantifying uncertainty. These approaches do not examine the systems for components with different membership functions. The present study is an effort in this direction and evaluates the fuzzy reliability of the CHU system in a coal fired thermal power plant for components with different membership functions. This is the main contribution of the paper.

The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system (FFLS) with no non negative restrictions on the triangular fuzzy numbers chosen as parameters. Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions. The first method eliminates the non‐negativity constraint from the coefficient matrix while the second method eliminates the constraint of non‐negativity on the solution vector. The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.

The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system. Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.

The results that are obtained reveal interesting properties of a FFLS. By using the proposed methods, the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions, i.e. trivial, unique or infinite. Further it is also seen that an n×n FFLS may yield finitely many solutions which may not be entirely feasible (strong). Also the methods successfully remove the non‐negativity restriction on the coefficient matrix and the solution vector, respectively.

Evolving methods with better computational complexity and that which remove the non‐negativity restriction jointly on all the parameters are left as an open problem.

The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists. The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations. Heretofore, the usability of FFLS is largely dormant.

The objective of this paper is to provide a brief review of recent developments in the area of applications of ANN, Fuzzy Logic, and Wavelet Transform in fault diagnosis. The purpose of this work is to provide an approach for maintenance engineers for online fault diagnosis through the development of a machine condition‐monitoring system.

A detailed review of previous work carried out by several researchers and maintenance engineers in the area of machine‐fault signature‐analysis is performed. A hybrid expert system is developed using ANN, Fuzzy Logic and Wavelet Transform. A Knowledge Base (KB) is created with the help of fuzzy membership function. The triangular membership function is used for the generation of the knowledge base. The fuzzy‐BP approach is used successfully by using LR‐type fuzzy numbers of wavelet‐packet decomposition features.

The development of a hybrid system, with the use of LR‐type fuzzy numbers, ANN, Wavelets decomposition, and fuzzy logic is found. Results show that this approach can successfully diagnose the bearing condition and that accuracy is good compared with conventionally EBPNN‐based fault diagnosis.

The work presents a laboratory investigation carried out through an experimental set‐up for the study of mechanical faults, mainly related to the rolling element bearings.

The main contribution of the work has been the development of an expert system, which identifies the fault accurately online. The approaches can now be extended to the development of a fault diagnostics system for other mechanical faults such as gear fault, coupling fault, misalignment, looseness, and unbalance, etc.

Supply chain performance (SCP) extent can be attributed as a function of multiple criteria/attributes. Most of the criterions/attributes being intangible in nature; SCP appraisement relies on the subjective judgment of the decision makers. Moreover, quantitative appraisement of SCP appears to be very difficult due to involvement of ill-defined (vague) performance measures as well as metrics. The purpose of this paper is to develop an efficient decision support system (DSS) to facilitate SCP appraisement, benchmarking and related decision making.

This study explores the concept of fuzzy logic in order to tackle incomplete and inconsistent subjective judgment of the decision makers’ whilst evaluating supply chain’s overall performance. Grey relational analysis has been adopted in the later stage to derive appropriate ranking of alternative companies/enterprises (in the same industry) in view of ongoing SCP extent.

In this work, a performance appraisement index system has been postulated to gather evaluation information (weights and ratings) in relation to SCP measures and metrics. Combining the concepts of fuzzy set theory, entropy, ideal and grey relation analysis, a fuzzy grey relation method for SCP benchmarking problem has been presented. First, triangular fuzzy numbers and linguistic evaluation information characterized by triangular fuzzy numbers have been used to evaluate the importance weights of all criteria and the superiority of all alternatives vs various criteria above the alternative level. Then, the concept of entropy has been utilized to solve the adjusted integration weight of all objective criteria above the alternative level. Moreover, using the concept of the grey ration grades, various alternatives have been ranked accordingly.

Finally, an empirical example of selecting most appropriate company has been used to demonstrate the ease of applicability of the aforesaid approach. The study results showed that this method appears to be an effective means for tackling multi-criteria decision-making problems in uncertain environments. Empirical data have been analysed and results obtained thereof, have been reported to exhibit application potential of the said fuzzy grey relation based DSS in appropriate situation.

This study aims to present the cost and revenue efficiency evaluation models in data envelopment analysis in the presence of fuzzy inputs, outputs and their prices that the prices are also fuzzy. This study applies the proposed approach in the energy sector of the oil industry.

This study proposes a value-based technology according to fuzzy input-cost and revenue-output data, and based on this technology, the authors propose an approach to calculate fuzzy cost and revenue efficiency based on a directional distance function approach. These papers incorporated a decision-maker’s (DM) a priori knowledge into the fuzzy cost (revenue) efficiency analysis.

This study shows that the proposed approach obtains the components of fuzzy numbers corresponding to fuzzy cost efficiency scores in the interval [0, 1] corresponding to each of the decision-making units (DMUs). The models presented in this paper satisfies the most important properties: translation invariance, translation invariance, handle with negative data. The proposed approach obtains the fuzzy efficient targets corresponding to each DMU.

In the proposed approach, by selecting the appropriate direction vector in the model, we can incorporate preference information of the DM in the process of evaluating fuzzy cost or revenue efficiency and this shows the efficiency of the method and the advantages of the proposed model in a fully fuzzy environment.

Supplier selection is a complex multiple criteria decision (MCDM) problem which directly depends on decision makers’ choice. Some decisions are getting involved with linguistic variables and they are not mathematically operable. To solve a typical decision problem through MCDM techniques, a number or a numerical interval should be defined. The purpose of this paper is to focus on that numerical interval and in a case of supplier selection, the aim is to close the decisions to the real number that the decision maker mentions and this number is in a numerical interval.

The proposed method deals with grey relational analysis (GRA) and develops it by applying triangular fuzzy numbers. The grey numbers have two defined bounds; the proposed method defines two fuzzy bounds for each grey attribute. In the proposed method, the fuzzy membership function has been employed for each bounds of grey attribute to make them to fuzzy bounds with two undefined bounds. Also to make comparison, with employing of TOPSIS technique, both of the grey fuzzy combination decision matrix and the original grey decision matrix are obtained.

The results indicate that, except to the ideal solutions, the grey relation coefficient for each alternative is too close to each other. Indeed, they are too close to zero. Applying the proposed method in problem of supplier selection shows the difference between two selected supplier in proposed method and the original grey method.

As mentioned heretofore this paper aims to make decision makers’s decision more accurate and actually there is no other researches which used this combination method.