A BENCHMARK EXERCISE ON FUZZY SET THEORY BASED EXPERT JUDGEMENT TECHNIQUE

It is sometimes impossible to make a correct decision in a certain engineering task without the help from professional expert judgments. Even though there are different expert opinions available, however, they should be appropriately aggregated to a useful form for making an acceptable engineering decision. This paper proposed a technique which utilizes the fuzzy set theory in the aggregation of expert judgments. In the technique, two main key concepts are employed: linguistic variables and fuzzy numbers. Linguistic variables first represent the relative importance of evaluation criteria under consideration and the degree of confidence on each expert perceived by the decision maker, and then are replaced by suitable triangular fuzzy numbers for arithmetic manipulation. As a benchmark problem, the pressure increment in the containment of Sequoyah nuclear power plant due to reactor vessel breach was estimated to verify and validate the proposed technique.

A Modified Comprehensive Evaluation System of Groundwater Pollution Based on Fuzzy Set Theory

A modified comprehensive evaluation system of groundwater pollution based on Fuzzy set theory is introduced.In this evaluation system,a five-degree membership function and a comprehensive weight function are built by combining Delphi method with double weight method.By studying a typical engineering project,the features and advantages of the modified evaluation system are analyzed by comparing to the popular simple comparison method.This indicates that the weighted average model is applicable in the situation that the content of every evaluation factor is even and the evaluation aim is to externalize the contribution of every evaluation factor in groundwater environmental quality.

Big Data Audit of Banks Based on Fuzzy Set Theory to Evaluate Risk Level

The arrival of big data era has brought new opportunities and challenges to the development of various industries in China.The explosive growth of commercial bank data has brought great pressure on internal audit.The key audit of key products limited to key business areas can no longer meet the needs.It is difficult to find abnormal and exceptional risks only by sampling analysis and static analysis.Exploring the organic integration and business processing methods between big data and bank internal audit,Internal audit work can protect the stable and sustainable development of banks under the new situation.Therefore,based on fuzzy set theory,this paper determines the membership degree of audit data through membership function,and judges the risk level of audit data,and builds a risk level evaluation system.The main features of this paper are as follows.First,it analyzes the necessity of transformation of the bank auditing in the big data environment.The second is to combine the determination of the membership function in the fuzzy set theory with the bank audit analysis,and use the model to calculate the corresponding parameters,thus establishing a risk level assessment system.The third is to propose audit risk assessment recommendations,hoping to help bank audit risk management in the big data environment.There are some shortcomings in this paper.First,the amount of data acquired is not large enough.Second,due to the lack of author’knowledge,there are still some deficiencies in the analysis of audit risk of commercial banks.

New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory

The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.

Pattern recognition of acoustic sea-bed profiling records (An expert system based on the fuzzy set theory)

An expert system based on the fuzzy set theory has been developed for geological interpretation of Acoustic Seabed Profiling Records(ASPR). After successively extracting each state of several main pattern characteristics shown on the ASPRs, the similarities between this pattern characteristic-state set and the standard ones corresponding to different geological categories of marine sediments are computed respectively By comparillg these values of sidrilarities, the conclusion of geological classification to the ASPR can be derived.

Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

The aim of this study is to investigate the applicability of reliability theory on surface square/rectangular footing against bearing capacity failure using fuzzy set theory in conjunction with the finite element method.Soil is modeled as a three-dimensional spatially varying medium,where its parameters(cohesion,friction angle,unit weight,etc.)are considered as fuzzy variables that maintain some membership functions.Soil is idealized as an elastic-perfectly plastic material obeying the Mohr-Coulomb failure criterion,where both associated and non-associated flow rules are considered in estimating the ultimate bearing capacity of the footing.The spatial variability of the soil is incorporated for both isotropic and anisotropic fields,which are determined by the values of scales of fluctuation in both the horizontal and vertical directions.A new parameter namely,limiting applied pressure at zero failure probability is proposed,and it indirectly predicts the failure probability of the footing.The effect of the coefficient of variation of the friction angle of the soil on the probability of failure is analyzed,and it is observed that the effect is significant.Furthermore,the effect of the scale of fluctuation on the probability of failure is investigated,and the necessity for considering spatial variability in the reliability analysis is well proven.

Evaluation of the maintenance window scheme using fuzzy soft set theory

The maintenance window scheme(MWS) is one of the most important railway transportation organizational plans and plays an important role in ensuring railway operational safety. However, MWS setting is a very complicated process, and most countries currently do so with the help of a computer-aided decision system. In general, a decision system can generate multiple alternatives for MWS within an acceptable time. Therefore, how to choose the best option from the alternatives is a vital decision. This paper presents a novel framework for MWS evaluation based on the Chinese railway system. Specifically, the requirements of each department related to MWS setting are analysed, and we construct an evaluation indicator system for MWS based on the preferences of different departments. Then, we apply the fuzzy soft set theory to MWS evaluation, a method that not only effectively deals with evaluation of uncertain information, but also gives flexibility for experts to input their subjective judgment.Additionally, using the ‘‘AND’’ operation of soft set theory allows combing evaluation information from multiple evaluators to give comprehensive results. Finally, a case study illustrates the proposed framework, showing that the proposed evaluation indicator system and evaluation method are effective and practical.

Rough Set Theory over Fuzzy Lattices

Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.

An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture

The contribution rate of equipment system-of-systems architecture(ESoSA)is an important index to evaluate the equipment update,development,and architecture optimization.Since the traditional ESoSA contribution rate evaluation method does not make full use of the fuzzy information and uncertain information in the equipment system-of-systems(ESoS),and the Bayesian network is an effective tool to solve the uncertain information,a new ESoSA contribution rate evaluation method based on the fuzzy Bayesian network(FBN)is proposed.Firstly,based on the operation loop theory,an ESoSA is constructed considering three aspects:reconnaissance equipment,decision equipment,and strike equipment.Next,the fuzzy set theory is introduced to construct the FBN of ESoSA to deal with fuzzy information and uncertain information.Furthermore,the fuzzy importance index of the root node of the FBN is used to calculate the contribution rate of the ESoSA,and the ESoSA contribution rate evaluation model based on the root node fuzzy importance is established.Finally,the feasibility and rationality of this method are validated via an empirical case study of aviation ESoSA.Compared with traditional methods,the evaluation method based on FBN takes various failure states of equipment into consideration,is free of acquiring accurate probability of traditional equipment failure,and models the uncertainty of the relationship between equipment.The proposed method not only supplements and improves the ESoSA contribution rate assessment method,but also broadens the application scope of the Bayesian network.

Fuzzy Model for Trust Evaluation

Based on fuzzy set theory, a fuzzy trust model is established by using membership function to describe the fuzziness of trust. The trust vectors of subjective trust are obtained based on a mathematical model of fuzzy synthetic evaluation. Considering the complicated and changeable relationships between various subjects, the multi-level mathematical model of fuzzy synthetic evaluation is introduced. An example of a two-level fuzzy synthetic evaluation model confirms the feasibility of the multi-level fuzzy synthesis evaluation model. The proposed fuzzy model for trust evaluation may provide a promising method for research of trust model in open networks.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

A Fuzzy Neural Network for Fault Pattern Recognition

This paper combines fuzzy set theory with ART neural net-work , and demonstrates some important properties of the fuzzy ART neural net-work algorithm. The results from application on a ball bearing diagnosis indicate that a fuzzy ART neural net-work has an effect of fast stable recognition for fuzzy patterns.

Optimal Design for Anti-Skid Control of Electric Vehicles by Fuzzy Approach

In this paper,a new fuzzy approach is applied to optimal design of the anti-skid control for electric vehicles.The anti-skid control is used to maintain the wheel speed when there are uncertainties.The control is able to provide an appropriate torque for wheels when the vehicle is about to skid.The friction coefficient and the moments of inertia of wheels and motor are considered as uncertain parameters.These nonlinear,bounded and time-varying uncertainties are described by fuzzy set theory.The control is deterministic and is not based on IF-THEN fuzzy rules.Then,the optimal design for this fuzzy system and control cost is proposed by fuzzy information.In this way,the uniform boundedness and uniform ultimate boundedness are guaranteed and the average fuzzy performance is minimized.Numerical simulations show that the control can prevent vehicle skidding with the minimum control cost under uncertainties.

Solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped Spring-Mass Structural Systems Using Novel Fuzzy-Affine Approach

The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact values.But in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers.This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers viz.triangular and trapezoidal.Based on the parametric form,fuzzy numbers have been transformed into family of standard intervals.Further due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been implemented.In the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine approach.Several application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed procedure.Lastly,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.Few comparisons are also demonstrated to show the reliability and efficacy of the present approach.

Fuzzy Methodology for Taxonomy and Knowledge Base Design

This paper summarizes the research results dealing with washer and nut taxonomy and knowledge base design, making the use of fuzzy methodology. In particular, the theory of fuzzy membership functions, similarity matrices, and the operation of fuzzy inference play important roles.A realistic set of 25 washers and nuts are employed to conduct extensive experiments and simulations.The investigation includes a complete demonstration of engineering design. The results obtained from this feasibility study are very encouraging indeed because they represent the lower bound with respect to performance, namely correctrecognition rate, of what fuzzy methodology can do. This lower bound shows high recognition rate even with noisy input patterns, robustness in terms of noise tolerance, and simplicity in hardware implementation. Possible future works are suggested in the conclusion.

FAULT DIAGNOSIS OF ROTATING MACHINERY USING KNOWLEDGE-BASED FUZZY NEURAL NETWORK

A novel knowledge-based fuzzy neural network （KBFNN） for fault diagnosis is presented. Crude rules were extracted and the corresponding dependent factors and antecedent coverage factors were calculated firstly from the diagnostic sample based on rough sets theory. Then the number of rules was used to construct partially the structure of a fuzzy neural network and those factors were implemented as initial weights, with fuzzy output parameters being optimized by genetic algorithm. Such fuzzy neural network was called KBFNN. This KBFNN was utilized to identify typical faults of rotating machinery. Diagnostic results show that it has those merits of shorter training time and higher right diagnostic level compared to general fuzzy neural networks.

Development of a database system for operational use in the selection of titanium alloys

The selection of titanium alloys has become a complex decision-making task due to the growing number of creation and utilization for titanium alloys,with each having its own characteristics,advantages,and limitations.In choosing the most appropriate titanium alloys,it is very essential to offer a reasonable and intelligent service for technical engineers.One possible solution of this problem is to develop a database system（DS） to help retrieve rational proposals from different databases and information sources and analyze them to provide useful and explicit information.For this purpose,a design strategy of the fuzzy set theory is proposed,and a distributed database system is developed.Through ranking of the candidate titanium alloys,the most suitable material is determined.It is found that the selection results are in good agreement with the practical situation.

Application of Grey Multi-hierarchy Decision to Evaluation of Stock Quality

In order to evaluate stock quality scientifically, a synthetic evaluation system of stock quality is proposed on the basis of fuzzy set theory and grey multi-hierarchy decision method. Then the evaluation system is applied to an example. The results show that the evaluation system can overcome the errors of expert＇s subjective judgment.

Optimal harvesting of a fuzzy water hyacinth-fish model with Kuznets curve effect

In this paper,we consider the effects of environmental perturbations such as the variations of temperature and climate on the growth of water hyacinth and fish species,as well as the economic and application values of these two species.We first present a triangular fuzzy water hyacinth-fish ecological model with Kuznets curve effect and linear harvesting.Then,we discuss the existence of the equilibria and their stability.It is then followed by analyzing the existence of bionomic equilibrium and determining the optimal harvesting policy via Pontryagin's Maximum Principle.Finally,numerical simulations are performed to validate the theoretical results.Our research indicates that fuzzy parameters may affect the optimal harvesting strategy.

New generalized fuzzy transform computations for solving fractional partial differential equations arising in oceanography

This paper presents a study of nonlinear waves in shallow water.The Korteweg-de Vries(KdV)equa-tion has a canonical version based on oceanography theory,the shallow water waves in the oceans,and the internal ion-acoustic waves in plasma.Indeed,the main goal of this investigation is to employ a semi-analytical method based on the homotopy perturbation transform method(HPTM)to obtain the numerical findings of nonlinear dispersive and fifth order KdV models for investigating the behaviour of magneto-acoustic waves in plasma via fuzziness.This approach is connected with the fuzzy generalized integral transform and HPTM.Besides that,two novel results for fuzzy generalized integral transforma-tion concerning fuzzy partial gH-derivatives are presented.Several illustrative examples are illustrated to show the effectiveness and supremacy of the proposed method.Furthermore,2D and 3D simulations de-pict the comparison analysis between two fractional derivative operators(Caputo and Atangana-Baleanu fractional derivative operators in the Caputo sense)under generalized gH-differentiability.The projected method(GHPTM)demonstrates a diverse spectrum of applications for dealing with nonlinear wave equa-tions in scientific domains.The current work,as a novel use of GHPTM,demonstrates some key differ-ences from existing similar methods.