New Image Recognition Method Based on Rough-Sets and Fuzzy Theory

A new image recognition method based on fuzzy rough sets theory is proposed, and its implementation discussed. The performance of this method as applied to ferrography image recognition is evaluated. It is shown that the new method gives better results than fuzzy or rough sets method when used alone.

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.

A NEW UNSUPERVISED CLASSIFICATION ALGORITHM FOR POLARIMETRIC SAR IMAGES BASED ON FUZZY SET THEORY

In this letter, a new method is proposed for unsupervised classification of terrain types and man-made objects using POLarimetric Synthetic Aperture Radar (POLSAR) data. This technique is a combi-nation of the usage of polarimetric information of SAR images and the unsupervised classification method based on fuzzy set theory. Image quantization and image enhancement are used to preprocess the POLSAR data. Then the polarimetric information and Fuzzy C-Means (FCM) clustering algorithm are used to classify the preprocessed images. The advantages of this algorithm are the automated classification, its high classifica-tion accuracy, fast convergence and high stability. The effectiveness of this algorithm is demonstrated by ex-periments using SIR-C/X-SAR (Spaceborne Imaging Radar-C/X-band Synthetic Aperture Radar) data.

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.

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.

Multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory-based environmental risk evaluation for tailings reservoirs

Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.

Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control

The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.

Modeling Multisource-heterogeneous Information Based on Random Set and Fuzzy Set Theory

This paper presents a new idea, named as modeling multisensor-heterogeneous information, to incorporate the fuzzy logic methodologies with mulitsensor-multitarget system under the framework of random set theory. Firstly, based on strong random set and weak random set, the unified form to describe both data (unambiguous information) and fuzzy evidence (uncertain information) is introduced. Secondly, according to signatures of fuzzy evidence, two Bayesian-markov nonlinear measurement models are proposed to fuse effectively data and fuzzy evidence. Thirdly, by use of "the models-based signature-matching scheme", the operation of the statistics of fuzzy evidence defined as random set can be translated into that of the membership functions of relative point state variables. These works are the basis to construct qualitative measurement models and to fuse data and fuzzy evidence.

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.

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.

A NEW METHOD FOR CONSTRUCTING FUZZY EVIDENCE BASED ON THE NON-CONSONANT RANDOM SET

Natural-language information is often mathematically expressed by fuzzy sets. With the random set theory as a bridge, this kind of information can be transformed into fuzzy evidence in Dempster-Shafer (DS) theory. Then Dempster's combination rule or other combination rules of evi- dence can be used perfectly for fusing natural-language and other information. However, this traditional transformation involves the use of α -cutsets to construct the focal elements which have to be repre- sented as consonant sets. This construction is very inflexible and unreasonable in some practical ap- plications. In this paper, with the desire to overcome this limitation, a method for constructing more general non-consonant focal elements is proposed based on the random set theory. Some examples are given to show the generality and the efficiency of this new method. Finally, we validate that non-consonant constructions provide less degrees of total uncertainty than that of the consonant case in these examples by using the evaluation criterion of total uncertainty.

Modelling spatial vagueness based on type-2 fuzzy set

The modelling and formal characterization of spatial vagueness plays an increasingly important role in the imple- mentation of Geographic Information System (GIS). The concepts involved in spatial objects of GIS have been investigated and acknowledged as being vague and ambiguous. Models and methods which describe and handle fuzzy or vague (rather than crisp or determinate) spatial objects, will be more necessary in GIS. This paper proposes a new method for modelling spatial vagueness based on type-2 fuzzy set, which is distinguished from the traditional type-1 fuzzy methods and more suitable for describing and implementing the vague concepts and objects in GIS.

Two Hybrid Methods Based on Rough Set Theory for Network Intrusion Detection

In this paper,we propose two intrusion detection methods which combine rough set theory and Fuzzy C-Means for network intrusion detection.The first step consists of feature selection which is based on rough set theory.The next phase is clustering by using Fuzzy C-Means.Rough set theory is an efficient tool for further reducing redundancy.Fuzzy C-Means allows the objects to belong to several clusters simultaneously,with different degrees of membership.To evaluate the performance of the introduced approaches,we apply them to the international Knowledge Discovery and Data mining intrusion detection dataset.In the experimentations,we compare the performance of two rough set theory based hybrid methods for network intrusion detection.Experimental results illustrate that our algorithms are accurate models for handling complex attack patterns in large network.And these two methods can increase the efficiency and reduce the dataset by looking for overlapping categories.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Prospect Theory Based Hesitant Fuzzy Multi-Criteria Decision Making for Low Sulphur Fuel of Maritime Transportation

The environmental impact of maritime transport has now become a relevant issue in sustainable policy formulation and has attracted increasing interest from academia.For the sustainable development of maritime transport,International Maritime Organization stipulates that the sulfur content of ship emissions will reach 0.5 from 2020.With the approaching of the stipulated implementation date,shipowners need to adopt scientific methods to make decision on low sulfur fuel.In this study,we applied a prospect theory based hesitant fuzzy multi-criteria decision-making model to obtain the optimal decision of low Sulphur marine fuel.For this purpose,the hesitant fuzzy decision matrix is established to collect expert opinions,the maximizing deviation method is adopted to determine criteria weights.According to calculate the Euclidean distance from the reference points,we obtain the comprehensive prospect values of alternatives.Lastly,a case study is carried out to illustrate the significance and effectiveness of the proposed methodology.The innovation of this study is that it is the first-time adopting prospect theory and hesitate fuzzy sets to multi-criteria decision making for low Sulphur marine fuel,which provides an effective decision model for shipping companies under Low Sulphur regulations,and can also be extended to other industries.

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.

应用Fuzzy集理论对地下水位动态分类

本文应用Fuzzy集理论,给出一个对地下水位动态进行分类的数学模型,并借助计算机对西安市部分地区地下水位进行了分类。

基于RoughSet理论的推理机制的研究

对RoughSet理论中属性域约简、决策表及Rough算子等问题进行了研究,分析了RoughSet理论与模糊集理论及证据理论的关系,着重对基于RoughSet理论的推理机制进行了研究。