Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.

Intuitionistic Fuzzy Rough Sets Based on Two Intuitionistic Fuzzy Implicators

This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.

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.

NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

Variable Precision Rough Set and a Fuzzy Measure of Knowledge Based on Variable Precision Rough Set

Variable precision rough set (VPRS) is an extension of rough set theory (RST). By setting threshold value β , VPRS looses the strict definition of approximate boundary in RST. Confident threshold value for β is discussed and the method for deriving decision making rules from an information system is given by an example. An approach to fuzzy measures of knowledge is proposed by applying VPRS to fuzzy sets. Some properties of this measure are studied and a pair of lower and upper approximation operato...

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

On uniqueness of (fuzzy) relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.

Power transformer fault diagnosis model based on rough set theory with fuzzy representation

Objective Due to the incompleteness and complexity of fault diagnosis for power transformers,a comprehensive rough-fuzzy scheme for solving fault diagnosis problems is presented.Fuzzy set theory is used both for representation of incipient faults' indications and producing a fuzzy granulation of the feature space.Rough set theory is used to obtain dependency rules that model indicative regions in the granulated feature space.The fuzzy membership functions corresponding to the indicative regions,modelled by rules,are stored as cases.Results Diagnostic conclusions are made using a similarity measure based on these membership functions.Each case involves only a reduced number of relevant features making this scheme suitable for fault diagnosis.Conclusion Superiority of this method in terms of classification accuracy and case generation is demonstrated.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

Rough Set Based Fuzzy Neural Network for Pattern Classification

A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performance of global convergence. In addition, the numbers of rules and the initial weights and structure of fuzzy neural networks are difficult to determine. Here rough sets are introduced to decide the numbers of rules and original weights. Finally, experiment results show the algorithm may get better effect than the BP algorithm.

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.

Characteristics Prediction Method of Electro-hydraulic Servo Valve Based on Rough Set and Adaptive Neuro-fuzzy Inference System

Synthesis characteristics of the electro-hydraulic servo valve are key factors to determine eligibility of the hydraulic production. Testing all synthesis characteristics of the electro-hydraulic servo valve after assembling leads to high repair rate and reject rate, so accurate prediction for the synthesis characteristics in the industrial production is particular important in decreasing the repair rate and the reject rate of the product. However, the research in forecasting synthesis characteristics of the electro-hydraulic servo valve is rare. In this work, a hybrid prediction method was proposed based on rough set（RS） and adaptive neuro-fuzzy inference system（ANFIS） in order to predict synthesis characteristics of electro-hydraulic servo valve. Since the geometric factors affecting the synthesis characteristics of the electro-hydraulic servo valve are from workers＇ experience, the inputs of the prediction method are uncertain. RS-based attributes reduction was used as the preprocessor, and then the exact geometric factors affecting the synthesis characteristics of the electro-hydraulic servo valve were obtained. On the basis of the exact geometric factors, ANFIS was used to build the final prediction model. A typical electro-hydraulic servo valve production was used to demonstrate the proposed prediction method. The prediction results showed that the proposed prediction method was more applicable than the artificial neural networks（ANN） in predicting the synthesis characteristics of electro-hydraulic servo valve, and the proposed prediction method was a powerful tool to predict synthesis characteristics of the electro-hydraulic servo valve. Moreover, with the use of the advantages of RS and ANFIS, the highly effective forecasting framework in this study can also be applied to other problems involving synthesis characteristics forecasting.

Representation Theorem of Fuzzy Rough Set

This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.

Rough Set Fuzzy Optimum Selecting in Multidisciplinary System

Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.

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.

L-Fuzzy Rough Set Based on Complete Residuated Lattice

Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.

基于Rough sets和Fuzzy sets理论的约简算法

对决策表约简的一些roughsets和fuzzysets相关概念进行了阐述。在应用Rough集对决策系统进行约简的基础上,结合模糊聚类分析方法,论述了这一可行的决策表约简算法。该算法以属性核与属性重要性的代数定义形式为基础,利用聚类分析的模糊处理方法,解决了约简过程。并给出了对一电器公司全国连锁销售数据约简处理结果,得出了能帮助不同级别决策者进行决策的辅助性的规则知识。