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.

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.

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.

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.

Fuzzy rough sets in Sostak sense

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

Rough similarity degree and rough close degree in rough fuzzy sets and the applications

Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.

Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

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.

Emergency Decision-Making Based on q-Rung Orthopair Fuzzy Rough Aggregation Information

With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.

THRFuzzy:Tangential holoentropy-enabled rough fuzzy classifier to classification of evolving data streams

The rapid developments in the fields of telecommunication, sensor data, financial applications, analyzing of data streams, and so on, increase the rate of data arrival, among which the data mining technique is considered a vital process. The data analysis process consists of different tasks, among which the data stream classification approaches face more challenges than the other commonly used techniques. Even though the classification is a continuous process, it requires a design that can adapt the classification model so as to adjust the concept change or the boundary change between the classes. Hence, we design a novel fuzzy classifier known as THRFuzzy to classify new incoming data streams. Rough set theory along with tangential holoentropy function helps in the designing the dynamic classification model. The classification approach uses kernel fuzzy c-means(FCM) clustering for the generation of the rules and tangential holoentropy function to update the membership function. The performance of the proposed THRFuzzy method is verified using three datasets, namely skin segmentation, localization, and breast cancer datasets, and the evaluated metrics, accuracy and time, comparing its performance with HRFuzzy and adaptive k-NN classifiers. The experimental results conclude that THRFuzzy classifier shows better classification results providing a maximum accuracy consuming a minimal time than the existing classifiers.

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 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.

Multi-Span and Multiple Relevant Time Series Prediction Based on Neighborhood Rough Set

Rough set theory has been widely researched for time series prediction problems such as rainfall runoff.Accurate forecasting of rainfall runoff is a long standing but still mostly signicant problem for water resource planning and management,reservoir and river regulation.Most research is focused on constructing the better model for improving prediction accuracy.In this paper,a rainfall runoff forecast model based on the variable-precision fuzzy neighborhood rough set(VPFNRS)is constructed to predict Watershed runoff value.Fuzzy neighborhood rough set dene the fuzzy decision of a sample by using the concept of fuzzy neighborhood.The fuzzy neighborhood rough set model with variable-precision can reduce the redundant attributes,and the essential equivalent data can improve the predictive capabilities of model.Meanwhile VFPFNRS can handle the numerical data,while it also deals well with the noise data.In the discussed approach,VPFNRS is used to reduce superuous attributes of the original data,the compact data are employed for predicting the rainfall runoff.The proposed method is examined utilizing data in the Luo River Basin located in Guangdong,China.The prediction accuracy is compared with that of support vector machines and long shortterm memory(LSTM).The experiments show that the method put forward achieves a higher predictive performance.

Definability and Textural Rough Set Algebras

In this paper,a counterpart of definability is studied in texture spaces.The concept of textural complete field is defined and the relations with textural definable sets are investigated.If a texture is discrete,then textural definability coincides with definability.Using this fact,we obtain some basic results for definability in rough set algebras.Further,we discuss on definability for fuzzy rough sets considering textural fuzzy direlations.

Game Theory-Based Dynamic Weighted Ensemble for Retinal Disease Classification

An automated retinal disease detection system has long been in exis-tence and it provides a safe,no-contact and cost-effective solution for detecting this disease.This paper presents a game theory-based dynamic weighted ensem-ble of a feature extraction-based machine learning model and a deep transfer learning model for automatic retinal disease detection.The feature extraction-based machine learning model uses Gaussian kernel-based fuzzy rough sets for reduction of features,and XGBoost classifier for the classification.The transfer learning model uses VGG16 or ResNet50 or Inception-ResNet-v2.A novel ensemble classifier based on the game theory approach is proposed for the fusion of the outputs of the transfer learning model and the XGBoost classifier model.The ensemble approach significantly improves the accuracy of retinal disease pre-diction and results in an excellent performance when compared to the individual deep learning and feature-based models.

Knowledge modeling based on interval-valued fuzzy rough set and similarity inference: prediction of welding distortion

Knowledge-based modeling is a trend in complex system modeling technology. To extract the process knowledge from an information system, an approach of knowledge modeling based on interval-valued fuzzy rough set is presented in this paper, in which attribute reduction is a key to obtain the simplified knowledge model. Through defining dependency and inclusion functions, algorithms for attribute reduction and rule extraction are obtained. The approximation inference plays an important role in the development of the fuzzy system. To improve the inference mechanism, we provide a method of similaritybased inference in an interval-valued fuzzy environment. Combining the conventional compositional rule of inference with similarity based approximate reasoning, an inference result is deduced via rule translation, similarity matching, relation modification, and projection operation. This approach is applied to the problem of predicting welding distortion in marine structures, and the experimental results validate the effectiveness of the proposed methods of knowledge modeling and similarity-based inference.

Fuzzy Rough Relation and Its Properties

In this paper, the concept of fuzzy rough relation(FRR) and the max-min composition of FRR are given. Then the properties of the composition of FRRs are studied.

Identifying the key factors of subsidiary supervision and management using an innovative hybrid architecture in a big data environment

In a highly intertwined and connected business environment,globalized layout planning can be an effective way for enterprises to expand their market.Nevertheless,conflicts and contradictions always exist between parent and subsidiary enterprises;if they are in different countries,these conflicts can become especially problematic.Internal control systems for subsidiary supervision and management seem to be particularly important when aiming to align subsidiaries’decisions with parent enterprises’strategic intentions,and such systems undoubtedly involve numerous criteria/dimensions.An effective tool is urgently needed to clarify the relevant issues and discern the cause-and-effect relationships among them in these conflicts.Traditional statistical approaches cannot fully explain these situations due to the complexity and invisibility of the criteria/dimensions;thus,the fuzzy rough set theory(FRST),with its superior data exploration ability and impreciseness tolerance,can be considered to adequately address the complexities.Motivated by efficient integrated systems,aggregating multiple dissimilar systems’outputs and converting them into a consensus result can be useful for realizing outstanding performances.Based on this concept,we insert selected criteria/dimensions via FRST into DEMATEL to identify and analyze the dependency and feedback relations among variables of parent/subsidiary gaps and conflicts.The results present the improvement priorities based on their magnitude of impact,in the following order:organizational control structure,business and financial information system management,major financial management,business strategy management,construction of a management system,and integrated audit management.Managers can consider the potential implications herein when formulating future targeted policies to improve subsidiary supervision and strengthen overall corporate governance.

Developing a GIS-based rough fuzzy set granulation model to handle spatial uncertainty for hydrocarbon structure classification,case study:Fars domain,Iran

It is well agreed that geologic risk occurs during hydrocarbon exploration because diverse uncertainties accompany the entire hydrocarbon system parameters such as the source rock,reservoir rock,trap and seal rock.In order to overcome such attributes with uncertainties,a number of soft computing methods are used.Information granules could be provided by the Rough Fuzzy Set Granulation(RFSG)with a thorough quality evaluation.This is capable of attribute reduction that has been claimed to be essential in investigating the hydrocarbon systems.This paper is an endeavor to recommend a Geospatial Information System(GIS)-based model with the aim of categorizing the hydrocarbon structures map consistent with the uncertainty range concepts of geologic risk in the rough fuzzy sets and granular computing.The model used the RFSG for the attribute reduction by a Decision Logic language(DLlanguage).The RFSG was employed in order to classify hydrocarbon structures according to geological risk and extract the fuzzy rules with a predefined range of uncertainty.In order to assess the precisions of the fuzzy decisions on the hydrocarbon structure classification,the fuzzy entropy and fuzzy cross-entropy are applied.The proposed RFSG model applied for 62 structures as the training data,average fuzzy entropy has been calculated as 0.85,whereas the average fuzzy cross-entropy has been calculated 0.18.As it can be discerned,just seven structures had cross-entropies greater than 0.1,while three structures were larger than 0.3.It is implied that the precision of the proposed model is about 89%.The results yielded two reductions for the condition attributes and 11 fuzzy rules being filtered by the granular computing values.

Attribute reduction based on fuzziness of approximation set in multi-granulation spaces

Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuristic attribute reduction algorithms usually keep the positive region of a target set unchanged and ignore boundary region information. So, how to acquire knowledge from the boundary region of a target set in a multi-granulation space is an interesting issue. In this paper, a new concept, fuzziness of an approximation set of rough set is put forward firstly. Then the change rules of fuzziness in changing granularity spaces are analyzed. Finally, a new algorithm for attribute reduction based on the fuzziness of 0.5-approximation set is presented. Several experimental results show that the attribute reduction by the proposed method has relative better classification characteristics compared with various classification algorithms.