On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.

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.

Domain-Oriented Data-Driven Data Mining Based on Rough Sets

Data mining (also known as Knowledge Discovery in Databases - KDD) is defined as the nontrivial extraction of implicit, previously unknown, and potentially useful information from data. The aims and objectives of data mining are to discover knowledge of interest to user needs.Data mining is really a useful tool in many domains such as marketing, decision making, etc. However, some basic issues of data mining are ignored. What is data mining? What is the product of a data mining process? What are we doing in a data mining process? Is there any rule we should obey in a data mining process? In order to discover patterns and knowledge really interesting and actionable to the real world Zhang et al proposed a domain-driven human-machine-cooperated data mining process.Zhao and Yao proposed an interactive user-driven classification method using the granule network. In our work, we find that data mining is a kind of knowledge transforming process to transform knowledge from data format into symbol format. Thus, no new knowledge could be generated (born) in a data mining process. In a data mining process, knowledge is just transformed from data format, which is not understandable for human, into symbol format,which is understandable for human and easy to be used.It is similar to the process of translating a book from Chinese into English.In this translating process,the knowledge itself in the book should remain unchanged. What will be changed is the format of the knowledge only. That is, the knowledge in the English book should be kept the same as the knowledge in the Chinese one.Otherwise, there must be some mistakes in the translating proces, that is, we are transforming knowledge from one format into another format while not producing new knowledge in a data mining process. The knowledge is originally stored in data (data is a representation format of knowledge). Unfortunately, we can not read, understand, or use it, since we can not understand data. With this understanding of data mining, we proposed a data-driven knowledge acquisition method based on rough sets. It also improved the performance of classical knowledge acquisition methods. In fact, we also find that the domain-driven data mining and user-driven data mining do not conflict with our data-driven data mining. They could be integrated into domain-oriented data-driven data mining. It is just like the views of data base. Users with different views could look at different partial data of a data base. Thus, users with different tasks or objectives wish, or could discover different knowledge (partial knowledge) from the same data base. However, all these partial knowledge should be originally existed in the data base. So, a domain-oriented data-driven data mining method would help us to extract the knowledge which is really existed in a data base, and really interesting and actionable to the real world.

A New Method for Constructing Decision Tree Based on Rough Sets Theory

Decision trees induction algorithms have been used for classification in a wide range of application domains. In the process of constructing a tree, the criteria of selecting test attributes will influence the classification accuracy of the tree.In this paper,the degree of dependency of decision attribute to condition attribute,based on rough set theory,is used as a heuristic for selecting the attribute that will best separate the samples into individual classes.The result of an example shows that compared with the entropy-based approach,our approach is a better way to select nodes for constructing decision trees.

Machine intelligence,rough sets and rough-fuzzy granular computing:uncertainty handling in bio-informatics and Web intelligence

Machine intelligence,is out of the system by the artificial intelligence shown.It is usually achieved by the average computer intelligence.Rough sets and Information Granules in uncertainty management and soft computing and granular computing is widely used in many fields,such as in protein sequence analysis and biobasis determination,TSM and Web service classification Etc.

Numerical Characterizations of Covering Rough Sets Based on Evidence Theory

Covering rough sets are improvements of traditional rough sets by considering cover of universe instead of partition.In this paper,we develop several measures based on evidence theory to characterize covering rough sets.First,we present belief and plausibility functions in covering information systems and study their properties.With these measures we characterize lower and upper approximation operators and attribute reductions in covering information systems and decision systems respectively.With these discussions we propose a basic framework of numerical characterizations of covering rough sets.

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.

Call for Papers The Third International Conference on Rough Sets and Knowledge Technology (RSKT2008)

Since the introduction of rough sets in 1982 by Professor Zdzisaw Pawlak, we have witnessed great advances in both theory and applications. Rough set theory is closely related to knowledge technology in a variety of forms such as knowledge discovery, approximate reasoning, intelligent and multiagent system design, knowledge intensive computations. The cutting-edge knowledge technologies have great impact on learning, pattern recognition, machine intelligence and automation of acquisition, transformation, communication, exploration and exploitation of knowledge. A principal thrust of such technologies is the utilization of methodologies that facilitate knowledge processing. To present the state-of-the-art scientific results, encourage academic and industrial interaction, and promote collaborative research in rough sets and knowledge technology worldwide, the 3rd International Conference on Rough Sets and Knowledge Technology will be held in Chengdu, China, May 17～19, 2008. It will provide a forum for researchers to discuss new results and exchange ideas, following the successful RSKT'06 (Chongqing, China) and JRS'07 (RSKT'07 together with RSFDGrC'07) (Toronto, Canada).

Rough Sets and Three Valued Connectives Extended Abstract

1 Introduction In[5]we investigated the significance of some truth-functional three valued logics of ill-known sets described by pairs of disjoint(or pairs of nested) subsets.In particular,we referred to the case of rough sets showing that if from a mathematical standpoint we obtain sound results,the interpretation with respect

Fuzzy Sets and Rough Sets:a Comparison through an Extension of Obtulowicz's Category

This paper is a purely mathematical one dealing with a common possible foundation of Fuzzy Set Theory and Rough Set Theory.It begins with a generalization of Obtulowicz's paper,rough sets and Heyting algebra valued sets,published in Bull.Polish Acad Sc.(math),198.In this paper Obtulowicz proposes a special subcategory

Rough Sets for Human Resource Competence Evaluation and Experiences

The evaluation of labor competences is an important activity for proper management of human resources. To assess labor competences, different techniques have been proposed, but these proposals represent invasive mechanisms so that its implementation affects the efficiency of the project, and do not store the experiences for further processing. The aim of this paper is to propose two alternative algorithms to recover the evidences of performance of human resources by identifying their relationship with labor competences, using rough sets and text distance. The experimental application of the algorithms demonstrated efficiency levels in line with the human evaluators and efficiency improvement in the evaluation process, compared with methods like 360 degrees.

On Random Rough Sets

In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.

Rough Sets in Approximate Solution Space

As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.

Matrix-based method for solving decision domains of neighbourhood multigranulation decision-theoretic rough sets

It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions.The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision-making problems from multi-levels and multi-angles,and the neighbourhood rough set model(NRS)can facilitate the analysis and processing of numerical or mixed type data,and can address the limitation of multigranulation decision-theoretic rough sets(MG-DTRS),which is not easy to cope with complex data.Based on the in-depth study of hybrid-valued decision systems and MG-DTRS models,this study analysed neigh-bourhood MG-DTRS(NMG-DTRS)deeply by fusing MG-DTRS and NRS;a matrix-based approach for approximation sets of NMG-DTRS model was proposed on the basis of the matrix representations of concepts;the positive,boundary and negative domains were constructed from the matrix perspective,and the concept of positive decision recognition rate was introduced.Furthermore,the authors explored the related properties of NMG-DTRS model,and designed and described the corresponding solving algorithms in detail.Finally,some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm,but also showed the relationship between the decision recognition rate and the granularity and threshold.

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.

Core Competitiveness Evaluation of Financial Institution with Rough Sets and Gray Correlation Analysis

The comprehensive evaluation method of enterprise core competitiveness is proposed by combining rough sets and gray correlation theories. Firstly,the initial index is screened through rough set attribute reduction algorithm,and the evaluation weight of each index is obtained through the rough set theory. Then,based on the gray correlation theory, an evaluation model is built for empirical analysis. The 30 financial institutions on the Yangtze River Delta are examined from the theoretical and empirical perspective.The result demonstrates not only the feasibility of rough set attribute reduction algorithm in the core competitiveness index system of the financial institution,but also the accuracy of the combination of these two methods in the comprehensive evaluation of corporate core competitiveness.

Evaluation of Parameters Importance in Cloud Service Selection Using Rough Sets

With the rapid development of the cloud computing technology, it has matured enough for a lot of individuals and organizations to move their work into the cloud. Correspondingly, a variety of cloud services are emerging. It is a key issue to assess the cloud services in order to help the cloud users select the most suitable cloud service and the cloud providers offer this service with the highest quality. The criteria parameters defining the cloud services are complex which lead to cloud service deviation. In this paper, we propose an assessment method of parameters importance in cloud services using rough set theory. The method can effectively compute the importance of cloud services parameters and sort them. On the one hand, the calculation can be used as the credible reference when users choose their appropriate cloud services. On the other hand, it can help cloud service providers to meet user requirements and enhance the user experience. The simulation results show the effectiveness of the method and its relevance in the cloud context.

Granularity of Knowledge Computed by Genetic Algorithms Based on Rough Sets Theory

Rough set philosophy hinges on the granularity of data, which is used to build all its basic concepts, like approximations, dependencies, reduction etc. Genetic Algorithms provides a general frame to optimize problem solution of complex system without depending on the domain of problem.It is robust to many kinds of problems.The paper combines Genetic Algorithms and rough sets theory to compute granular of knowledge through an example of information table. The combination enable us to compute granular of knowledge effectively.It is also useful for computer auto-computing and information processing.

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.