New Soft Rough Set Approximations

Shawkat Alkhazaleh,Emad A. Marei 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.2

The soft rough set model was introduced by Fing in 2011 and can be considered as a generalized rough set model, in which an interesting connection was established between two mathematical approaches to vagueness: rough sets and soft sets. It was also shown that Pawlak’s rough set model can be viewed as a special case of soft rough sets. There are two problems with this model in using this concept in real-life applications. The first problem is that some soft rough sets are not contained in their upper approximations, which contradicts Pawlak’s thoughts. The second problem is that the boundary region of any considered set, in the soft rough set model, must be decreased to make it possible to take a true decision of any application problem. In this study, the soft rough set model is modified to solve these problems. The basic properties of the modified approximations are introduced and supported with propositions and illustrative examples. Modified concepts can be viewed as a general mathematical model for qualitative and quantitative real-life problems. A comparison between the suggested approach to soft rough sets and the traditional soft rough set model is provided.

Marcus–Wyse topological rough sets and their applications

Elsevier 2019 International journal of approximate reasoning Vol.106 No.-

<P><B>Abstract</B></P> <P>The aim of this paper is to establish two new types of rough set structures associated with the Marcus–Wyse (<I>MW</I>-, for brevity) topology, such as an <I>M</I>-rough set and an <I>MW</I>-topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in <SUP> Z 2 </SUP> , where Z is the set of integers. These two rough set structures are related to each other via an <I>M</I>-digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (<I>LFC</I>-, for short) space ( U , C ) and a subset <I>X</I> of <I>U</I>, we firstly introduce a new neighborhood system on <I>U</I> related to <I>X</I>. Next, we formulate the lower and upper approximations with respect to <I>X</I>, where all of the sets <I>U</I> and X ( ⊆ U ) need not be finite and the covering <B>C</B> is locally finite. Actually, the notion of <I>M</I>-digitization of a 2-dimensional Euclidean space plays an important role in developing an <I>M</I>-rough and <I>MW</I>-topological rough set structures. Further, we prove that <I>M</I>-rough set operators have a duality between them. However, each of <I>MW</I>-topological rough set operators need not have the property as an interior or a closure from the viewpoint of <I>MW</I>-topology.</P>

Roughness measures of locally finite covering rough sets

Elsevier 2019 International journal of approximate reasoning Vol.105 No.-

<P><B>Abstract</B></P> <P>The present paper defines four new kinds of measures of roughness of covering rough sets induced by <I>locally finite covering approximation</I> (<I>LFC</I>-, for brevity) spaces which are generalizations of finite covering approximation spaces. More precisely, consider an <I>LFC</I>-space ( U , C ) and a nonempty set X ( ⊆ U ) . Using a reduction of a given <I>LFC</I>-space ( U , C ) , the present paper firstly establishes two types of rough membership functions of the set <I>X</I> with respect to <I>LFC</I>-spaces ( U , C ) , where each of the cardinalities of the sets <I>U</I>, <B>C</B>, and <I>X</I> need not be finite. Next, it also develops another two kinds of notions of roughness of digital topological rough sets. Indeed, these notions are based on the concepts of accuracy of rough sets derived from <I>LFC</I>-spaces. Furthermore, we use them to the estimation of roughness of a covering rough set of X ( ⊆ U ) . Besides, we estimate roughness of a digital topological rough set, such as measures of roughness of the Khalimsky and Marcus–Wyse topological rough sets. Moreover, we compare between the measures of the Khalimsky topological and the Marcus–Wyse topological roughness.</P>

Soft sets in fuzzy setting

Xueyou Chen 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.16 No.2

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. In 1982, Pawlak initiated the rough set theory, Dubois and Prade combined fuzzy sets and rough sets all together. In 1999, Molodtsov introduced the concept of soft sets to solve complicated problems and various types of uncertainties. Maji et al. studied the (Zadeh's) fuzzification of the soft set theory. As a generalization, I define the notion of a soft set in L-set theory, introduce several operators for L-soft set theory, and investigate the rough operators on $L^X$ induced by an L-soft set.

Topology of the Redefined Intuitionistic Fuzzy Rough Sets

Sang Min Yun,Yeon Seok Eom,Seok Jong Lee 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.4

In our previous paper, we proposed a new definition of intuitionistic fuzzy rough sets. In this paper, we propose a topology for redefined intuitionistic fuzzy rough sets and investigate the basic properties of their subspaces, transition spaces, and continuous functions. Moreover, we obtain the adjointness between the categories of fuzzy rough sets and intuitionistic fuzzy rough sets. The results obtained from this new definition differ from those of previous studies.

Multi-granulation rough set: from crisp to fuzzy case

Xi-Bei Yang,Xiaoning Song,Huili Dou,Jingyu Yang 원광대학교 기초자연과학연구소 2011 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.1 No.1

Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy $T$–similarity relations are used to define the optimistic and pessimistic fuzzy rough sets respectively. The basic properties about these fuzzy rough sets are then discussed. Finally, the relationships among single relation based fuzzy rough set, optimistic and pessimistic multi–granulation fuzzy rough sets are addressed.

Feature Reduction using a GA-Rough Hybrid Approach on Bio-medical data

Chang Su Lee 제어로봇시스템학회 2011 제어로봇시스템학회 국제학술대회 논문집 Vol.2011 No.10

In this paper, a new approach is proposed for feature reduction using a GA-Rough hybrid approach on Bio-medical data. The given set of bio-medical data is pre-processed with the min-max normalization method. Then the subsequent evaluation on each feature with respect to the output class is carried out utilizing the information gain-based approach using the entropy-based discretization. Features with zero worth on the evaluated set of features are eliminated. The genetic algorithm is applied for performing a search for most relevant features on the set of features remained. These processes continue until there is no further change on the final reduced set of features. The rough set-based approach is applied on this set of features by applying discernibility matrix-based approach in order to obtain the final reduct. The reduced set of features, or a final reduct, is tested for classification using a TS-type rough-fuzzy classifier to show the viability of the proposed feature reduction approach. The results showed that the proposed feature reduction approach effectively achieved to reduce number of features significantly which reduced to 7 out of 120 features along with compatible classification results on the given bio-medical data compared to other approaches.

Maximal and minimal neighborhoods of rough fuzzy sets

Ismail Ibedou,S. E. Abbas 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.26 No.2

It has a comment on two patterns of generalizations of the roughness of some fuzzy set. The authors in 2022, based on the minimal neighborhoods of rough fuzzy sets, introduced a generalization of rough fuzzy sets. This paper will be used maximal neighborhoods in defining a new generalization of rough fuzzy sets in a pattern similar to this generalization introduced by the authors in 2022. Mainly, it is shown that the new boundary region set computed using maximal neighborhoods does not depend on that set computed using minimal neighborhoods as given by the authors in 2022. As an application, it is shown that the connectedness of rough fuzzy topological spaces could be defined using maximal neighborhoods. Still, this connectedness is not related to the connectedness expressed by the authors in 2022 using minimal neighborhoods.

Rough Set Approach for Identification of Accident on Water Route Segment

Hao ZHANG,Ying-jie XIAO,Liang CHEN 보안공학연구지원센터 2015 International Journal of u- and e- Service, Scienc Vol.8 No.8

This paper presents a novel non-parametric methodology – rough set theory – for accident occurrence exploration. The rough set theory allows researchers to analyze accidents in multiple dimensions and to model accident occurrence as factor chains. Factor chains are composed of Seaman characteristic, ship’s characteristics, navigational behavior and environment factors that imply typical accident occurrence. Rose2 software tool is used. The purpose of this application is to find out the critical attributes to reduce the number of the fatality in maritime accidents. This paper explains the application on the accident reports of Accident Data database, containing data records for all categories of maritime accidents between the years of 2003 and 2009. Variable precision rough set is used to reduce the attributes of data set. The categorization tools and decision trees are used to find the relations and rules about the accidents resulted in fatality. Some rules about the fatality are obtained and also the attributes that affect the fatality in the incident have determined.

On rough cubic sets

Xueyou Chen 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.21 No.3

Zadeh initiated fuzzy sets, as a generalization, Jun et al. introduced the notion of a cubic set. Pawlak initiated rough set theory to study incomplete and insufficient information. Dubois, Prade first investigated fuzzy rough set and rough fuzzy set. Then many researchers studied the theory of rough sets in variously fuzzy structures. In the paper, we define two rough operators on cubic sets by means of a cubic relation, and investigate some of their properties with respect to two systems operators on cubic sets.