The cost-sensitive approximation of neighborhood rough sets and granular layer selection

Neighborhood rough sets (NRS) are the extended model of the classical rough sets. The NRS describe the target concept by upper and lower neighborhood approximation boundaries. However, the method of approximately describing the uncertain target concept with existed neighborhood information granules is not given. To solve this problem, the cost-sensitive approximation model of the NRS is proposed in this paper, and its related properties are analyzed. To obtain the optimal approximation granular layer, the cost-sensitive progressive mechanism is proposed by considering user requirements. The case study shows that the reasonable granular layer and its approximation can be obtained under certain constraints, which is suitable for cost-sensitive application scenarios. The experimental results show that the advantage of the proposed approximation model, moreover, the decision cost of the NRS approximation model will monotonically decrease with granularity being finer.

Graded rough sets based on neighborhood operator over two different universes and their applications in decision-making problems

In this paper, we will propose the novel notion of neighborhood rough sets on a universe set and study some of their basic properties. Then, the relationships between the neighborhood rough sets and covering rough sets are established. Further, the several related notions of probabilistic neighborhood rough sets are investigated and their basic theoretical are discussed. In addition, the notion of neighborhood rough sets over two different universes is defined, and interesting in their properties are explained. Depend on the neighborhood rough sets over two different universes, two algorithms are designed to solve the rough decision-making problems and clarify their applicability by two illustrative examples, respectively. Finally, a comparison between Liu et al.’s approach and our approach is given.

Fuzzy Knowledge Distance with Three-Layer Perspectives in Neighborhood System

Information granule is the basic element in granular computing (GrC), and it can be obtained according to the granulation criterion. In neighborhood rough sets, current uncertainty measures focus on computing the knowledge granulation of single granular space and have two main limitations: (i) neglecting the structural information of boundary regions and (ii) the inability to reflect the difference between neighborhood granular spaces with the same uncertainty for approximating a target concept. Firstly, a fuzziness-based uncertainty measure for neighborhood rough sets is introduced to characterize the structural information of boundary regions. Moreover, from the perspective of distance, based on the idea of density peaks, we present a fuzzy-neighborhood-granule-distance- (FNGD-) based method to discover the relationship between granules in a granular space. Then, to characterize the difference between granular spaces for approximating a target concept, we present the fuzzy neighborhood granular space distance (FNGSD) and fuzzy neighborhood boundary region distance (FNBRD). FNGD, FNGSD, and FNBRD are hierarchically organized from fineness to coarseness according to the semantics of granularity, which provide three-layer perspectives in the neighborhood system.

Graded Rough Sets based on Neighborhood Operator Over two Different Universes and its Application

Abstract The major concern of this paper is to present the notion of rough set based on neighborhood operator on universe set, along with its properties, and examples. Then, we generalize several notions of covering rough sets to neighborhood rough sets with respect to the graded n. Further, we present some notions such as probabilistic neighborhood rough approximations of X, (Type-I / Type-II) probabilistic neighborhood rough approximations of X with error α and β, and (Type-I / Type-II) probabilistic neighborhood rough approximations of X with respect to N . The interesting properties of above notions are investigated in detail. On the other hand, we define the notion of rough set based on neighborhood operator over two different universes. Subsequently, we present some notions (Type-I / Type-II / Type-III) graded n-neighborhood rough sets and give a two approaches to decision-making problems based on the (Type-II / Type-III) grade n-neighborhood rough sets. Then, we construct the decision steps and give two algorithms of the decision methods. Also, we will give two illustrative examples to show the applicability of the rough set based on neighborhood operator over two different universes to solve the rough decision-making problems. Finally, we give a comparison between the Liu et al.’s approach and our approach.