An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application

In this paper, with the aid of fuzzy soft $$\beta $$
 -neighborhoods, we introduce fuzzy soft covering-based multi-granulation fuzzy rough set models. We examine some of the relevant properties of fuzzy soft covering based on optimistic, pessimistic, and variable precision multi-granulation fuzzy rough set models. Then, we give fuzzy soft coverings based on $$\psi $$
 -optimistic and $${\mathscr {D}}$$
 -optimistic (
 $$\psi $$
 -pessimistic and $${\mathscr {D}}$$
 -pessimistic) multi-granulation fuzzy rough sets from fuzzy soft measures. It also discusses the interactions between these forms of fuzzy soft coverings based on multi-granulation fuzzy rough sets. Eventually, we apply the proposed models for solving MAGDM problems. The effectiveness and feasibility of our approach are noted from the introduced comparisons between our method and some methods given in the previous studies.

Fuzzy soft covering-based multi-granulation fuzzy rough sets and their applications

Rough set theory is a non-statistical approach to handle uncertainty and uncertain knowledge. It is characterized by two methods called classification (lower and upper approximations) and accuracy measure. The closeness of notions and results in topology and rough set theory motivates researchers to explore the topological aspects and their applications in rough set theory. To contribute to this area, this paper applies a topological concept called “somewhere dense sets” to improve the approximations and accuracy measure in rough set theory. We firstly discuss further topological properties of somewhere dense and cs-dense sets and give explicitly formulations to calculate S-interior and S-closure operators. Then, we utilize these two sets to define new concepts in rough set context such as SD-lower and SD-upper approximations, SD-boundary region, and SD-accuracy measure of a subset. We establish the fundamental properties of these concepts as well as show their relationships with the previous ones. In the end, we compare the current method of approximations with the previous ones and provide two examples to elucidate that the current method is more accurate.

Improvement of the approximations and accuracy measure of a rough set using somewhere dense sets

Abstract In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>ρ</mml:mi> </mml:msub> </mml:math> -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work. 

/pdf/topological-approach-to-generate-new-rough-set-models-1zgk8ryf.pdf

Topological approach to generate new rough set models

Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe informa...

Different kinds of generalized rough sets based on neighborhoods with a medical application

This paper puts forward some rough approximations which are motivated from topology. Given a subset , we can use 8 types of - neighborhoods to construct approximations of an arbitrary on the one hand. On the other hand, we can also construct approximations relying on a topology which is induced by an - neighborhood. Properties of these approximations and relationships between them are studied. For convenience of use, we also give some useful and easy-to-understand examples and make a comparison between our approximations and those in the published literature.

/pdf/new-rough-approximations-based-on-e-neighborhoods-1noey05o7m.pdf

Wen Qing Fu

Papers

New Rough Approximations Based on E-Neighborhoods