Covering-based Fuzzy Rough Set Research Articles

Covering-based variable precision L-fuzzy rough sets based on residuated lattices and corresponding applications

There are many extensions of Pawlak’s rough sets. Particularly, fuzzy rough set theory based on residuated lattices is considered as one of the generalizations that extends the truth values to lattices. In this paper, we attempt to combine the idea of “variable precision” with covering-based fuzzy rough sets based on residuated lattices and present the concept of covering-based variable precision L-fuzzy rough sets. After the presentation of this concept, some basic properties of the proposed rough set model are discussed. Then, with the aid of the PROMETHEE and TOPSIS methods, we put forth a novel multi-attribute decision-making (MADM) method based on covering-based variable precision L-fuzzy rough sets (for $$L=[0,1]$$ ). Finally, an illustrative example is give to demonstrate the proposed decision-making method. By a sensitivity analysis along with a comparative analysis, we reveal the applicability and validity of the proposed decision-making method.

PROMETHEE II method based on variable precision fuzzy rough sets with fuzzy neighborhoods

The model of covering-based fuzzy rough sets (CFRSs) can be regarded as a hybrid one by combining covering-based rough sets with fuzzy sets. In this paper, based on fuzzy neighborhoods, we propose two types of covering-based variable precision fuzzy rough sets (CVPFRSs) via fuzzy logical operators, i.e., type-I CVPFRSs and type-II CVPFRSs. Then, several basic properties of the two types of CVPFRSs are discussed. In addition, by virtue of the idea of PROMETHEE II methods, we construct a novel method to multi-attribute decision-making (MADM) in the context of medical diagnosis based on the proposed rough approximation operators. Finally, a test example for illustrating the proposed method is given. Meanwhile, a comparative analysis and an experimental evaluation are further discussed to interpret and evaluate the effectiveness and superiority of the proposed method. The proposed rough set model not only extends the theory of CFRSs, but also provides a new perspective for MADM with fuzzy evaluation information.

TOPSIS-WAA method based on a covering-based fuzzy rough set: An application to rating problem

In this paper, we firstly study two pairs of covering-based fuzzy rough set models and propose the TOPSIS-WAA method based on a covering-based fuzzy rough set. Subsequently, we design a rating scheme based on a multi-criteria decision-making method in a finite fuzzy covering approximation space. The rating scheme is implemented based on the preset subjective ratio and the calculated objective ranking of all alternatives. Furthermore, we use the relevant data of some customers of Industrial and Commercial Bank of China (ICBC) to illustrate the feasibility of our method. At the same time, two test rules are used to verify the validity of the proposed method. Moreover, we compare five different decision-making methods with our method to demonstrate the superiority of our method. Finally, the performance of our method is verified from the perspectives of the best alternative and the optimal ranking.

TOPSIS method based on a fuzzy covering approximation space: An application to biological nano-materials selection

The applications of nanomaterials in biomedicine have received increasing attentions. Therefore, how to choose the most suitable material among a variety of bio-nanomaterials with similar properties is a significant problem. Aiming at this problem, we describe it as a multi-criteria decision-making problem in a fuzzy covering approximation space and solve it via the TOPSIS method. Firstly, combining fuzzy neighborhood operators with fuzzy rough set models, we propose two pairs of covering-based fuzzy rough set models and study the basic properties together with classifications of these two pairs of models. Subsequently, we reveal a new method for determining objective weights using the first pair of covering-based fuzzy rough set models. Combining the objective criteria weight determination method with the TOPSIS method, we provide a solution to solve the problem of bone transplant replacement materials selection. Then, we discuss the experimental effects of our proposed method and the other eight different decision-making methods in practical problems to explain the rationality and enforceability of our approach. Finally, we validate the performance of our approach with the support of ideas of cross-validation and hypothesis testing.

Covering-based fuzzy rough sets

Many researchers have combined rough set theory and fuzzy set theory in order to easily approach problems of imprecision and uncertainty. Covering-based rough sets are one of the important generalizations of classical rough sets. Naturally, covering-based fuzzy rough sets can be studied as a combination of covering-based rough set theory and fuzzy set theory. It is clear that Pawlak's rough set model and fuzzy rough set model are special cases of the covering-based fuzzy rough set model. This paper investigates the properties of covering-based fuzzy rough sets. In addition, operations of intersection, union and complement on covering-based fuzzy rough sets are investigated. Finally, the corresponding algebraic properties are discussed in detail.