Classical rough set theory is considered a useful tool for dealing with the uncertainty of categorical data. The major deficiency of this model is that the classical rough set model is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy similarity relations was introduced to describe the similarity between samples with categorical attributes. However, these kinds of similarity relations also have deficiencies when they are used in fuzzy rough computation. In this article, we propose a new fuzzy-rough-set model for categorical data by introducing a variable parameter to control the similarity of samples. This model employs the iterative computation strategy to define fuzzy rough approximations and dependence functions. It is proved that the proposed rough dependence function is monotonic. Finally, the proposed model is applied to the attribute reduction of categorical data. The experimental results indicate that the proposed model is more effective for categorical data than some existing algorithms.

Fuzzy Rough Attribute Reduction for Categorical Data

Double-quantitative variable consistency dominance-based rough set approach

Classical fuzzy rough set often uses fuzzy rough dependency as an evaluation function of feature selection. However, this function only retains the maximum membership degree of a sample to one decision class, it cannot describe the classification error. Therefore, in this article, a novel criterion function for feature selection is proposed to overcome this weakness. To characterize the classification error rate, we first introduce a class of irreflexive and symmetric fuzzy binary relations to redefine the concepts of fuzzy rough approximations. Then, we propose a novel concept of dependency: inner product dependency to describe the classification error and construct a criterion function to evaluate the importance of candidate features. The proposed criterion function not only can maintain a maximum dependency function, but also guarantees the minimum classification error. The experimental analysis shows that the proposed criterion function is effective for datasets with a large overlap between different categories. 

Feature Selection With Fuzzy-Rough Minimum Classification Error Criterion

In the realistic decision-making (DM) process, the DM results were provided by multiple DM experts, which are more accurate than those based on one DM expert. Therefore, the multi-granulation rough set (MGRS) model is more accurate in DM problems. It is imperative to apply the idea of multi-granulation to the complex fuzzy uncertain information. By combining q-rung dual hesitant fuzzy sets (q-DHFSs) with multi-granulation rough sets (MGRSs) over two universes, we propose a q-rung dual hesitant fuzzy multi-granulation rough set (q-RDHFMGRS) over two universes, and prove some of their basic properties. Then, based on this model, we propose a new multi-attribute DM algorithm. Finally, we validate the practicability and validity of the algorithm through an example of medical diagnosis.

A general framework for multi-granulation rough decision-making method under q -rung dual hesitant fuzzy environment

The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian et al, extended this model and defined multigranulation rough sets by using finite number of equivalence relations. This model provide new direction to the research. Recently, Shabir et al. proposed a rough set model which depends on a soft relation from an universe V to an universe W . In this paper we are present multigranulation roughness based on soft relations. Firstly we approximate a non-empty subset with respect to aftersets and foresets of finite number of soft binary relations. In this way we get two sets of soft sets called the lower approximation and upper approximation with respect to aftersets and with respect to foresets. Then we investigate some properties of lower and upper approximations of the new multigranulation rough set model. It can be found that the Pawlak rough set model, Qian et al. multigranulation rough set model, Shabir et al. rough set model are special cases of this new multigranulation rough set model. Finally, we added two examples to illustrate this multigranulation rough set model.

Multigranulation roughness based on soft relations

Multigranulation rough set over two universes provides a new perspective to combine multiple granulation knowledge in a multigranulation space in practical reality. Note that there are always non-essential neighborhood granulations, which would affect the efficiency and quality of decision making. Therefore, selecting valuable granulations and reducing worthless ones are necessary for the application of multigranulation rough set in decision process. In this paper, we first define several measurements to compare the granularity of neighborhood granulations, using which the granulation selection with multigranulation rough set is characterized. Then, the selection algorithms in the multigranulation space are developed. Third, we generate “OR” and “AND” decision rules based on multigranulation fusion strategies. As an application, these decision rules are employed to make decisions in the presence of disease diagnosis problems. In the end, the effectiveness and efficiency of the proposed algorithms are examined with numerical experiments on selective data sets.

Shimei Zhao

Papers

Granulation selection and decision making with multigranulation rough set over two universes