Covering based multigranulation [formula omitted]-fuzzy rough set models and applications in multi-attribute group decision-making

Fuzzy rough set theory can model uncertainty in data and has been applied to feature selection for machine learning tasks. The existence of noise in data is one of the reasons for data uncertainty. However, most classical fuzzy rough set models are often sensitive to the noise in data, which somewhat degrades their applicability to process uncertainty of data. Furthermore, a robust feature evaluation function is nontrivial in a fuzzy rough set model as a nonoptimal feature subsets may be selected due to the perturbations from redundant features. In this article, we delve into local density and indispensable features for fuzzy rough feature selection to address these challenges. We first propose a local density-based fuzzy rough set (LDFRS) model to tackle noisy data. Mutual information is then plugged into the proposed LDFRS model to evaluate uncertainty in data. A joint feature evaluation function on the indispensability and relevance of features is constructed to evaluate the significance of features. On this basis, a fuzzy rough feature selection algorithm is built upon the LDFRS model. Experimental results using four typical classifiers demonstrate the robustness and effectiveness of the proposed model including our feature selection algorithm and its superiority against baseline methods.

Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and upper approximations of a fuzzy set are defined on multiple fuzzy tolerance relations. It follows the research on the properties of the fuzzy lower and upper approximations of the new models. The fuzzy rough set model, rough set model on a tolerance relation and multi-granulation rough sets models are special cases of the new ones from the perspective of the considered concepts, related relations and granular computing. The new models are meaningful generalizations of the classical rough sets.

Different classes’ ratio fuzzy rough set based robust feature selection

Attribute reduction for multi-label learning with fuzzy rough set

The definition of basic rough sets [3] depends upon either a single equivalence relation defined on a universe or several equivalence relations defined over the universe, taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. Extending this notion, a rough set model based on multi-granulations (MGRS) was introduced in [5]. In this approach, approximations of sets were defined through multiple equivalence relations on the universe and their properties were investigated. Using hybridization of fuzzy set [13] with rough set the concept of rough fuzzy set was introduced by Dubois and Prade [1]. Recently, a Rough Fuzzy Set Model was introduced and studied by Wu and Kou [12], which is based on Multiple Granulation. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [10]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [11]. In this paper we introduce incomplete multigranulation on rough fuzzy sets, study their basic properties and extend the topological properties in [11] to this context. Our findings are true for both complete and incomplete fuzzy rough set models based upon multi granulation.KeywordsRough SetsFuzzy rough setsequivalence relationstolerance relationstype of rough setsmulti granular fuzzy rough sets

On (IO,O)-fuzzy rough sets based on overlap functions

Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets

On the granular representation of fuzzy quantifier-based fuzzy rough sets

Energy is an indispensable material resource for human production and life. It is a powerful engine and an important guarantee for human survival, economic and social sustainable development and world change. The economy is developing rapidly, the demand for energy continues to grow, energy consumption has increased sharply in a short period, and the security of energy supply and demand has also shown a severe trend. Predicting energy demand is especially important. However, due to the many influencing factors and the lack of energy data, the energy demand prediction has great uncertainty in the prediction results. Because of the above problems, this paper proposes an energy big data demand prediction model based on a fuzzy rough set model. Firstly, according to the data, the factors affecting the energy demand are determined, and the fuzzy C-means clustering algorithm is used to discretize the data according to the characteristics of the fuzzy rough set. Then the decision table is established and the attribute importance is calculated, and then the neighborhood rough set is used for attribute reduction. Then extract the correlation rules to establish a prediction model. Compare the prediction model proposed in this paper with the existing gray prediction method and energy elasticity coefficient method. The results show that this method can more scientifically predict the changes in energy big data demand. Finally, based on the experimental results, the corresponding strategies for optimizing the energy structure are proposed to provide reference for the optimization and development of energy demand.

In the real world, we often encounter varying membership grades due to varying information source values. The fuzzy rough set model is refurbished to develop probabilistic variable precision fuzzy rough set (P-VP-FRS) to deal with this imprecision. The main inspiration behind the proposed P-VP-FRS is our inability to precisely represent the imprecision, which necessitates generalization in the approximations. The adjustable parameters in P-VP-FRS control the tradeoff between the generalization and accuracy. A few measures for quality of approximation and generalization are proposed. The usefulness of P-VP-FRS is shown through a case study.

The dependency function proposed in the rough set model and fuzzy rough set model is widely employed in feature evaluation and attribute reduction. It is shown that the relations between fuzzy memberships haven't used in the function. We introduce the concept of fuzzy similarity measure and propose a new model in evaluating feature dependency. The properties of the model were discussed. Experimental results show that the model is feasible and effective.

On the topological properties of fuzzy rough sets

Three-way decision models based on multigranulation support intuitionistic fuzzy rough sets

This paper investigates the diversified multi-attribute group decision-making problem which means that the different decision-makers have different evaluation attribute sets for all candidate alternatives. We analyze the diversified multi-attribute group decision-making problem from the perspective of granular computing models and creatively combine soft sets with multigranulation fuzzy rough sets to construct the multigranulation soft fuzzy rough set model. Subsequently, we define the optimistic upper and lower approximations and pessimistic upper and lower approximations with respect to multigranulation soft fuzzy rough set model. Meanwhile, we discuss some important mathematical conclusions and properties based on the established model. Then, we propose a novel approach to the diversified multi-attribute group decision-making problem based on multigranulation soft fuzzy rough set and TODIM method, which fully consider the reference dependence and loss aversion of decision-makers in the decision-making process. Finally, we use a numerical example of evaluation for the policy selection group decision-making problem to describe and explain the calculation principle and process and compare the results with existing related work, and our approach has great stability and rationality. And the contributions of this paper include the following two points: (1) construct the multigranulation soft fuzzy rough set model; (2) combine the established model with TODIM method to provide a novel perspective to solve the diversified multi-attribute group decision-making problem.

The basic notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation. This paper proposes an intuitionistic fuzzy rough set (IFRS) model which is a combination of intuitionistic fuzzy set (IFS) and rough set. We approximate an IFS by using soft binary relations instead of fixed binary relations. By using this technique, we get two pairs of intuitionistic fuzzy (IF) soft sets, called the upper approximation and lower approximation with respect to foresets and aftersets. Properties of newly defined rough set model (IFRS) are studied. Similarity relations between IFS with respect to this rough set model (IFRS) are also studied. Finally, an algorithm is constructed depending on these approximations of IFSs and score function for decision-making problems, although a method of decision-making algorithm has been introduced for fuzzy sets already. But, this new IFRS model is more accurate to solve the problem because IFS has degree of nonmembership and degree of hesitant.