Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets

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.

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

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.

Different classes’ ratio fuzzy rough set based robust feature selection

Geometrical interpretation and applications of membership functions with fuzzy rough sets

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

In this paper, a generalized fuzzy compatibility relation between two universes is defined. By a generalized fuzzy compatibility relation between two universes, a covering and a tolerance relation are induced to a single universe. Based on the above covering and tolerance relation, the new extended patterns of three types of fuzzy rough set models on two universes are proposed. An important common characteristic of these new extended patterns is that the new approximation operators can be obtained by the composition of the approximation operators and the inverse approximation operators. We mainly construct the new extended models of fuzzy rough sets, -fuzzy rough sets and -fuzzy rough sets on two universes and investigate their properties.

This paper researched and constructed residuation implication operator of intuitionistic fuzzy T-norms.Based on this,the paper deducted the intuitionistic fuzzy rough sets model,and proved that the Pawlak rough sets,intuitionistic fuzzy sets,fuzzy rough sets,rough fuzzy sets and fuzzy T-norms rough sets were special cases of intuitionistic fuzzy rough sets.At last,some properties of intuitionistic fuzzy sets were presented and proved.

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

Recently, many methods based on fuzzy rough sets are proposed to reduce fuzzy attributes. The common characteristic of these methods is that all of them are based on fuzzy equivalence relation. In other words, the underlying concept of rough sets, indispensability relation, is generalized to fuzzy equivalence relation. Here fuzzy equivalence relation is the binary relation, which is reflexive, symmetric and transitive. This paper tries to generalize the fuzzy equivalence relation to fuzzy similarity relation, which is more helpful to keeping the fuzzy information of initial data than fuzzy equivalence relation. Based on the fuzzy similarity relation, fuzzy matrix computation for information system is proposed which can be used to reduce fuzzy attributes. Firstly, fuzzy similarity relation who is isomorphic with the fuzzy similarity matrix is given as fuzzy indispensability relation. Then all the information of initial data, such as the similarity among objects and fuzzy inconsistence degree between two objects, can be represented by fuzzy similarity matrix. Secondly, by considering that the small perturbation of the fuzzy similarity matrix can be ignorable, we propose some basic concepts of knowledge reduction such as fuzzy attributes reduct, core and fuzzy significance of attributes etc in this paper. Thirdly, a heuristic algorithm based on the fuzzy significance of attributes is proposed to find close-to-minimal fuzzy attributes reduct. Finally, experimental comparisons with other methods of attributes reduction are given. The experimental results show that our method is feasible and effective

In this paper we argue that fuzzy sets and rough sets aim to different purposes and that it is more natural to try to combine the two models of uncertainty (vagueness for fuzzy sets and coarseness for rough sets) in order to get a more accurate account of imperfect information. First, the upper and lower approximations of a fuzzy set are defined, when the universe of discourse of a fuzzy sets is coarsened by means of an equivalence relation. We then come close to Caianiello’s C-calculus. Shafer’s concept of coarsened belief functions also belongs to the same line of thought and is reviewed here. Another idea is to turn the equivalence relation relation into a fuzzy similarity relation, for a more expressive modeling of coarseness. New results on the representation of similarity relations by means of a fuzzy partition of fuzzy clusters of more or less indiscernible points are surveyed. The properties of upper and lower approximations of fuzzy sets by similarity relations are thoroughly studied. Lastly the potential usefulness of the fuzzy rough set notions for logical inference in the presence of both fuzzy predicates and graded indiscernibility is indicated. Especially fuzzy rough sets may provide a nice semantic background for modal logic involving fuzzy modalities and/or fuzzy sentences.

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.

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

Rough set theory for the interval-valued fuzzy information systems