# On a Hybridization of Deep Learning and Rough Set Based Granular Computing
## 1 Introduction  
This paper is divided into parts dedicated to deep learning, rough sets, granular computing by means of rough mereology. Deep learning as a collection of techniques and is rooted in artificial neural networks (ANN's) [1; 2; 3]. The idea of a neural network is that of an acyclic directed graph whose nodes are computing units--neurons--joined by edges labelled with weights. Nodes with input degrees of zero are called inputs while nodes with the output degree zero are said to be outputs. The flow of information is forward: from input nodes to output nodes. Nodes are classified into layers, each layer defined recurrently starting from the input nodes layer. Exemplary Computation by a neural net begins with the input vector and in the simple case of a sigmoidal perceptron, with the input \(x\), the output is given as \(f(x)\), \(f\) being an activation sigmoidal function. The result of the computation is the vector output by the output layer of neurons. The learning procedure for ANN's is a series of computations on sequences of training vectors \(x_{i}\) which stops when the output vector is sufficiently close to the target vector on each input vector. Theoretically justified by the Perceptron Learning Theorem [4], the method of learning by changing weights by the delta rule turned effective when the backpropagation technique came into usage [5]. Deep learning proceeds further by enhancing the neural net with many filters allowing for exhibiting of many local features. Some variants like LSTM allow for reaching deep back into memory of theprocess which makes such networks especially effective in, for example, speech processing [6]. For a general introduction please consult [7]. Interesting research on the field of granular computation with the use of neural network techniques can be found in the works [8; 9; 10]. To the best of our knowledge, there is no similarity to our research in this context, so direct comparison is difficult. In addition, the aim of our work is to check whether the data prepared by our granulation techniques are learned through deep neural networks. It is not our goal to show that we have the best technique to reduce training systems. Rough set theory [11] approaches data in set-theoretical terms by assuming that on each collection of vectors representing some objects, a partition is obtained, its classes representing distinct concepts/categories pertaining to those objects. A general concept, i.e., a set of objects in a given collection (the universe) is perceived through categories: some concepts can be expressed by categories in a deterministic way and some may not. The former are exact concepts (modulo the given partition into categories) while the latter are inexact (rough) concepts. Each rough concept can only be expressed in terms of its relation to categories by approximations: the lower approximation of a concept consists of categories (or, exact concepts) contained in the concept whereas the upper approximation consists of categories intersecting the given concept. A means for dealing with data is provided by the notion of an information system (see [PERSON], op.cit.) which is a tuple \((U,A,V,f)\) where \(U\) is a universe of objects, \(A\) is a set of attributes, \(V\) is a set of attribute values, and, \(f\) is a mapping which assigns to each object \(x\in U\) and each attribute \(a\in A\), the value \(f(x,a)\in V\). Categories obtained in this case are classes of the indiscernibility relation \(IND_{B}(x,y)=true\)\(if\)\(and\)\(only\)\(if\)\(a(x)=a(y)\) for each \(a\in B\), where \(B\) is a subset of the set \(A\) of attributes. A special case of information systems is a decision system with signature \((U,A,V,f,d)\) where \(d\) is a new attribute not in \(A\), called the decision. A relation between sets \(IND_{B}\) and \(IND_{d}\) for some \(B\) is called a decision algorithm over \(B\). For algorithmic methods of inducing decision rules please see [12; 13]. A far reaching extension of rough set theory is rough mereology [14].