Abstract: In recent years, the rough set research more and more, especially on rough set theory with other soft computing combination of research is more prominent, made a lot of meaningful research results, therefore, this aspect of the current main a summary of the situation, mainly describes the current rough sets and fuzzy sets, neural networks, and some other evidence theory combination between soft computing theory research situation, and the future development of this area made some of their own ideas.

Rough set is developed rapidly in recent years, a theory, which is used to analyze and deal with uncertain, imprecise mathematical theory was developed by Polish mathematician Pawlak [2] in 1982 made it The basic idea is an equivalence relation on the domain of the domain will be divided into a number of equivalence classes, and then use this knowledge to the required processing imprecise or uncertain thing for an approximate characterization.

Rough Set Theory biggest feature is its division of the domain depends only on the collection of data for processing by itself, does not require any a priori information, so a description of the problem or deal with uncertainty is more objective, which is also its point with other soft computing significant difference between the theory, however, rough set in the original data imprecise or uncertain, is unable to process the data, which coincided with the soft computing in other theories have very complementary so rough sets and other soft computing theories and methods of combining rough sets has become an important element in this paper will be rough sets and fuzzy sets, neural networks, and evidence theory concept lattice theory combined with soft computing research conducted presentations and pointed out that in this respect the future research directions.

Knowledge Definition 2 Given a domain U and U tuft on the equivalence relation S, called tuple K = (U, S) is a knowledge base about the domain U or similar space.

Definition 3 indiscernible relation Given a domain U and U tuft on the equivalence relation S, if the PS, and P ≠?, Then ∩ P is still the domain of an equivalence relation on U, called P on indiscernible relation, denoted by IND (P).

Given a knowledge base K = (U, S), the PS,? R ∈ P, if IND (P) = IND (P-{R}) holds, then R is P, unnecessary, or said R is necessary in P if P in each R are necessary, then P is independent.

Definition 5 reduction, nuclear, given a knowledge base K = (U, S) and knowledge base equivalence relation on a cluster of PS, for any GP, if G is independent and IND (G) = IND (P ), then G is called a reduction of P, denoted G ∈ RED (P). P consisting of all the necessary knowledge of the core collection called P, denoted Core (P). Reduction and nuclear relationship Core (P) = ∩ RED (P), which is the reduction of nuclear intersection.

Common knowledge reduction in rough set algorithms are blind to delete reduction method, based on Pawlak attribute importance reduction method and the reduction based on discernibility matrix method in which the blind method is arbitrarily chosen to delete a property, to see whether is necessary, if it is necessary for the preservation, or delete the attribute, this method is simple and intuitive, but the reduction is not necessarily satisfactory results; Pawlak attribute importance based approach is based on the attribute importance to carry around Jane, which is characterized by this method can get the optimal reduction of information systems or sub-optimal reduction, but it can not find a reduction possibilities exist; based on discernibility matrix approach is to distinguish between any two of the domain collection of properties of objects in the form of a matrix represented by this matrix can be intuitively derived information systems core and all reductions, although this method can be very intuitive to draw all the reduction of information systems and nuclear, but question will produce large combinatorial explosion. Moreover, some scholars of knowledge about Jane made some new and improved algorithms. literature [10, 11] based on neighborhood rough set of attributes and attribute values are optimized reduction processing; literature [12] proposed a new attribute reduction method ReCA, improved data on the continuity properties of knowledge reduction performance.

Rough sets in handling uncertain problems unique new method attracted a great deal of interest to many scholars have made the theory scalability study [13 to 17], including the covering rough set [18 ~ 21], variable precision rough Set [22], and many other new content. literature [23] on the rough set axiomatic conducted in-depth research, got two on rough sets minimum Axiom Group; literature [24] by relaxing indistinguishability between objects and compatibility conditions, give a new harmonious relationship based rough set model; literature [25] constructed on the decision table object distinction conditions, and with the distinction between matrix and discernibility function presents a complete reduction Methods; literature [16] will be combined entropy and combination granulation introducing the concept of rough set, establishes the relationship between the two; literature [26] proposed a Inconsistent Information Systems Knowledge Reduction in new ways; literature [ 27] proposed division of property and property left right framing the view, the design of a division-based attribute reduction algorithm ARABP; literature [28] from the property and the perspective of information entropy of rough set measure of the uncertainty of these research has greatly promoted the development of rough set theory and applications.

Membership function is the core foundation of the concept of fuzzy sets, which it has to identify and describe a fuzzy set for the same universe of discourse, different fuzzy membership function to determine the different sets, such as μ? A (x) and μ? B (x) domain U is the two different membership functions, which can be determined by two different fuzzy sets A and B. The fuzzy set theory is a classic collection of the expansion, when a fuzzy set membership can only be 0 or 1 that μ? A (x) ∈ {0,1}, fuzzy set A will degenerate into an ordinary collection of classical set theory.

Rough fuzzy set is mainly through the use of fuzzy set membership functions centralized collection on rough approximation and lower approximation method to be described, in order to enhance the objectivity of fuzzy sets deal with the problem it is to focus on the upper and lower rough approximation of the characteristics of integrated into the fuzzy set among the membership function of the fuzzy concept focused on expansion into the membership function approximation and lower approximation membership functions, membership functions by these two values as determined by the membership to form an interval; using this interval to describe a elements belonging to a fuzzy set range of possibilities, rather than the previous one correspondence between the elements and the membership situation in which x ∈ A membership is no longer μ? A (x) ∈ [0,1 ], but in the [lower approximation membership, membership on the approximation of] this interval. rough fuzzy set basic definition is as follows:

Rough Fuzzy Sets Definition 7 Let U be a universe, R is an equivalence relation on U, A is a fuzzy set on U, μ? A (x) is the membership function of A, R (A) and (A) A, respectively, on approximation and lower approximation, their corresponding membership functions are:

Fuzzy rough set is the membership function of the fuzzy set concept applied to the rough set which, according to the fuzzy membership function to determine the concentration of an equivalence relation in rough set, that is, the membership function obtained by the same degree of membership of such elements belong to the same price category, resulting in a domain U division, which is actually known fuzzy focus, determined without further judgment knowledge into rough set equivalence relation on the set to get a bunch of rough equivalence classes improve the efficiency of rough sets deal with the problem of fuzzy rough sets basic concepts are defined as follows:

Definition 8 fuzzy rough set, given a universe U, A is a fuzzy set of U, μ? A (x) is the membership function A Let R? A is an equivalence relation on U and satisfies for? x, y ∈ U, xR? Ay? μ? A (x) = μ? A (y). Order [x] R?? A that represents the elements in x equivalence class, if the XU, X ≠?, then X on R? A lower and upper approximation, respectively

Rough fuzzy sets and fuzzy rough sets and fuzzy sets rough sets a good complementary treatment has been applied in many fields [30-33], and have achieved good results. Many academics they have been Further comparative studies [34 ~ 37], made some improvements and expansion of the literature [38] In covering rough sets based on the combination of the recent unusual set of fuzzy sets, covering generalized rough sets introduced the concept of ambiguity, given a fuzzy calculation methods, and demonstrate the ambiguity of some of the important properties; literature [39] proposed the concept of fuzzy indiscernible relation to enhance the value of fuzzy rough set attribute processing capabilities.

3.2 Rough Sets and Neural Network Contact

Rough set of things recognition and judgment is not based on the identified relationship on the domain, it does not require any a priori information on the importance degree of the system parameters describe things function to obtain the importance degree of each attribute, and so can not only properties The reduction, but also can be used to grasp the main features of things, to improve the ability to identify rough sets can be achieved on information systems knowledge reduction, removal of redundant information, reducing the space dimension of input information, improve processing efficiency, but rough Set anti-interference ability is poor, are more sensitive to noise in noisy environments on the performance unsatisfactorily.

Neural network characteristics is through training and learning to produce a non-linear mapping to simulate the way people think, with good adaptability can be achieved supervised and unsupervised learning, and the information can be processed in parallel; same time, It has very good ability to suppress noise, but there is also a neural network obvious defects, it can be helpful to input information or redundancy judgment of the input information can not be simplified, which makes it the treatment space the larger dimension of the information will be very difficult and inefficient.

Rough set and neural network respective strengths and weaknesses so that people find that they have a good complementary; addition, from the simulation of human thinking perspective rough set method to simulate the human abstract logical thinking, and neural network simulation of human image Intuition, therefore, to combine the two, with the characteristics of rough sets to make up neural network for dimensional data on the lack of Gao, and strong anti-jamming with neural networks rough set of features to make up the sensitivity to noise, will simulate human thinking and abstract images combined with intuitive thinking, you will get better results. Currently, research in this area has become an important research direction.

For rough sets and neural network combined with research, as well as other scholars study presents some new combination of methods, such as strong coupling integration [55] approach to solve the neural network design network hidden layer, hidden layer nodes and determine the value of the initial weights and network semantics provides an easy implementation of new ideas. With soft computing theory in a variety of theories and techniques of continuous development and innovation, such as neural networks and evolutionary algorithms, concept lattices, evidence theory and strengthen the integration of chaos science and other research, I believe will get more exciting achievements.

Literature [57] According discernible relationship between lower triangular matrix using genetic algorithm is proposed based on rough set genetic algorithm knowledge reduction algorithm, which can not only get the correct reduction, but also to solve the rough set heuristics Part of the problem can not be solved; literature [61] will be defined in terms of information theory measure of the attribute importance to introduce genetic algorithms as heuristic information and construct a new operator modifypop (t +1) to be repaired on the population, both to ensure the algorithm The overall optimization, but also improves the speed of convergence in the data mining literature [60] rough sets and genetic algorithms combining data from a large table is proposed to obtain the decision rules approach. The method uses rough set attribute importance and nuclear thinking of getting attribute reduction, then using genetic algorithms to find an optimum solution.

Formal Concept Definition 10 Let (U, A, I) is a formal context, if a tuple (X, B) satisfy X? * = B and B? * = X, called (X, B) is a form of concept, referred to the concept of which, X called the extension of the concept, B is called the connotation.

Definition 11 [67] The sub-concepts, the parent concept if (X? 1, B? 1) ≤ (X? 2, B? 2), and between them there is a different concept and (Y, C), satisfied (X? 1,? B? 1) ≤ (Y, C) ≤ (X? 2, B? 2), called (X? 1, B? 1) is (X? 2, B? 2) of sub-concepts, (X? 2, B? 2) is (X? 1, B? 1) the parent concept. Links to free download http://eng.hi138.com

Evidence theory [74] also often called DS theory, is a use of a set of functions to handle the uncertainty theory of evidence theory is the study of the evidence refers to properties of an object or an expert experience.

6.1 based on evidence theory

Let Θ represents a problem for the set of all possible answers, in which each answer θ is a subset of Θ, no intersection between the subsets, called Θ for the identification frame.

Definition 12 [75] basic probability assignment function Let Θ be a frame of discernment, if the set function m: 2? Θ → [0,1] satisfy m (Φ) = 0, and? A? Θm (A) = 1, then m is Θ on the basic probability distribution function;? A? Θ, m (A) is called A basic credibility.

Where: Bel expressed belief function for each proposition reliability; likelihood function pl (X) expressed proposition X is not the degree of suspicion; public function Q (X) reflects a collection that contains all the basic X's credibility and.

6.2 Rough Sets and Evidence Theory Contact

Evidence theory based on probability assignment function to define the belief function, the likelihood function, through which function under the given assumptions to estimate the evidence and evaluation of evidence theory, evidence is mainly known properties of things or expertise and some a priori knowledge, which makes a strong subjective evidence reasoning, limiting its scope of use. evidence theory and rough set these characteristics obvious complementarity and similarity rough set for problem solving is based on a pair of objective approximation operators, with strong objectivity; rather rough set lower and upper approximation theory with evidence of trust functions, the likelihood function in form but also has a certain similarity would be the advantages of both complementary and similar for binding studies nature, has become an important direction in this area.

Literature [76, 77] by a stochastic approximation space on rough set theory with evidence similar studies, concluded: Evidence theory and belief function likelihood function can be used on rough set lower approximation and the approximate probability Description:

This paper describes the rapid development in recent years and has a very novel features of rough set theory with soft computing theory with some of the other studies the situation, which you can see this combination of artificial intelligence, data mining, knowledge discovery, attribute Jane, automatic control and other aspects of medicine made remarkable achievements. Moreover, the word computing [79] has become a hot research field of artificial intelligence, computing with words based on the word or text terms as objects, rather than the value of the object is calculated , while the word or text itself has the characteristics of uncertain significance, which coincided with the rough set description of the problem characteristics very similar, therefore, the combination of rough sets and computing with words research will also be the future development of a rough set of content, which so I believe that with the right soft computing theory with the deepening of research, you will see even more gratifying success.

Currently soft computing theory combined studies generally confined between the two theories in which to expand certain, and the author in the actual study also found that even this pairwise combination to be perfect, and there are many areas for improvement, which requires In future studies will bring more soft computing theory to study together, learn from each other, complement each other and improve the level of research in this field.

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