Generalizations Of Z.PAWLAK Rough Set Theory And Research On Their Applications

Nowadays, the electronically stored data and information made dramatic increase in various fields, and the amount of these data and information increases exponentially with time. Thus, it presents a large challenge for human intelligent information processing capacity how to mine potential and useful information from these data. In order to maintain and utilize this abundance of information effectively, automatic methods must be developed. Hence, a new area of artificial intelligence study, which contains data mining (DM) and knowledge discovery in databases (DKK), is established.There are a number of approaches relevant to DM and DKK, and the rough sets approach is a more effective method. During the past decade, rough set theory has become a topic of great interest to researchers and has been applied to many domains. Given a data set with discretised attribute values, it is possible to find a subset of the original attributes using rough sets approach. And the subset, which is a data reduction of the data set, is the most informative. The other attributes can be removed from the data set with minimal information loss.However, it is most often the case that the values of attributes may be real-valued. It is impossible in the theory to say clearly whether two attribute values are similar or not and to what extent they are the same. And this is the problem that traditional rough set theory encounters.One of the answers to this problom has been to discretize the data set beforehand, producing a new data set with discretized values. This, however, is often still inadequate, as the degrees of membership of values to discretized values are not considered at all, which is a source of information loss. It is therefore desirable to develop these techniques to provide the means of data reduction for real-value attribute data sets. In fact, this could be achieved through the use of fuzzy rough sets.Fuzzy rough set theory was first proposed by D.Dubios and H.Prade, and fuzzy rough sets encapsulate the related but distinct concepts of vagueness (for fuzzy sets) and indiscernibility (for rough sets), both of which occur as a result of uncertainty in knowledge.Another way, which can be used to solve the problem as above, is function rough sets approach. Every object with its attributes in a data set is looked on as a function depending on its attributes, i.e., function rough set approach mines the holistic characteristic of the objects by being a function law. Based on the generalizations of rough set theory, this paper gives their research and discussion. This paper is divided into six chapters, and the main content and creative results are as follows:I. Research Content1. For fuzzy rough sets, we put forward the concept of the family of the ordinal transfer functions on an attribute set. The definition of the jth order decomposition classes and jth reduction classes are given based on that. If there exist transfer functions in a set of attributes, the equivalence classes will change, and the fuzzy rough sets of fuzzy objects, which to be recognized, will change correspondingly. This paper studies the transform and discusses the change feature in the structure of fuzzy rough sets corresponding to the fuzzy objects to be recognized under the influence of transfer functions. Lastly, it tells the relation between fuzzy rough sets (as fuzzy sets) andλ- cut sets (as classical sets)of the upper and lower approximation of fuzzy rough sets.2. Considering the system of multi-agent information communication, how to define the form of objects in the process of communication when the transferred objects are fuzzy concepts. Since information of the transferred objects changes continuously, it is a problem how to weigh the amount of information. And the question of the reliability of information communication among some agents is discussed. There may be two cases, when the same concept is transferred among some agents. One case is that every agent has only one discernibility knowledge, and the other case is that some agents may have more discernibility knowledge. In order to get the optimum transfer line based on the total reliability in the process of information communication. It is discussed how to built mathematics model and how to solve this model, wich is considered as a tool for dealing with several information sources where only one concept is present in the two cases.3. Based on the attribute of interval, the decomposition form of function equivalence classes and function rough sets are studied. The relation between Z.Pawlak rough sets and function rough sets is discussed in the continuous sense.4. In function rough set theory, it is a problem how to construct orginal function equivalence classes. Moreover, the strict inclusion relation and the operation of intersection restrict its application in many real-life problems. To solve these problems, the fuzzy similarity relation on a function universe is studied, and the definition ofε- function rough sets is put forward. Then, it is discussed how to select investment portfolio in a investment system. Otherwise, the definition of the sequential information system is presented, and the solution of attribute reduction and rule generation is given usingε- function rough sets approach. The indiscernibility relation is put forward in a continuous information system, and the idea of attribute reduction is given.5. Sum up all discussion in this paperII. Creative points in this paperCreative point 1. For fuzzy rough sets, we put forward the concept of the family of the ordinal transfer functions on an attribute set. Based on that, the definition of the jth order decomposition classes and jth reduction classes are given. The F - decomposition and F - reduction theorem of fuzzy rough sets are proposed. We obtain the relation between fuzzy rough sets and X - cut sets of the upper and lower approximation of fuzzy rough sets as followsand F - union decomposition theorem is advanced. Creative point 1 can be found in chapter 2. Creative point 2. Rough communication presented by Amin Mousavi isgeneralized, and fuzzy rough communication is put forward. We define the total amount of the missed information about the transferred concept I_A(A ,A ) and thetotal reliability of the transfer line p(A) in fuzzy rough communication from agent1 to agentn. In order to find the optimum transfer line in several informationsources where only one concept is present in two cases as above, the mathematics model is built. And the algorithm how to solve this kind of mathematics model is provided. Finally, the example verifies the validity of the algorithm.Creative point 2 can be found in chapter 3.Creative point 3.The decomposition form of function equivalence classes and function rough sets are studied based on interval attribute.it is showed that function rough sets is the general form of Z.Pawlak rough sets and Z.Pawlak rough sets is the special case of function rough sets.Creative point 3 can be found in chapter 4.Creative point 4. We give the definition of the degree of fuzzy similarity between functions, and function rough sets is generalized toε- function rough sets based on that. The relative discerniblity of a law set is discussed and the threshold value theorem is proposed. The investment model is built, and the method of selecting investment portfolio is presented using the tool ofε- function rough sets. The sequential information system is defined, moreover, the solutions of attribute reduction and rule generation are put forward.Creative point 4 can be found in chapter 5.