A little understanding of decision rough sets (three decisions), probabilistic rough sets and game rough sets

Boss Task a lot, for breathing ~ ~ ~

I've been watching for two weeks. Some articles on Decision-theoretic Rough set, as well as the probabilistic rough sets produced by the combination of RS and probability theory probabilistic Rough Set and DTRs slightly different gtrs (game-theoretic Rough set), so a little summary, so as not to forget later.

Before looking back, let's talk about some of the methods of research. The Great American physicist Feynman has a law about the same theory or the same law in different forms, but mathematically equivalent. But different representations can give different interpretations of cognition, and the extension of the law implies a different direction. At the same time, these different representations help us to understand the problem from different angles and more comprehensively, because of this, I think the rough set will have so colorful deformation and development! This inspires us to delve into every form of expression and the theory behind it, perhaps with a new world of discovery.

The cause of the approximation in the 1.Rough set.

First, we can clearly classify equivalence classes according to discernibility function, whereas the description of objects in information table is accurate, with each object having a definite exact value on each property. So, how is the approximation of rough sets produced, and what does it approximate?

The data analysis method of RS is based on the construction and analysis of concept (concept). Concept has a pair of definitions: Intension, which describes the essential attributes of a concept, can be used to determine whether an object belongs to this concept, and extension is an instance set of concepts. In an article by Mr. Yao, the RS approximation is mainly explained in two ways:

A. Approximation of an undefined concept: an undefined concept is approximated by a definable concept. The undefined concept here is that some objects in the collection cannot be accurately described in the decision logic language.

B. Approximation of complex concepts: approximate complex concepts with simple concepts (excessive attribute descriptions), similar to the process of attribute reduction in Rs.

Another representation of 2.Pawlak classic Rough sets: Introducing conditional probabilities into the study of rough sets. Pr (c|[ X]) represents the conditional probability that any entity belongs to Class C under the conditions of the equivalence class [x]:

The RS three approximate fields are expressed as:

Correspondingly, if the boundary threshold value is changed to 0.5, there is a 0.5 probability rough set.

3. Decision rough set: The use of a pair of thresholds (β) instead of the probability of rough set of 0,1,0.5 and other precise values, a more general model-decision rough Set (DTRS), expressed as follows:

4. Game Rough Set (Game-theoretical Rough set):

The traditional Pawlak rough sets are determined for the division of positive and negative domains, and only those elements in the boundary domain are uncertain, so in order to reduce these uncertainties, the elements in the BND should be divided into positive or negative fields. The cost of doing this is to increase the uncertainty of the positive and negative domains. The rough set of game is produced in the process of balancing the two sides, the aim is to seek the best balance between the two.

PS: Xiao Ye today review write my eyes good pain%>_<% about DTRs and gtrs detailed explanation tomorrow continue, fighting~

A little understanding of decision rough sets (three decisions), probabilistic rough sets and game rough sets