Abstract: This paper presents several combinations of grain under the rough set model, and with the single one under the rough set were compared, while the next logical operations with grain rough set model for comparison, get creative combination tablets, as well as a single logical operation under grain rough set model the relationship between the results showed that the combination of tablets and capsules constitute a logical chain structure, which is based on information granules explore knowledge acquisition and dynamic grain reasoning laid the foundation.

Keywords: Combination tablets; grain logic operations; single one; rough set; approximation

Abstract: This paper proposed the rough set model under combination granule, and compared it with that under single granular, also with rough set model under logical computing of granule, which contributed to the relationship between rough set models under combination granule, singular granules and logical computing of granules. Results show that combination granule and logical computing of granule construct a chain, which will lay a foundation for knowledge acquisition based on information granule and induction based on dynamic granule.

Rough Set [3] is defined as the relationship between a given set of upper and lower approximation constitutes an ordered pair approximation has been successfully applied to machine learning, decision analysis, process control, pattern recognition and data mining and other fields [4]. Traditional rough set theory is based on the definition of a single one, namely static grains. literature [5-7] proposed a multi-grain operation under rough set theory model, namely MGRS (multi-granulations rough set, MGRS), and discussed the relevant mathematical properties. Taking into account the literature [5-7] in the collection of mainly discussed in size P and Q P + Q, P ∩ Q collection of computing the lower and upper approximations, the paper under the multi-grain rough set model calculation carried out further discussion of them with a single granularity rough set model are compared; same time, the multi-grain operation under rough set model and combination granulation under rough set model was? comparison.

Define a propositional logic, propositions P and Q is denoted conjunction P ∧ QP ∧ Q is true if and only if P and Q are both true; propositional disjunction of P and Q is denoted P ∨ Q, P ∨ Q is False if and only if P and Q are both false.

Information system (U, A), if the two bodies x, y ∈ U on the properties of the same value a ∈ A, then we say both in the attribute a is not resolved, if x, y in each of the set BA an attribute b ∈ B are indistinguishable, claimed both in the set B is indistinguishable with x in the set B indistinguishable on the set of all individuals in the collection called x equivalence classes generated on B, is denoted by [x]? B, it can be seen from the x-indiscernible grain structure of an information element of [8] (information granule).

This theorem shows that the set A of all equivalence classes generated on the domain constitutes a partition of the equivalence class equivalence class is called the base.

Definition 4 any subset of the domain U XU, if it can be represented as a certain equivalence classes and sets, called x is accurate (or known as definable), otherwise known as rough, if a XU concept is rough, you can use two precisely defined to approximate the set, called the lower approximation of X or upper approximation, denoted by PX and X, defined as follows:

PXXX

Definition 5 If the set X is rough, it is called an ordered pair <PX,X> rough set of the rough set approximation quality @? P (X) is defined as follows:

U / IND (Q) = {{e? 1, e? 2}, {e? 3, e? 4, e? 5}, {e? 6, e? 7, e? 8}}

U / IND (P ∪ Q) = {e? 1, e? 2, e? 7}, {e? 1, e? 2, e? 3, e? 4, e? 5, e? 6}, { e? 2, e? 3, e? 4, e? 5, e? 6},? {e? 2, e? 3, e? 4, e? 5, e? 6, e? 7, e? 8 }, {e? 1, e? 6, e? 7, e? 8}, {e? 8}

Prove the equivalence relation satisfy reflexive, by P, Q construct equivalence class [x? I]? P and [x? I]? Q, there is x? I ∈ [x? I]? P and x ? i ∈ [x? i]? Q. So there? ∪ x? i ([x? i]? P ∩ [x? i]? Q) = ∪ x? i [x? i]? P ∪ [x ? i]? Q) = U established, while there? [x? i]? P ∩ [x? i]? Q ≠?, [x? i]? P ∪ [x? i]? Q ≠?, ie U / IND (P ∩ Q) and U / IND (P ∪ Q) forming a field coverage.

If x? J? [X? I]? P ∩ [x? I]? Q, you may have the following three cases: a) x? J? [X? I]? P, x? J? [X? i]? Q; b) x? j? [x? i]? P, x? j ∈ [x? i]? Q; c) x? j ∈ [x? i]? P, x? j? [ x? i]? Q. Accordingly, based on the nature of equivalence classes can be obtained: a) x? i? [x? j]? P, x? i? [x? j]? Q; b) x? i ? [x? j]? P, x? i ∈ [x? j]? Q; c) x? i ∈ [x? j]? P, x? j? [x? i]? Q, so that x ? i? [x? j]? P ∩ [x? j]? Q.

Can be obtained through the above two cases, or [x? I]? P ∩ [x? I]? Q = [x? J]? P ∩ [x? J]? Q established, or ([x? I]? P ∩ [x? i]? Q) ∩ ([x? j]? P ∩ [x? j]? Q) =? established, so U / IND (P ∩ Q) form a partition of the domain.

QED.

Definition 8 Given information system (U, A), P and Q are two information systems information granules, tablets logic operation is under rough set model is defined as

Combination tablets will be discussed below under the single grain under rough set and rough set model as well as the relationship between the combination of grains and grain rough set under the next logical relationships between rough set.

In this paper, the use of a combination of tablets, capsules and logical operations with the rough set model for further comparison, we can get the following theorem.

b)? x ∈? P ∩ QX, there are ([x]? P ∩ [x]? Q) ∩ X ≠?. because [x]? P ∩ [x]? Q [x]? P, [x] ? P ∩ [x]? Q [x]? Q, there is [x]? P ∩ X ≠? And [x]? Q ∩ X ≠?, so there is x ∈ X ∩ X, ie P ∩ QXX ∩ X.

QED. Links to free download http://eng.hi138.com

The theorem shows two particle P, Q combination produces a quotient space U / IND (P ∩ Q) than the combination of size P ∧ Q finer structure of knowledge, and thus on the approximation of the set X is more accurate.

a)? x ∈? P ∪ QX, there is [x]? P ∪ [x]? QX established because of [x]? P [x]?? P ∪ [x]? Q, [x? Q] [x ]? P ∪ [x]? Q, there is [x]? PX and [x]? QX established that

? X ∈ PX ∩ QX, by definition there is x ∈ PX and x ∈ QX, therefore [x]? PX and [x]? QX established because of [x]? PX and [x]? QX established with [x ]? P ∪ [x]? QX established so there is x ∈? P ∪ QX, namely PX ∩ QX? P ∪ QX.

QED.

b)? x ∈? P ∩ QX, by definition there ([x]? P ∩ [x]? Q) ∩ X ≠?; Also, because [x]? P ∩ [x]? Q [x]? P ∪ [x]? Q, there is ([x]? P ∪ [x]? Q) ∩ X ≠?, available? x ∈? P ∪ QX, so there? P ∩ QX? P ∪ QX.

QED.

QED.

a)? x ∈? P ∨ QX, there is [x]? PX or [x]? QX established due? [x]? P ∩ [x]? Q [x]? P and [x]? P ∩ [ x]? Q [x]? Q, there is [x]? P ∩ [x]? QX holds, then there is x ∈? P ∩ QX established. therefore P ∨ QX? P ∩ QX.

b)? x ∈? P ∩ QX, there are ([x]? P ∩ [x]? Q) ∩ X ≠?. because [x]? P ∩ [x]? Q [x]? P and [x] ? P ∩ [x]? Q [x]? Q. There [x]? P ∩ X ≠?, and [x]? Q ∩ X ≠? true, then there is x ∈? P ∨ QX. therefore P ∩ QX ? P ∨ QX.

QED.

QED.

QED.

The above theorem can be obtained through the combination of the rough set model grain grain logic operation with the relationship between the rough set model, and found that the knowledge of the relevant grain roughness has the following relationship:

Definition 9 Given information system (U, A), P, Q are two information granules constructed quotient space, called P? Q, if for any collection XU, both @? Q ≤ @? P holds.

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