Judging the membership degree of the evaluation object to the evaluation elements from a single factor is called single factor fuzzy evaluation. Assuming that the ui in the factor set is judged, the membership degree of vj in the evaluation set is rij, which can be expressed by fuzzy set as:

Ri=(ri 1ri2…rin)

Ri is called a single factor set. A matrix composed of membership rows of each single factor evaluation set;

Fine quantitative characterization and comprehensive evaluation model of coal reservoir

It is called a single factor matrix. Since RIJ represents the degree of membership between UI and VJ, R is called the fuzzy relationship from U to V.

6.3. 1.2 single-level comprehensive evaluation model

There are two finite sets: factor set U = (U 1U2 … UN) and evaluation set V = (V 1V2 … VN). If r is the fuzzy relation between u and v, the fuzzy set on u is:

Fine quantitative characterization and comprehensive evaluation model of coal reservoir

The fuzzy set on v is:

The comprehensive evaluation results of this evaluation object are as follows:

A=(a 1，a2，…，an)

These include:

(∨, ∧) is a generalized operator in fuzzy exchange; Is the composition rule of fuzzy matrix. The above formula is called single-level comprehensive evaluation model. On the real scale, the model is a three-dimensional model composed of (ABR). A is the weight on the factor set u; R is a fuzzy mapping from factor set u to evaluation set v; B is the evaluation result, and bj is the membership degree of the evaluation object to the j-th element in the evaluation set when all factors are considered comprehensively.

6.3. 1.3 multilevel fuzzy evaluation model

Comprehensive geological evaluation of coalbed methane is a multi-factor and multi-level complex system, which must be dealt with by multi-level fuzzy comprehensive evaluation model. Multi-level fuzzy comprehensive evaluation is based on single-level evaluation, which first constitutes a single-level evaluation subset of several evaluation groups, and then takes the evaluation subset of the evaluation group as a new node for higher-level evaluation.

The single factor evaluation in the fuzzy comprehensive evaluation of branches should be the corresponding fuzzy comprehensive evaluation at the next higher level, so the single factor evaluation matrix of multi-level (taking the second level as an example) fuzzy comprehensive evaluation should be:

Fine quantitative characterization and comprehensive evaluation model of coal reservoir

Where: rik=bjk(i= 1, 2,3, …, p).

So the two-level fuzzy comprehensive evaluation set is:

Fine quantitative characterization and comprehensive evaluation model of coal reservoir

These include:

Similarly, a multi-stage fuzzy evaluation model can be constructed.

Because of the different weight coefficients and operator models of nodes at different levels, the comprehensive evaluation of multi-level fuzzy mathematics is not a simple superposition of single levels.

6.3. 1.4 Multi-level fuzzy comprehensive evaluation

The evaluation results obtained by the single-level comprehensive evaluation with the evaluation team as the unit can be used as the evaluation of the above factors on the next level's own comments, that is, a row vector R(uj) in the evaluation matrix of the single factor on the next level's own comments, so the evaluation matrix of any level can be expressed as:

Ri=(Ri(ui)Ri(u2)…Ri(un))

For a given weight:

Ai=(A 1 1，A 12，…，A 1n)

Multi-level comprehensive evaluation is:

Riz=Ai？ nautical/sea mile