INTRODUCTION
The coupling between gas flow and solid deformation in porous media has received a considerable attention because of its importance in the area of multiphysicalfields analysis, contaminant transport and safety management during coal mining (Zhao et al., 1994a, b, 2004; Zhao and Valliappan, 1995; Valliappan and Zhang, 1996, 1999; Wu et al., 1998; Ville, 1998; Sun and Xian, 1998, 1999; Sun, 2002, 2005; Sun and Wan, 2004). Safety management of coal mine is a complex system because coal mine mining engineering is complicated and volatile (Sun and Yu, 1988; Sun, 1990, 1991; Sun and Xian, 1998; Young, 1998; Valliappan and Zhang, 1999; Sun, 2002, 2005; Saghafi et al., 2006 ). It will help to enhance safety management of enterprise and raise coal mine safety management level if safety management level can be evaluated by all kinds of industrial accident, i.e., based on the evaluation, we can determine which mine is best managed and which one is worst, at the same time, find out the degree between the best and worst. The evaluation also can provide basis data for management department to examine management level and award the best one.
In present, the death rate was introduced generally to evaluate the level of
coal mine safety management. But such single indicator can’t have comprehension
assessment on the safety management level. It is difficult to reflect safety
management levels when apply to a small scale coal mine in the south of China
because of low coal production and complex safety condition. It is hard to evaluate
and arrange on level in proportion. Sometimes the real condition of coal mine
safety management can not be reflected even. Generally speaking, the uncertainty
is always existed in the judgment on the coal mine safety management, i.e.,
there is no clearly boundary between best and worst on management level. Because
of reasons mentioned above accurate evaluation for safety management of coal
mines is difficult. Hence, this article aimed at proposed a new evaluation approach
which is focused on the fuzzy mathematics theory for coal mine safety management.
CONSTRUCTION OF MEMBERSHIP FUNCTION
The safety index choosing: The accident is not only the index of mine
safety but also an important reflection of the level of mine safety management.
Conventionally, the accident whether happened, accident rate, the nature and
seriousness of accident are the main factors for evaluation. Generally speaking,
the accident rate will decrease if the safety precautions is perfection and
the safety rules are sound as well as what is more safety rules should be executed
with absolute strictness. Evidently, the accident happened whether or not is
corresponding with the level of safety management and so accident rate is a
function of safety management. In this study, four indicators (i.e., death rate
per million tons, seriously wounded rate per thousand persons, slightly wounded
rate per thousand persons and rest days per person) were chosen for evaluation.
Certainly, other safety indicators also can be considered such as electromechanical
facility accident or accident economic losses etc. But here coal mine safety
management comprehensive evaluation approach was introduced only considering
the accident rate.
Introduction to fuzzy comprehensive evaluation approach:
So called fuzzy comprehensive evaluation approach is the process that mine
safety indicator set (y) converted to fuzzy evaluation factor set (U) by membership
function. Then, a fuzzy comprehensive evaluation was completed on the evaluation
space S = (X, U, R) and then the result of evaluation index vector B was determined.
The component values of index vector B can be used to evaluate the level of
mine safety management focus on degree and classification.
In the evaluation space S= (X, U, R), supposed that X = {x_{1}, x_{2} ● ● ●, x_{n}} is the evaluation objects set; U = {u_{1}, u_{2}, ● ● ●, u_{m}} is the fuzzy evaluation factor set; R is fuzzy evaluation matrix which is fuzzy relationship from X to U. The elements of R were determined by the membership function of R: μ_{R} (u, x). μ_{R} (u_{i}, x_{i}) corresponds to the related elements while (u_{i}, x_{j})(i = 1,2, ● ● ●, m; j = 1, 2, ● ● ●, n) are given, i.e.,
Formula 1 shows that relationship r_{ij} is the reflection of factor
u_{i} reflecting from mine x_{j} (0 ≤r_{ij}≤1)
and r_{ij} is defined as the membership degree of binary fuzzy sets
R at points (u_{i}, x_{j}).
Where,
a_{i} is weight value of safety index u_{i}. From formula 2 the different importance degree distribution of all safety indexes can be seen and such distribution is the key to fuzzy comprehensive evaluation model. However the methods adopted for determination of weight matrix A in previous literature were determined by both expert appraisals and weight value deciding subjectively, obviously, such method can’t reflect the problem of weight interval distributing of the evaluation factors objectively. Hence, the problem mentioned above is discussed in this article and a new computational approach for weight matrix is proposed.
According to the fuzzy relationship composition, a fuzzy comprehensive evaluation model can be obtained, i.e:
Where,
the weighted average is adopted for calculation of fuzzy relationship composition; Ordinary logical real number square method is used for multiplication; addition ⊕ is defined as:
Fuzzy set B is the evaluation result, each element b_{i} of B is corresponded to an evaluated mine. The level of all mine’s safety management can be determined according to the value of elements
Where, components of B converted to 0≤bj*≤100, j = 1, 2, ● ● ●, n). According to the formulas above combined with the rules of comprehensive
evaluation, evaluation result sets of mine safety management levels can be classified
into five groups:
I 
: 
mine safety management is the best [90, 100]; 
II 
: 
mine safety management is better [80, 90]; 
III 
: 
mine safety management is general [70, 80]; 
IV 
: 
mine safety management is poor [60, 70]; 
V 
: 
mine safety management is worse [0, 60]. 
The meaning and construct of membership function: Construct the membership
function by accident rate i.e., membership function will be constructed according
to four indicators include death rate per million tons, seriously wounded rate
per thousand persons, slightly wounded rate per thousand persons and rest days
per person. Combined with the classification interval, the construction and
the meaning also can be shown as following.
• 
The planning death rate per million tons in evaluation times
is setting at 100 and the lower the better. Assuming X_{aj} is the
percentage of real death rate to planning death rate in mine j, so: 
Table 1: 
Four functions for accident rate of coal mines 

• 
The planning seriously wounded rate per thousand persons in
evaluation times is setting at 100 and the lower the better. x_{bj}
is the percentage of real seriously wounded rate to planning seriously wounded
rate in mine j, so: 
• 
The planning slightly wounded rate per thousand persons in
evaluation times is setting at 100 and the lower the better. x_{cj}
is the percentage of real slightly wounded rate to planning slightly wounded
rate in mine j, so: 
• 
The planning rest days per person in evaluation times is setting
at 100 and real rest days is supposed the lower the better. x_{dj}
is the percentage of real rest days to planning rest days in mine j, so: 
According to four conditions of accident rate mentioned above and the conditions
given by these four evaluation factors, membership function can be deduced as
shown in Table 1.
CALCULATION APPROACH FOR
WEIGHT MATRIX
We propose a new calculation approach for weight matrix as below.
• 
Setting up a comparison matrix. It is assumed that U = {u_{1},
u_{2}, ● ● ●, u_{m}} is a factor set. Each
pair of elements u_{i} and u_{j} in U are chosen for comparing
by experts according to the evaluation criterion and uİ≠u_{j}.
Comparison matrix C = (C_{ij})_{mχm} can be formed after
the results of comparison are indicated. 
The evaluation criterion is shown below.
If u_{i} is one as important as u_{j}, i.e., there is no difference for contribution between u_{i} and u_{j}, C_{ij}= 1 or C_{ji} = 1;
If u_{i} is a little more important than u_{j}, i.e., the contribution of u_{i} is a little more than u_{j} but not obviously, C_{ij} = 2;
If u_{i} is more important than u_{j}, i.e., the contribution of u_{i} is more than u_{j}, but not outstanding, C_{ij} = 3;
If u_{i} is much more important than u_{j}, i.e., the contribution of u_{i} is much more than u_{j}, but a little outstanding, C_{ij} = 4;
If u_{i} is absolutely more important than u_{j}, i.e., the contribution of u_{i} is quite more than u_{j}, C_{ij} = 5;
If importance degree obtained from comparison between u_{i} and u_{j} is the value between two levels, an average value can be token (e.g., 5/2, 7/2, 9/2 etc.).
If u_{i} is not only more important than u_{j} bus also have done great contribution, c_{ij} can equal to 5 but can not exceed 5.
Moreover C_{ij} = 1/ C_{ji}. After the comparison between the
elements each, a comparison matrix C is formed.
• 
The comparison matrix which is constructed according the comparatively
importance of each factors consist of the natures as below: 
C_{ij}>0,
C_{ij} ’ C_{ji} =1, i ≠j; i, j = 1, 2, , ● ● ● ●, m;
C_{ii} =1, i=1, 2,, ● ● ● ●, m.
• 
Determine the largest eigenvalue λ_{max} and
corresponding eigenvector W. Weight matrix A can be obtained after standardization
of eigenvector. For simplification, an approximate calculation approach
is employed as following. 
• 
Each row of comparison matrix C should be standardized; All component
of the comparison matrix C are added on column after the standardization;
Vector (one row, m column) after aggregation should be standardize again
and then the result matrix (We) which is the weight matrix (A ) we want
can be obtained; Calculate the largest eigenvalue λ_{max} of
comparison matrix C. 
• 
The consistency indicator for verifying the consistency of
comparison matrix C should be determined. 
The smaller the η value, the higher consistency degree for the comparison
matrix C; Comparison matrix can be considered satisfactory while η<0.1.
Therefore the comparison matrix C should be adjusted unless η<0.1.
CASE STUDY OF FUZZY COMPREHENSIVE EVALUATION APPROACH
Case study of fuzzy comprehensive evaluation approach was based on one year’s
four indicators of mine safety management for Changguang Coal Mine Corp. Ltd.
of Zhejiang province, China. The objection achieved rate of the enterprise was
shown in Table 2 and try to comprehensive evaluate the level
of mine safety management. The level of mine safety management was classificated
according to the evaluation results when evaluation results were determined.
Fuzzy evaluation matrix R can be determined according to Table
1 and 2.
Fuzzy weight matrix (A) was determined by next step. In hypothesis, evaluation
factor set U = (u_{1}, u_{2}, u_{3}, u_{4})
= (death rate per million tons, seriously wounded rate per thousand peoples,
slightly wounded rate per thousand persons, rest days per person). Comparison
matrix C can be determined based on evaluation criterion and these four evaluation
factors which were focused on reflecting the importance of mine safety management
level as Table 3.
Table 2: 
Four indicators of mine safety management for Changguang Coal
Mine Corp. Ltd 

Table 3: 
Matrix C 

Table 4: 
Evaluation result of mine safety management 

Then, the result can be calculated as bellows:
Realized from the consistence indicator η, the comparison matrix C constructed
is satisfied. Moreover, weight matrix A of four factors corresponds to situation.
Then we have:
Matrix A can be determined according to fuzzy relationship composition model
(3) and R in the example:
So, B* = The results of fuzzy comprehensive evaluation approach of mine safety
management were list in Table 4.
CONCLUSIONS
• 
The advantages of fuzzy mathematical theory in application
to comprehensive evaluation on mine safety management level includes: Considering
problem holistically, the opportunities of subjective and onesided are
reduce and be conventional in quantitative analysis. The fuzzy mathematical
theory can avoid the situation that personal feelings may color evaluation.
The level of enterprise safety management can be raised when scientific
and democratic methods are employed for evaluation and management. 
• 
The result for case study of fuzzy comprehensive evaluation approach showed
that the weight distribution determined by this weight matrix calculation
approach was reasonable and the classification degree for the level of mine
safety management was consistent with the real situation of coal mines.

• 
Combined with numerical simulation technique, fuzzy comprehensive evaluation
approach can be used to handle with complicated matters and large scale
computational mathematic models and enterprise safety management can be
automation. 