3.1 Basic model
First of all, we need to introduce the detail methods of Fuzzy Comprehensive Measurement Method (FCMM). Fuzzy comprehensive evaluation is a very effective multivariate decision-making method for making comprehensive assessment affected by many factors [
15].
Assuming U = {u1, u2, u3, … , u
n
} have n factors and V = {v1, v2, …, v
m
} have m judgments, their number of elements and names can be subjectively defined by people according to practical problems. Due to the different status of various factors, so the role is not the same, and for sure, the weight and judgment are also different. People are not absolutely feeling positive or negative about m kinds of judgments, so the comprehensive judgment should be a fuzzy subset of V, and B = {b1, b2, …, b
m
} ∈ Φ(V), where b
j
(j = 1, 2, …, m) reflects the j’s position-v
j
in the comprehensive judgment(that is v
j
degree of membership of fuzzy sets: B(v
j
) = b
j
). Comprehensive judgment B depends on the weight of each factor, and each weight is a fuzzy subset A = {a
I
, a1, …, a
n
} ∈ Φ(U) on U, and \( \sum \limits_{I=1}^n{a}_I=1 \), a
I
denotes the weight of the I factor. Therefore, once a weight is given, a comprehensive judgment B can be obtained accordingly.
According to the specific problems, we need to establish a fuzzy transformation T from U to V. If we make a separate judgment f(u
i
) for each factor u
i
, this can be regarded as the fuzzy projection f from U to V, that is, f : U → Φ(V) and u
i
↦ f(u
i
) ∈ Φ(V).
From f, we can derive a fuzzy transformation T
f
from U to V, and we can regard T
f
as the mathematical model of comprehensive evaluation B obtained from weight A.
From the above analysis, we can see that the mathematical model of fuzzy comprehensive evaluation consists of three elements, the steps are divided into four: (1) factor set U = {u1, u2,u3,…,un}; (2) judgment set V = {v1, v2,…,vm}; (3) single factor evaluation: f : U → Φ(V) and u
i
↦ f(u
i
) = (ri1, ri2, …, ri1) ∈ Φ(V) . Fuzzy mapping f can induce a fuzzy relationship R
f
∈ (U × V), that is \( {R}_{f\left({u}_i\times {v}_i\right)}=f\left({u}_i\right)\left({v}_i\right)={r}_{ij} \), Thus R
f
can be represented by the fuzzy matrix R∈μn×m: \( R=\left[\begin{array}{l}{r}_{11},{r}_{12},{r}_{13},{r}_{14},{r}_{1m}\\ {}{r}_{21},{r}_{22},{r}_{23},{r}_{24},{r}_{2m}\\ {}\dots \kern2.5em \dots \kern2.5em \dots \kern1.5em \dots \\ {}{r}_{n1},{r}_{n2},{r}_{n3},{r}_{n4},{r}_{nm}\end{array}\right] \). We call R a single factor evaluation matrix, and the fuzzy transformation T
f
from U to V can be induced by the fuzzy relation R. U(U1, U2, …, U
n
) form a fuzzy comprehensive decision-making model, U
1
, U
2
,···, U
n
is the n elements of the model. (4) Comprehensive Evaluation: for the weight A = (a1 a2 a3 a4 a5 a6), according to fuzzy mathematical evaluation model formula A * R = B, fuzzy comprehensive evaluation operation, where B = (b1 b2 b3 b4 b5 b6) is the total assessment results. In accordance with the principle of maximum membership, the highest value of b
jmax
in b
j
corresponding to the grade V
j
is the result of comprehensive evaluation, as result, the risk level of the object being evaluated.
3.2 Specific examples
A large state-owned enterprise has many years of transport, warehousing, freight forwarding, and other service experience, with strong financial strength. The indicator design is to divide into two layers and requires two fuzzy operations. According to the actual situation of the logistic project, with reference to domestic and foreign research results, we can set 23 indicators for the existence of six types of risk in the above-mentioned logistic project to evaluate the risk investment of the logistic project: (1) Market risk (U1): service innovation (U11); customer demand level (U12); logistic services competitors (U13); logistic market growth (U14); (2) management risk (U2): entrepreneurial style (U21); management quality (U22); management ability (U23); management moral hazard (U24); corporate culture (U25); (3) Technical risk (U3); substitutability of technology (U31); advanced technology (U32); technical applicability (U33); technical reliability (U34); (4) financial risk (U4): changes in interest and exchange rate (U41); changes in the rate of return on investment (U42); difficulties in property transactions (U43); financial risk (U44), (5) operational risk (U5): equipment condition (U51); operator condition (U52); standardization of operation (U53); (6) environment risk (U6): National Macro-political Economics Environment (U61); policies and regulations (U62); and micro basic environment of investment sites (U63). The risk level is divided into five levels: low risk (
V1), medium low risk (
V2), general risk (
V3), medium high risk (
V4), and high risk (
V5). The above five evaluation rank elements constitute the evaluation level set.
V={
V1,
V2,
V3,
V4, (
V5}. For the six weights of the evaluation indicators, we used the Delphi method to issue a consultation letter to 10 experts (including scholars, business leaders, and managers) and scored the weight of six sub-sets of evaluation indicators (Table
1).
Table 1
Weight of evaluation index subset of logistic project
Weight | 0.24 | 0.19 | 0.27 | 0.22 | 0.36 | 0.16 |
Apply mathematical model
Ai*
Ri =
Bi. The fuzzy subset B
i
= (
b
i1
b
i2
b
i3
b
i4
b
i5
) (
i = 1,2,3,4,5,6,
bij∈[0,1]) is the first level of comprehensive evaluation results, indicating that each
U
i
(
i = 1,2,3,4,5,6) (Table
1) within the scope of the logistic project, respectively, to the extent of the percentage is in five levels: “low risk,” “medium low risk,” “general risk,” “medium high risk,” and “high risk”. The calculated results:
B = (0.283 0.336 0.271 0.039 0.012). The result shows that the maximum membership degree of matrix B is 0.4, and the overall risk level of the logistic project is low risk.