Abstract
Since China’s adoption of reform and open-up policy in 1978, Jiangsu Province has achieved a fast economic development, with the average annual increasement rate of GDP per capita at 11.3% (counted with comparative price). In this process, the role of infrastructure in pushing the economic growth receives great attention. Study on the pushing effect of infrastructure on the economic growth will help the stipulation of proper infrastructure development strategy, so as to push forward economy and narrow the regional gap. In this paper, we investigates the comprehensive evaluation problems of regional economy development level in Jiangsu Province with 2-tuple linguistic information. Then we propose dependent 2-tuple linguistic Maclaurin symmetric mean (D2TLMSM) operator and then apply D2TLMSM operator for evaluating the regional economy development level in Jiangsu Province with 2-tuple linguistic information. At last, a practical example is proposed to test the effectiveness of the given method.
Keywords
Introduction
In recent years, China’s economy develops with a high speed. Between the year 1978 to 2009, the average annual GDP growth was 9%, GDP grown more than 8% per capita average annual, and per capita income raised substantially, people’s living standards improved gradually, creating a remarkable “China miracle”. At the same time, China’s regional economy stepped into the overall high growth period, and a rapid increase in total economic output and per capita amount in each region had been seen, playing an important role in China’s sustained, rapid and healthy development. However, since China has a vast area with many ethnic groups, society, customs, cultural differences, historical traditions, and regional endowments, plus the impact of a number of factors such as geographic location and preferential policies, China’s regional economic development is very uneven among regions and there is still large gap between regions which gradually becomes an important problem constraining the healthy and sustainable development of China’s economic harmony. Therefore, how to correctly face the changes of regional disparities, reduce regional economic development gap and promote the harmony, sustainable development of our country and the region’s economy becomes hot issues that China’s economic circles, business community as well as the Government concern about.
However, in many situations, the input arguments take the form of 2-tuples linguistic variables due to the time pressure, and lack of knowledge [1–15]. The comprehensive evaluation problems for evaluating the financial management performance with 2-tuple linguistic information is the multiple attribute decision making (MADM) problems [16–28]. In this paper, we investigates the comprehensive evaluation problems of regional economy development level in Jiangsu Province with 2-tuple linguistic information. Then we propose dependent 2-tuple linguistic Maclaurin symmetric mean (D2TLMSM) operator and then apply D2TLMSM operator for evaluating the regional economy development level in Jiangsu Province with 2-tuple linguistic information. Finally, a practical example is proposed to test the effectiveness of the proposed method.
Preliminaries
The Maclaurin symmetric mean (MSM) was firstly discussed by Maclaurin in [29], that is a powerful technology characterized by the capability to obtain the relationship between the multi-input arguments. Afterwards, we propose the Definition of MSM:
We can see that the MSM have the following properties:
Assume that S ={ s i |i = 1, 2, ⋯ , t } is a linguistic term set with odd cardinality. Any label, s i represents a possible value for a linguistic variable, and it should satisfy the following characteristics [5, 6]:
(1) The set is ranked: s
i
> s
j
, if i > j; (2) Max operator: max(s
i
, s
j
) = s
i
, if s
i
≥ s
j
; (3) Min operator: min(s
i
, s
j
) = s
i
, if s
i
≤ s
j
. Particularly, S can be defined as follows.
Utilizing the Definition 1, Zhang et al. [30] gave the definition of the 2-tuple linguistic Maclaurin symmetric mean (2TLMSM) operator as follows:
Considering that the input arguments may have different importance, furthermore, Zhang et al. [30] defined the 2-tuple linguistic weighted Maclaurin symmetric mean (2TLWMSM) operator.
Utilizing Equation 7, the 2TLMSM weights can be defined as follows.
We can see that w j ≥ 0, j = 1, 2, ⋯ , n and .
By (7), we have
We call (12) a dependent 2-tuple linguistic Maclaurin symmetric mean (D2TLMSM) operator.
Next, we will analyze several special cases of the D2TLMSM operator by taking various values of the parameter k.
We use the D2TLMSM to comprehensive evaluation for evaluating the regional economy development level in Jiangsu Province with 2-tuple linguistic information. Assume that A ={ A1, A2, ⋯ , A m } is a discrete set of alternatives, and G ={ G1, G2, ⋯ , G n } is the set of attributes, whose weight vector is ω = (ω1, ω2, ⋯ , ω n ), with ω j ≥ 0, j = 1, 2, ⋯ , n, . Assume that that R = (r ij ) m×n is the comprehensive evaluation matrix, where r ij ∈ S is the attribute values, that is used to generate the linguistic variable utilizing the alternative A i ∈ A corresponding to the attribute G j ∈ G.
Afterwards, we use the D2TLMSM operator to design a method to comprehensive evaluation problems for evaluating the regional economy development level in Jiangsu Province with 2-tuple linguistic information, which is able to be illustrated as follows.
The world’s innovation of technology has shown deep influence in the world’s economy and become an important impetus to the world after the world war II. The government pay more attentions ton integrate resources of all fields and promoting technical innovation. Especially since the communication revolution growing rapidly, government is very important to encourage the regional economy development investment of both the society and enterprises, and leading the direction of the regional economy development input. Furthermore, it has become a vital factor of enhancing the competitiveness. Thus the new function of every country’s government is to enhance the competitiveness and promote economic development. Nowadays, to enhance innovation competence independently is one of Jiangsu’s development strategies. Although regional economy development has become the leading department in Jiangsu, governmental public regional economy development will still play an important role in a long time because of the limitation of corporations and other reasons. Therefore, it is significative to discover the functionary mechanism between public economic development, so as to exert an influence on Jiangsu’s economic development, and enhance regional innovation competence independently. This section presents a numerical example for evaluating the regional economy development level in Jiangsu Province with linguistic information to describe the method proposed in this paper. The expert group must determine in terms of four attributes: G1 is the per capita social consumable total volume of retail sales; G2 is the per capita income of public financial budget; G3 is the per capita disposable income of urban households; G4 is the per capita net income of rural residents. The five possible cities A
i
(i = 1, 2, ⋯ , 5) can be estimated utilizing the linguistic term set
Next, to choose the most suitable city, we exploit the 2TLWMSM operator to develop models for evaluating the regional economy development level in Jiangsu Province with linguistic information, that is able to described as follows.
Firstly, we transform the linguistic decision information given in Table 1 into 2-tuple linguistic decision matrix which are given in Table 2.
Then, aggregate all 2-tuple linguistic preference value by using D2TLMSM to derive the overall linguistic preference values of the enterprises A i . The aggregating results are illustrated as follows.
In the end, in terms of the aggregating results given in Table 3, the rank of the cities are illustrated in Table 4. Note that the symbol > denotes “preferred to”. The ordering of the alternatives is seen in Table 4 and the best city is A3.
Conclusion
Regional economy strength between different area exists object during the economy development. Economic strength distance between cities result from several reasons and goes arise or down in the dynamic development. But how to analyze this distance objective and justice is a key problem for the government to make a policy or notice the problem during the economic development. In this paper, we investigates the comprehensive evaluation problems of regional economy development level in Jiangsu Province with 2-tuple linguistic information. Then we propose dependent 2-tuple linguistic Maclaurin symmetric mean (D2TLMSM) operator and then apply D2TLMSM operator for evaluating the regional economy development level in Jiangsu Province with 2-tuple linguistic information. In the end, a practical example is proposed to testify the developed method. Next, we will investigate the comprehensive evaluation problems of regional economy development level in Jiangsu Province with other fuzzy evaluating models [32–46].
