Study on location selection of client-supplied goods and materials support center for the Sichuan-Tibet railway based on dynamic intuitionistic fuzzy multi-attribute decision-making

Abstract

The construction of the Sichuan-Tibet railway is encountered with some problems such as complicated geological conditions, bad climate, active plate movement, and sensitive ecological environment. Therefore, scientific and reasonable site selection is an essential guarantee for the smooth construction of the Sichuan-Tibet railway. Through constructing weighted scoring function and intuitionistic fuzzy similarity model and researching the dynamic intuitionistic fuzzy multi-attribute decision-making method considering time factor, the location decision of client-supplied goods and materials support center for Sichuan-Tibet railway construction can be complete, and the research theories and methods of location problem worldwide can be analyzed. Given the route direction and engineering construction of the Ya’an-Linzhi section of the Sichuan-Tibet railway, this paper aims to set up seven client-supplied goods and materials support centers as alternative site selection schemes, which integrates six factors (transportation, geological conditions, climate environment, site selection characteristics, engineering construction, and communication conditions) and constructs 12 index systems for client-supplied goods and materials support center location selection. Combining with the index system, the intuitionistic fuzzy decision-making matrices for four periods are established. Besides, using a dynamic intuitionistic multi-attribute decision-making method, the weighted results of similarity decision-making matrices are compared, and the location schemes of client-supplied goods and materials support centers are sequenced. The results demonstrate that Linzhi is the best site selection scheme for the construction client-supplied goods and materials support center of Ya’an to Linzhi section of the Sichuan-Tibet Railway, providing reference significance for supporting the construction of the Sichuan-Tibet Railway Project.

Keywords

Sichuan-tibet railway client-supplied goods and materials location decision dynamic multiple attribute decision intuitionistic fuzzy set similarity degree

1 Introduction

The Sichuan-Tibet region of China refers to the region where Sichuan Province and the Tibet Autonomous Region are located, located in southwestern China. The Tibet Autonomous Region is an essential area for China’s “One Belt, One Road” construction, a strategic hub and an open gateway to South Asia, a key area designated by the state for the opening and development of border areas and an important channel for South Asia, and a significant gateway to the Bangladesh-China-India-Myanmar Economic Corridor. Sichuan Province, as the main access to Tibet, plays a pivotal role in the overall development and long-term stability of Tibet. Besides, the construction of the Sichuan-Tibet Railway between Tibet and Sichuan plays a crucial role in promoting ethnic unity, maintaining national unity, consolidating border stability, and promoting regional development, and it has been highly valued by the Chinese government. The Sichuan-Tibet railway starts in Chengdu, Sichuan province, and passes through Ya’an, Kangding, Changdu, Linzhi to Lhasa, Tibet. The total length of the railway is 1838 km. The proportion of bridges and tunnels is as high as 86%. The total construction period is estimated to be 12 years [1]. The Sichuan-Tibet Railway is characterized by huge topographic drop, complex geological structure, changeable climate, active plate movement, and sensitive ecological environment, making it extremely difficult to supply materials. Therefore, it is urgent to solve the problem of locating the client-supplied goods and materials support center during the construction of the Sichuan-Tibet railway, and this is also one of the focuses of the Chinese government.

Many experts and researchers worldwide began to investigate the logistics location problem very early. Their research mainly includes the problem of no alternative location and the problem of alternative location. Regarding the problem of no-alternative location, the existing research focuses on single-level and multi-level analysis. To reduce costs, shorten transport routes, and accelerate the coordination of production and consumption [2], researchers solve the problems about location, function, and capacity of facilities mainly using intelligent algorithms such as genetic algorithm, ant colony algorithm, and tabu search algorithm [3]. Xu et al. [4] established a mathematical model with the goal of minimizing cost and time to solve the multi-objective location problem of equipment manufacturing enterprises; Ren et al. [5] constructed an evaluation index system from five aspects: land cost, construction cost, road traffic flow, power grid conditions, and surrounding environment, established a site selection model with the smallest total social cost, and solved it with genetic algorithm; Erskine et al. [6] used the spatial decision support system to investigate the location of new retail stores. As for the problem of an alternative location, the existing research emphasizes the evaluation of the location model and the decision-making of location scheme to optimize the location strategy, improve the efficiency of location and the accuracy and rationality of location selection [4]; besides, they solve the problems of location scheme determination and evaluation under alternative location scenarios by the methods such as fuzzy comprehensive evaluation, neural network model, prospect theory, and evidence theory [5 –7]. For example, Zhao et al. [11] proposed a fuzzy multi-attribute group decision-making technology for the location of urban logistics centers from the perspective of sustainability; YALI et al. [12] studied the location of centralized collection stations for garbage collection systems using rough set theory and analytic hierarchy process; Kays et al. [13] adopted the Pythagorean fuzzy analytic hierarchy process to explore the location of e-waste recycling plants. Although the current research theories and methods on site selection are relatively mature, they are all studied in a static environment. The selection of the location of the Jiasong Material Guarantee Center for the Sichuan-Tibet Railway is a problem of alternative locations; the construction of the project is located in a complex, difficult, and dangerous mountainous area; the construction environment has large seasonal fluctuations and is dynamic. Therefore, the static method is difficult to apply.

To break through the limitations of the existing methods, we propose a dynamic intuitionistic fuzzy multi-attribute decision-making method suitable for the site selection of the Sichuan-Tibet Railway Engineering Construction Material Guarantee Center. In the previous research, Xu et al. [14] studied dynamic multi-attribute decision-making problems and introduced function distribution to quantify the dynamics of multi-attribute decision-making problems; Chen et al. [15] proposed a dynamic multi-attribute decision-making model based on triangular intuitionistic fuzzy numbers, and introduced aggregation operators to quantify the dynamics of information; LIU et al. [16] explored the dynamic intuitionistic fuzzy multi-attribute decision-making problem, pointed out that dynamic refers to the dynamics of data (that is, decision-related information can be collected in different periods), and proposed a dynamic intuitionistic fuzzy multi-attribute based on the evidential reasoning (ER) algorithm Attribute decision method; LI et al. [17] constructed a dynamic intuitionistic fuzzy multi-attribute decision-making method based on prospect theory and used dynamic operators to quantify the variability of information. It can be concluded that the dynamics in the existing DMADM problems mainly refer to the dynamics of decision information. In our research, the environment is changing, that is, the attributes are dynamic; there are few such methods of quantifying dynamics. Therefore, we propose to improve the traditional intuitionistic fuzzy set theory and introduce the time attributes of the four seasons of the year into its scoring function to measure dynamics. Besides, the similarity model between intuitionistic fuzzy sets is constructed. As demonstrated by comparing the similarity degree of intuitionistic fuzzy numbers, the similarity degree between intuitionistic fuzzy sets can determine the best location scheme, providing a new decision-making idea and method for the location of client-supplied goods and materials support center during the construction of the Sichuan-Tibet railway.

The rest of this paper is arranged as follows. Section 2 introduces intuitionistic fuzzy sets; Section 3 is the improvement of the dynamic intuitionistic fuzzy multi-attribute decision-making method; Section 4 is a case analysis, which is a decision-making solution for the location of the Sichuan-Tibet Railway Engineering Construction A Supply Material Guarantee Center; finally, the conclusion is drawn in Section 5.

2 Intuitionistic fuzzy sets and the definition of the similarity degree

2.1 Definition of intuitionistic fuzzy sets

Definition 1 [8]. Assuming that X ={ x₁, x₂, . . . , x_n } is a given non-empty set, an intuitionistic fuzzy set on X is A ={ < x, μ_A (x) , σ_A (x) > |x ∈ X }. In set A, μ_A (x) and σ_A (x) are the subordination and non-subordination of x to A in the nonempty set X. $μ_{A} (x) : X \to [0, 1], x \in X; μ_{A} (x) \in [0, 1],$ $σ_{A} (x) : X \to [0, 1], x \in X; σ_{A} (x) \in [0, 1],$

Meeting the conditions 0 ⩽ μ_A (x) + σ_A (x) ⩽1 (∀ x ∈ X).

Assuming π_A (x) =1 - μ_A (x) - σ_A (x) is hesitancy degree of x to A. For convenience, intuitionistic fuzzy sets can also be expressed as A = (μ_A (x) , σ_A (x) , π_A (x)).

2.2 Definition of the scoring function

The scoring function is a sort idea that converts intuitionistic fuzzy numbers into specific values to determine the ranking relationship of fuzzy sets using functional relations. It was first defined by Chen and Tan in 1994 [18]. $S (A) = μ_{A} (x) - σ_{A} (x)$

This membership degree of the intuitionistic fuzzy number expressed by the scoring function is the difference of the non-membership degree. Specifically, the larger the difference, the larger the intuitionistic fuzzy number. However, this scoring function ignores the effect of hesitancy degree π_A (x) on decision-making. The membership and non-membership degrees are different when the difference between two intuitionistic fuzzy numbers is the same, making it difficult to compare the size.

Hong and Choi defined the exact functions of intuitionistic fuzzy numbers [9]. $C (A) = μ_{A} (x) + σ_{A} (x)$

The larger the value of C (A), the more the information known about the scheme, and the better the scheme. However, the exact function must be used together with the score function to obtain the size of intuitionistic fuzzy numbers.

Ye considered hesitancy degree in the scoring function and used parameter λ to reflect the function of hesitancy degree π_A (x). His improved scoring function was defined as follows [10]. $S (A) = μ_{A} (x) - σ_{A} (x) + λ π_{A} (x)$ where, λ ∈ [0, 1]. However, the size of intuitionistic fuzzy numbers cannot be scientifically and reasonably reflected through the scoring function because it is difficult to find a reasonable basis for the determination of its value.

The above definition of a scoring function by different scholars is not suitable for the dynamic intuitionistic fuzzy number decision-making method under the temporal and multiple attributes in this paper. Therefore, it is necessary to reconstruct the scoring function according to the actual research situation in this paper.

2.3 Definition of similarity

At present, the method of comparing intuitionistic fuzzy numbers is relatively mature. Similarity [21 –23], as a widely recognized comparison method, is a commonly used measurement method in the fields of data mining, information retrieval, artificial intelligence, and knowledge management. It is often used to compare uncertain or vague information. Assuming that S is a mapping on θ (X) ² → [0, 1], where θ (X) ² represents the set of S, including two parameters. S (A, B) need to satisfy the following conditions.

A ∈ θ (X), B ∈ θ (X),

0 ⩽ S (A, B) ⩽1,

If A = B, then S (A, B) =1 and μ_A (x_i) = μ_B (x_i), σ_A (x_i) = σ_B (x_i),

S (A, B) = S (B, A),

If A ⊆ B ⊆ C, A, B, C ∈ θ (X), then S (A, B) ⩾ S (A, C) and S (B, C) ⩾ S (A, C).

The definition of S (A, B) is the similarity of intuitionistic fuzzy sets A ∈ θ (X) and B ∈ θ (X).

3 Dynamic intuitive fuzzy decision-making method

Based on the traditional intuitionistic fuzzy multi-attribute decision-making method, time attribute is introduced. Considering that different time conditions would affect the decision-making results, time weight and attribute weight need to be considered at the same time. The dynamic intuitionistic fuzzy multiple attribute decision-making problem with r different periods is defined as follows. $D (t_{k}) = [\begin{matrix} x_{11} (t_{k}) & x_{12} (t_{k}) & \dots & x_{1 j} (t_{k}) \\ x_{21} (t_{k}) & x_{22} (t_{k}) & \dots & x_{2 j} (t_{k}) \\ ⋮ & ⋮ & \dots & ⋮ \\ x_{i 1} (t_{k}) & x_{i 2} (t_{k}) & \dots & x_{ij} (t_{k}) \end{matrix}], k = 1, 2, 3, . . ., r$ (1) $p (t) = (p (t_{1}), p (t_{2}), . . ., p (t_{r}))$ (2) $w = (w_{1}, w_{2}, . . ., w_{n})$ (3)

where D (t_k) is an intuitionistic fuzzy decision matrix for the t_k period; x_ij (t_k) = (μ_ij (t_k) , σ_ij (t_k) , π_ij (t_k)) is an intuitionistic fuzzy attribute value; μ_ij (t_k), σ_ij (t_k) and π_ij (t_k) represent the membership degree, non-membership degree, and hesitancy degree of t_k period scheme, respectively; p (t_k) denotes the time weight of t_k period, meeting the conditions p (t_k) >0 and $\sum_{k = 1}^{r} p (t_{k}) = 1$ ; w_i is the weight of attribute c_i, meeting the conditions $w_{i} > 0, \sum_{i = 1}^{n} w_{i} = 1$ . There are r different intuitionistic fuzzy decision matrices in r different periods. The process of dynamic intuitionistic fuzzy multi-attribute decision-making is described as follows.

(1) Construct a new scoring function. A new scoring function is constructed to determine the overall optimal ranking of intuitionistic fuzzy sets in each period, and the scoring function listed above is summarized and optimized to construct a scoring function with higher evaluation accuracy. $M (E (A)) = μ_{A} - σ_{A} + \frac{μ_{A} - σ_{A}}{μ_{A} + σ_{A}} π_{A}$ (4)

There are three main reasons for the scoring function (4) constructed in this way: 1) formula (4) can fully consider the influence of membership degree and non-membership degree and express the deterministic information of intuitionistic fuzzy concentration; 2) formula (4) can consider the influence of the degree of hesitation and combine the relationship between the degree of membership and the degree of hesitation and the relationship between the degree of non-membership and the degree of hesitation, fully excavate part of the uncertain information of intuitionistic fuzzy numbers, and improve the accuracy of evaluation; 3) the expression of formula (4) can avoid choosing absolute advantages (1,0,0) to have a wrong influence on the decision-making problem.

The constructed scoring function (4) fully considers the influence of hesitancy degree, combines the relationship between membership and hesitation and the relationship between non-membership and hesitancy degree and excavates some uncertain information of intuitionistic fuzzy numbers, so as to improve the accuracy of intuitionistic fuzzy number evaluation.

(2) Optimize the new scoring function by attribute weighting. The optimal sequence of attribute values can be obtained by calculating M (E (A)) according to formula (4). Besides, attribute weight is introduced to improve the construction of scoring function with the purpose of making the use of scoring function more scientific and reasonable, after considering membership, non-membership, and hesitation. The final form of scoring function through attribute weighting optimization is expressed as follows.

$\begin{matrix} E (A) = M (E (A)) \cdot M (E (d)) \\ = \frac{1}{n} \sum_{i = 1}^{n} \sum_{j = 1}^{n} π_{ij} w_{i} \cdot (μ_{A} - σ_{A} + \frac{μ_{A} - σ_{A}}{μ_{A} + σ_{A}} π_{A}) \end{matrix}$ (5)

Formula (5) introduces attribute weights based on the formula (4), making it can comprehensively calculate the scores of different attributes in the same scheme to obtain the score of the entire scheme. This calculation method is convenient for judging the importance of attributes, and different weight values can reflect the different contributions of attributes to the scheme. Assuming that the sequence of optimal attribute values is $c^{\land} = (c_{1}^{\land}, c_{2}^{\land}, . . ., c_{i}^{\land})$ .

(3) Establish the similarity model of intuitionistic fuzzy sets. The similarity model can be used to obtain the similarity between the attribute value sequence of each scheme and the optimal attribute value sequence in each period, and the similarity model is provided as follows. $\begin{matrix} S (x_{i} (t_{k}), c^{\land}) = \frac{1}{n} \sum_{i = 1}^{n} w_{i} \\ \frac{μ_{x_{i}} μ_{c^{\land}} + σ_{x_{i}} σ_{c^{\land}} + π_{x_{i}} π_{c^{\land}}}{μ_{x_{i}} μ_{c^{\land}} + σ_{x_{i}} σ_{c^{\land}} + π_{x_{i}} π_{c^{\land}} + {(μ_{c^{\land}} - μ_{x_{i}})}^{2} + (v_{c^{\land}} - v_{x_{i}})^{2} + (π_{c^{\land}} - π_{x_{i}})^{2}} \end{matrix}$ (6)

The following conditions are satisfied, $\begin{matrix} x_{i} t (k) = (x_{i 1} (t_{k}), x_{i 2} (t_{k}), . . . x_{in} (t_{k})), i = 1, 2, . ., n, k = 1, 2, . . ., r, \\ 0 ⩽ S (x_{i} (t_{k}), c^{\land}) ⩽ 1, \\ If c^{\land} = x_{i} (t_{k}) then S (x_{i} (t_{k}), c^{\land}) = 1, \\ S (x_{i} (t_{k}), c^{\land}) = S (c^{\land}, x_{i} (t_{k})) . \end{matrix}$

The similarity decision matrix for each period is denoted as follows. $S (t_{k}) = [s_{11} (t_{k}), s_{12} (t_{k}), . . ., s_{1 n} (t_{k})], k = 1, 2, . . ., r$

(4) Similarity decision matrix weighted optimum selection in different periods and the comparison of the sizes of different schemes. The evaluation value of the similarity decision matrix S (t_k) in each period is obtained as $T_{i} = \sum_{k = 1}^{r} p_{k} s_{i} (t_{k}) i = 1, 2, 3, . . ., n$ by adding period weight. Schemes are sorted by comparing the size of T₁, T₂, . . . T_n.

4 Location selection of client-supplied goods and materials support center for Sichuan-Tibet railway project construction

At present, the Chengdu-Ya’an section of the Sichuan-Tibet Railway has been opened on December 19, 2018; the Linzhi-Lhasa section has started construction at the end of 2014, with a projected construction period of 6 years; the Ya’an-Linzhi section is expected to start construction formally in the third quarter of 2019, with a projected construction period of 12 years. Railway lines originated in Chengdu, Sichuan Province, and entered Ganzi Tibetan Autonomous Prefecture through Pujiang, Ya’an, and Tianquan. They crossed the Jinsha River into Changdu, Tibet Autonomous Region through Kangding, Litang, and Baiyu. After Changdu, Bangda, and Basu, they entered Linzhi, Tibet; after Bomi, and Linzhi, they entered Shannan; after Sangri, Naidong, and Gongga, they entered Lhasa City; the Sichuan-Tibet Railway is along the line. The elevation sketch is illustrated in Fig. 1.

Fig. 1

High-rise diagram of elevation along the Sichuan-Tibet railway.

4.1 Analysis of location selection for client-supplied goods and materials support center

The Sichuan-Tibet railway passes through five geomorphic units in turn: Sichuan Basin, Western Sichuan Alpine Canyon Area, Western Sichuan Alpine Plain Area, Hengduan Mountain Area in Southeast Tibet, and South Tibet Valley Bottom Area. The route passes through the mountains and valleys of the region, the topographic conditions are extremely complex, and geological disasters are frequent. Besides, construction projects need to span 14 rivers and 21 snow mountains over 4000 meters. The proportion of bridges and tunnels in the construction of the whole line is 86%, and the ratio of bridges and tunnels in the Ya’an-Linzhi section reached 92.6%. At present, Shou’an Logistics Park in Pujiang County has been designated as a supply center for the construction of the Sichuan-Tibet Railway. However, the materials needed for construction such as cement have short life cycle characteristics in the cold and dangerous mountainous areas due to the complex and harsh environment along the Ya’an-Linzhi section of the Sichuan-Tibet railway and the extremely inconvenient traffic. Consequently, it is necessary to meet the effectiveness of the transportation of construction materials as much as possible, and it is considered to build a new client-supplied goods and materials support center in Ya’an to Linzhi section. We assume that the selected experts fully understand the situation of alternative sites, and their evaluation results are not affected by personal preferences.

Considering comprehensively and objectively the location index and factors of material support center in Ya’an to Linzhi section of Sichuan-Tibet railway, the construction of Sichuan-Tibet railway can be smoothly guaranteed and the efficiency of material transportation can be improved. By summarizing a large number of documents, 12 indicators of location selection of A supply material support center for Sichuan-Tibet railway construction are finally determined by combining with the actual environment of Sichuan-Tibet railway construction and synthesizing experts’ opinions in related fields; they are integrated into six factors: transportation c₁, geological conditions c₂, climate environment c₃, communication conditions c₄, site selection characteristics c₅, and engineering construction c₆, as presented in Fig. 2.

Fig. 2

Site selection index factors of a material support center for Sichuan-Tibet railway.

4.2 Decision-making results of location selection of client-supplied goods and materials support center

According to the schematic plan of preliminary route selection for the Ya’an to Linzhi section of the Sichuan-Tibet railway in Fig. 3, seven points (Kangding, Litang, Batang, Zuogong, Baju, Bomi, and Linzhi) on the schematic map are chosen as alternative locations since there are logistics centers planned in Pujiang and the planning of logistics centers in Ya’an is not considered.

Fig. 3

Preliminary route selection schematic map of Ya’an-Linzhi section of Sichuan-Tibet railway.

Assuming that only one of the seven alternative sites should be selected by a construction unit as a material support center, six evaluation attributes (c₁ ∼ c₆) are formulated. The decision-makers of the construction unit evaluate the attributes of each alternative site in four different periods and construct an intuitionistic fuzzy decision matrix D (t_k) (k = 1, 2, 3, 4), as exhibited in Tables 1 –4.

Table 1

Intuitionistic fuzzy decision matrix D (t₁)

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆
KD	(0.7,0.2,0.1)	(0.6,0.3,0.1)	(0.5,0.4,0.1)	(0.7.0.3,0.0)	(0.4,0.5,0.1)	(0.9,0.1,0.0)
LT	(0.2,0.5,0.3)	(0.9,0.1,0.0)	(0.5,0.4,0.1)	(0.4,0.4,0.2)	(0.7,0.1,0.2)	(0.6,0.3,0.1)
BT	(0.3,0.4,0.3)	(0.7,0.2,0.1)	(0.6,0.2,0.2)	(0.6,0.3,0.1)	(0.5,0.4,0.1)	(0.8,0.1,0.1)
ZG	(0.8,0.1,0.1)	(0.5,0.4,0.1)	(0.4,0.5,0.1)	(0.7,0.3,0.0)	(0.6,0.4,0.0)	(0.5,0.5,0.0)
BS	(0.6,0.4,0.0)	(0.5,0.4,0.1)	(0.6,0.1,0.3)	(0.4,0.5,0.1)	(0.7,0.1,0.2)	(0.4,0.4,0.2)
BM	(0.5,0.3,0.2)	(0.6,0.3,0.1)	(0.4,0.5,0.1)	(0.6,0.3,0.1)	(0.3,0.4,0.3)	(0.7,0.2,0.1)
LZ	(0.7,0.2,0.1)	(0.7,0.1,0.2)	(0.5,0.3,0.2)	(0.8,0.2,0.0)	(0.3,0.5,0.2)	(0.8,0.1,0.0)

Table 2

Intuitionistic fuzzy decision matrix D (t₂)

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆
KD	(0.5,0.4,0.1)	(0.4,0.5,0.1)	(0.6,0.3,0.1)	(0.6.0.4,0.0)	(0.7,0.2,0.1)	(0.7,0.1,0.2)
LT	(0.4,0.3,0.3)	(0.7,0.1,0.2)	(0.7,0.1,0.2)	(0.5,0.4,0.1)	(0.5,0.3,0.2)	(0.7,0.2,0.1)
BT	(0.5,0.4,0.1)	(0.3,0.4,0.3)	(0.4,0.5,0.1)	(0.7,0.3,0.0)	(0.6,0.3,0.1)	(0.6,0.4,0.0)
ZG	(0.9,0.1,0.0)	(0.3,0.6,0.1)	(0.6,0.3,0.1)	(0.5,0.4,0.1)	(0.7,0.3,0.0)	(0.8,0.2,0.0)
BS	(0.5,0.4,0.1)	(0.7,0.2,0.1)	(0.4,0.3,0.3)	(0.8,0.1,0.1)	(0.5,0.4,0.1)	(0.7,0.2,0.1)
BM	(0.6,0.2,0.2)	(0.8,0.1,0.1)	(0.7,0.1,0.2)	(0.5,0.5,0.0)	(0.4,0.6,0.0)	(0.8,0.1,0.1)
LZ	(0.5,0.4,0.1)	(0.6,0.2,0.2)	(0.8,0.2,0.0)	(0.6,0.3,0.1)	(0.5,0.5,0.0)	(0.4,0.6,0.0)

Table 3

Intuitionistic fuzzy decision matrix D (t₃)

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆
KD	(0.8,0.2,0.0)	(0.6,0.4,0.0)	(0.7,0.2,0.1)	(0.6.0.4,0.0)	(0.5,0.2,0.3)	(0.9,0.1,0.0)
LT	(0.7,0.3,0.0)	(0.4,0.3,0.3)	(0.8,0.2,0.0)	(0.6,0.3,0.1)	(0.9,0.1,0.0)	(0.6,0.2,0.2)
BT	(0.3,0.6,0.1)	(0.5,0.5,0.0)	(0.7,0.1,0.2)	(0.6,0.3,0.1)	(0.4,0.3,0.3)	(0.8,0.1,0.1)
ZG	(0.8,0.2,0.0)	(0.4,0.5,0.1)	(0.7,0.3,0.0)	(0.8,0.1,0.1)	(0.5,0.2,0.3)	(0.6,0.4,0.0)
BS	(0.9,0.1,0.0)	(0.5,0.4,0.1)	(0.6,0.3,0.1)	(0.7,0.2,0.1)	(0.8,0.1,0.1)	(0.6,0.2,0.2)
BM	(0.5,0.5,0.0)	(0.6,0.4,0.0)	(0.3,0.6,0.1)	(0.2,0.5,0.3)	(0.8,0.1,0.1)	(0.4,0.5,0.1)
LZ	(0.7,0.2,0.1)	(0.4,0.2,0.4)	(0.6,0.1,0.3)	(0.7,0.2,0.1)	(0.4,0.5,0.1)	(0.7,0.3,0.0)

Table 4

Intuitionistic fuzzy decision matrix D (t₄)

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆
KD	(0.3,0.5,0.2)	(0.2,0.7,0.1)	(0.4,0.3,0.3)	(0.4.0.6,0.0)	(0.4,0.3,0.3)	(0.9,0.1,0.0)
LT	(0.6,0.3,0.1)	(0.5,0.1,0.4)	(0.8,0.1,0.1)	(0.5,0.4,0.1)	(0.6,0.2,0.2)	(0.8,0.2,0.0)
BT	(0.5,0.4,0.1)	(0.6,0.4,0.0)	(0.7,0.3,0.0)	(0.8,0.1,0.1)	(0.9,0.1,0.0)	(0.2,0.7,0.1)
ZG	(0.8,0.2,0.0)	(0.6,0.3,0.1)	(0.8,0.1,0.1)	(0.5,0.5,0.0)	(0.5,0.3,0.2)	(0.6,0.2,0.2)
BS	(0.3,0.7,0.0)	(0.5,0.4,0.1)	(0.3,0.5,0.2)	(0.8,0.2,0.0)	(0.8,0.1,0.0)	(0.4,0.3,0.3)
BM	(0.7,0.3,0.0)	(0.2,0.6,0.2)	(0.6,0.2,0.2)	(0.3,0.5,0.2)	(0.3,0.5,0.2)	(0.7,0.1,0.2)
LZ	(0.9,0.1,0.0)	(0.7,0.1,0.2)	(0.9,0.1,0.0)	(0.7,0.3,0.0)	(0.6,0.3,0.1)	(0.5,0.5,0.0)

Assume that p (t) = [0.35, 0.2, 0.3, 0.15] is the time weight vector of each period and w = [0.25, 0.25, 0.2, 0.05, 0.1, 0.15] is the weight vector of each attribute, keeping Kangding as KD, Litang as LT, Batang as BT, Zuogong as ZG, Basu as BS, Bomi as BM, and Linzhi as LZ.

The optimal attribute values of the intuitionistic fuzzy set in each period are determined by the scoring function (5) as follows. $\begin{matrix} c^{\land} = (c_{1}^{\land}, c_{2}^{\land}, c_{3}^{\land}, c_{4}^{\land}, c_{5}^{\land}, c_{6}^{\land}) = \\ ((0.9, 0.1, 0.0), (0.9, 0.1, 0.0), (0.9, 0.1, 0.0), (0.8, 0.1, 0.1), (0.9, 0.1, 0.0), (0.9, 0.1, 0.0)) \end{matrix}$

The decision matrix of each period can be calculated from the intuitionistic fuzzy set similarity model (6). $S (t_{1}) = [\begin{matrix} 0.9214 \\ 0.8862 \\ 0.8216 \\ 0.7287 \\ 0.7688 \\ 0.4461 \\ 0.9468 \end{matrix}], S (t_{2}) = [\begin{matrix} 0.9246 \\ 0.7868 \\ 0.7134 \\ 0.5689 \\ 0.6691 \\ 0.5214 \\ 0.9689 \end{matrix}], S (t_{3}) = [\begin{matrix} 0.9213 \\ 0.8745 \\ 0.7980 \\ 0.4868 \\ 0.7468 \\ 0.6645 \\ 0.8891 \end{matrix}], S (t_{4}) = [\begin{matrix} 0.8876 \\ 0.7689 \\ 0.6246 \\ 0.5986 \\ 0.6012 \\ 0.4246 \\ 0.9012 \end{matrix}]$

According to formula $T_{i} = \sum_{k = 1}^{r} p_{k} s_{i} (t_{k}), i = 1, 2, 3, . . ., n$ , seven alternative location schemes can be ranked. The weighted ranking results of seven alternative location schemes are illustrated in Fig. 4.

$\begin{matrix} T_{KD} = \sum_{k = 1}^{4} p_{k} s_{11} (t_{k}) = 0.9137 T_{LT} = \sum_{k = 1}^{4} p_{k} s_{21} (t_{k}) = 0.8291 \\ T_{BT} = \sum_{k = 1}^{4} p_{k} s_{31} (t_{k}) = 0.7394 T_{ZG} = \sum_{k = 1}^{4} p_{k} s_{41} (t_{k}) = 0.5958 \\ T_{BS} = \sum_{k = 1}^{4} p_{k} s_{51} (t_{k}) = 0.6965 T_{BM} = \sum_{k = 1}^{4} p_{k} s_{61} (t_{k}) = 0.5142 \\ T_{LZ} = \sum_{k = 1}^{4} p_{k} s_{71} (t_{k}) = 0.9265 \end{matrix}$

Fig. 4

Weighted sorting results of the similarity decision matrix.

According to the weighted results of the similarity decision matrix, the ranking results of seven alternative sites are as follows: LZ>KD>LT>BT > BS>ZG > BM. Therefore, Linzhi is the best choice for a client-supplied goods and materials support center in the Ya’an to Linzhi section of the Sichuan-Tibet railway.

4.3 Sensitivity analysis

To verify the robustness of the method, we conduct a sensitivity analysis on the changes in weights, including time weight p (t) and attribute weight w. First, attribute weight is kept unchanged, namely, w = [0.25, 0.25, 0.2, 0.05, 0.1, 0.15]; then, time weight is set to be: p (t) ₁ = [0.25, 0.25, 0.25, 0.25], p (t) ₂ = [0.2, 0.3, 0.3, 0.2], p (t) ₃ = [0.3, 0.2, 0.2, 0.3], p (t) ₄ = [0.3, 0.3, 0.2, 0.2]. The solution results are compared with p (t) = [0.35, 0.2, 0.3, 0.15], as illustrated in Fig. 5.

Fig. 5

Sensitivity analysis of time weight.

Similarly, attribute weight w is selected as w₁ = [0 . 17, 0 . 17, 0 . 17, 0 . 17, 0 . 16, 0 . 16], w₁ = [0 . 2, 0 . 2, 0 . 2, 0 . 1, 0 . 1, 0.2], w₂ = [0 . 1, 0 . 1, 0 . 1, 0 . 2, 0 . 2, 0 . 3], w₃ = [0 . 15, 0.2, 0.2, 0 . 2, 0 . 15, 0 . 1], and w₄ = [0 . 15, 0.2, 0 . 15, 0 . 15, 0 . 2, 0 . 15]. The solution results are compared to w = [0.25, 0.25, 0.2, 0.05, 0.1, 0.15], as presented in Fig. 6.

Fig. 6

Sensitivity analysis of attribute weight.

As indicated in Figs. 5 and 6, the value of the similarity decision matrix varies as the value of the weight changes. However, the overall trend remains unchanged, and the results of the site selection and sequencing have not changed. It can be demonstrated that the method proposed in this paper will not affect the decision result when the weight changes slightly, indicating that the method is stable.

4.4 Method comparison

To verify the advanced nature of the method, the results obtained are compared with those of the Hesitant Intuitionistic Fuzzy Multiple Attribute Decision Making Method proposed in the literature [24]. Among them, the weight vector of each attribute is consistent with the above, w = [0.25, 0.25, 0.2, 0.05, 0.1, 0.15]. Thus, comprehensive evaluation values of 7 alternative sites can be obtained, as illustrated in Fig. 7.

Fig. 7

Comprehensive evaluation results.

According to the calculation results in Fig. 5, the ranking results of the 7 alternative sites are: KD>LZ>BT>LT>BT>BS>ZG>BM. Therefore, it can be observed that the best location plan for the material guarantee center of the Yalin section of the Sichuan-Tibet Railway obtained by the hesitating direct fuzzy multi-attribute decision-making method is Kangding. Kangding is rich in resources and the regional economic development is relatively advanced; thus, it is reasonable as a material guarantee center. However, from the analysis of the actual situation, Kangding has a large altitude difference, a changeable climate, and obvious seasonal differences; this makes material storage face the challenges of large temperature differences and a changeable environment, which is not conducive to material security. On the contrary, although Linzhi’s economic development is lagging behind, its terrain is flat, the altitude difference is small, and seasonal climate changes during the year are not obvious. Consequently, Linzhi is more suitable for use in material security centers compared to Kangding. It can be concluded that the dynamic intuitionistic fuzzy multi-attribute decision-making method mentioned in this paper has a good application to engineering decision-making problems in complex environments, providing a theoretical foundation for the relevant decision-making of the engineering part and the planning department.

5 Conclusion

In the construction of the Sichuan-Tibet railway project, there are prominent contradictions among the large-scale material demand, the large-scale construction equipment, and the limited traffic conditions, as well as the lack of large-scale ground materials. Besides, the location conditions of the material support center in the construction are complex. In this paper, based on the intuitionistic fuzzy set, a dynamic intuitionistic fuzzy multi-attribute decision-making method is proposed, and time weight and attribute weight are introduced to improve the scoring function; moreover, the dynamic characteristics of the dynamic intuitionistic fuzzy multi-attribute decision-making method adopted in this paper are embodied in the influence of seasonal changes on the location of A-supply material support center during the construction period of Sichuan-Tibet Railway Project, and the attribute weight of time interval is introduced. Afterward, the location selection of the alternative material support center for Sichuan-Tibet railway construction is decided by constructing a weighted scoring function and weighted similarity decision-making model. The results indicate that the location of the Jiasong Material Guarantee Center for the Sichuan-Tibet Railway Project should be located in Linzhi. Simultaneously, a sensitivity analysis and method comparison of weight changes is conducted to verify the advantages of the method proposed in this paper, demonstrating that the decision result will not be affected when the weight changes slightly, and the method is robust. Compared with other methods, the method proposed in this paper is more suitable for decision-making problems in the Sichuan-Tibet railway project and has advanced nature.

The decision-making method adopted in this paper provides not only a new idea for dynamic intuitionistic fuzzy decision-making but also a new strategy for ensuring the smooth development of Sichuan-Tibet railway construction. But there are some limitations in this paper. The method proposed in this paper depends on the judgment of experts. Therefore, the selection of experts is a challenging task. The selected experts must have sufficient knowledge of the candidate points. At the same time, in order to weaken the influence of experts’ preference, the number of experts should not be too small, which can ensure the accuracy of the calculation results. In addition, the category of decision-makers has not been considered in this paper. In the future, we can improve the intuitionistic fuzzy multi-attribute decision-making method based on prospect theory and classify the decision-making results according to the category of decision-makers.

Data announcements

All the data used in the case analysis are from Sichuan Transport Sector, Tibet Transport Sector, Chinese Design Institute, and engineering construction units, which have been explained in the paper. However, restricted by the policy of the Chinese government, the entire road network data in the region cannot be disclosed. Thus, we only selected part for research and replaced the actual place names with numbers.

Footnotes

Acknowledgments

This study was supported by Key R & D projects of the Ministry of science and technology of China (863 Program) (Grant No.2018YFB1601400), Key R & D projects of Sichuan Science and Technology Department (Grant No.2019YFG0001) and China Railway Group Co., Ltd. (Grant No. KF2019-010-B).

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