Single-value neutrosophic cosine measure for evaluation of port logistics competitiveness

Abstract

Port as an irreplaceable important node in the process of logistics is a special form of the integrated logistics system, which completes the basic logistics service and value-added services in the global supply chain logistics system. At present, the port logistics service has become an important breakthrough in the competition of ports, the improvement of port logistics competitiveness has great influence on the development of port and port city and even the area economic development. Analyzing from the port logistics competitiveness, this paper establishes a comprehensive evaluation index system and proposes a single-value neutrosophic cosine measure method to evaluate the port logistics competitiveness of five sample ports, and gets the score sorting of the logistics competitiveness of these five ports. This method as a helpful tool is clear and easy for port logistics competitiveness evaluation during actual application.

Keywords

Single-valued neutrosophic set (SVNS)port logistics competitiveness cosine measure single-value neutrosophic cosine measure method

1 Introduction

As the infrastructure for national economic development, ports are characterized by large scale and large investments. The basic functions of ports are transportation, berthing, loading and unloading passengers, loading and unloading cargo, receiving and storing goods, supply and tourism services for ships. The modern port is a comprehensive industrial and commercial center with warehousing and transportation, commercial trade, industrial production and social service functions, and is a three-dimensional transportation hub combining sea, land and air. This requires the port playing its node role and distribution role in the logistics chain and relying on port resources to carry out a variety of value-added logistics services on the basis of completing loading, unloading, handling and processing services. Therefore, modern ports have formed an integrated logistics service platform with their large-scale gather and distribute capacity. At present, many port cities regard the development of port logistics as the breakthrough point of urban development, through the development of port logistics, they promote the development of port-neighboring industry, radiate the surrounding inland areas, and promote the growth of regional import and export trade, which in turn can promote the development of port logistics, thus realizing a virtuous circle. With the large-scale development and utilization of port resources in the world and the rapid development of port logistics in China, the evaluation of port logistics competitiveness plays a more and more important role in port development. The competitiveness of port logistics is the ability to surpass other ports in logistics by improving the efficiency of port operation and resource utilization on the basis of regional economy and infrastructure construction. As the port logistics is affected by equipment, site, weather and other factors, the evaluation of logistics competitiveness is a process of multi-index comprehensive evaluation.

In the evaluation of port logistics competitiveness, it is difficult to give accurate evaluation information due to the complexity of decision-making indicators and the subjectivity of decisionmakers, so different forms of information expression should be adopted according to the actual situation. The traditional fuzzy set only considers the membership degree and ignores the importance of the non-membership degree. Although the intuitionistic fuzzy set and the interval intuitionistic fuzzy set supplement the non-membership degree to the fuzzy set, they can only deal with incomplete information and cannot deal with indeterminate/inconsistent information. As a generalization of fuzzy sets, neutrosophic sets can not only describe incomplete information in reality but also describe uncertain and inconsistent information. At present, neutrosophic sets have been studied deeply by many experts and scholars, and have been applied to a wide range of practical fields and achieved fruitful results, such as model classification, decision analysis, medical diagnosis, ecological assessment, personnel assessment and many other fields, but there are few studies and applications of neutrosophic set in competitiveness evaluation of port logistics fields. By studying the connotation of port logistics resources, this paper analyzes the related factors that affect the development of port logistics, thus establishing the evaluation index system of port logistics competitiveness, and using the cosine measures of SVNS to objectively evaluate and analyze the port logistics competitiveness, in order to provide reference for the development of port logistics.

The other sections of this paper are organized as follows. Section 2 gives some literature about port logistics competitiveness evaluation and SVNS. Section 3 Constructs port logistics competitiveness evaluation index system. Section 4 describes some basic concepts and establishes port logistics competitiveness evaluation methods using the cosine measures of SVNSs. Section 5 presents an actual example to indicate the application of the proposed methods. Section 6 contains a conclusion of this paper.

2 Literature review

Domestic and foreign scholars’ researches on port logistics competitiveness mainly focus on three aspects: The first is the study of port logistics competitiveness and its influencing factors, such as famous Chinese logistics expert Ding [1] pointed out that the logistics competitiveness is formed and expressed by the area logistics factors with the abilities to rob resource, expanding market, occupying market and gaining profit in the process of the market competition based on transport facilities, industrial foundation, management efficiency and development potential, mainly including enterprise logistics competitiveness, city logistics competitiveness and national logistics competitiveness; Chen et al. [2] thought the port logistics competitiveness as the ability to attract cargo flow and resource accumulation and analyzed that capacity, cost and efficiency are important factors influencing the port logistics competitiveness. Huang [3] summarized the influencing factors of port competitiveness as internal factors and external factors, the internal factors include port logistics service quality, physical conditions, prices and so on; the external factors include economic environment, political environment, international shipping status, hinterland status and so on. Cao [4] analyzed and studied the influencing factors of Shanghai port logistics competitiveness by combining qualitative and quantitative methods based on Porter’s diamond model, and concluded that the gathering and distributing capacity of port logistics, the operation efficiency of port logistics and the environmental conditions of port logistics are the important factors influencing the competitiveness of Shanghai port logistics. Wu [5] introduced six factors that affect the port logistics competitiveness through qualitative research, and compared Luojin port with other ports through quantitative research, and analyzed the most advantageous factors and weak links, so as to help Luojin port achieve better positioning. The second is the study of port logistics industrial cluster. For example, Li et al. [6] analyzed and studied the competitive situation of port logistics industrial cluster in the Bohai rim region from three aspects: port status, logistics industry and hinterland economy. Shi et al. [7] studied the formation and development of port logistics industrial cluster by using the symbiosis theory. Li [8] used location entropy and spatial Gini coefficient to measure the level of logistics industrial cluster. Tian [9] elaborated the process of port logistics industrial cluster and hinterland economic linkage development confirmed the linkage between them by using co-integration analysis and constructed the dynamic influence relationship between them through simulation. The third is the evaluation of port logistics competitiveness. For example, Zhao [10] adopted the fuzzy comprehensive evaluation method to comprehensively evaluate the logistics competitiveness of major coastal ports in Jiangsu province. Yu et al. [11] used factor analysis to evaluate the logistics competitiveness of Chinese major coastal ports, and then find out the advantages and disadvantages of logistics competitiveness of Dalian port. Lai [12] used factor analysis to make a comprehensive analysis of the competitiveness of port logistics in Ningbo-Zhoushan port and Shanghai port and discussed the competitive relationship and cooperation model between the two ports. Wang [13] et al. calculated the weight of each index according to the entropy theory in the analytic hierarchy process and information theory, and obtained the comprehensive weight of the fusion evaluator‘s subjective preference and objective attribute of the data by using the comprehensive weight method, so as to establish a multi-index comprehensive weight evaluation model, which is applied to the evaluation of logistics competitiveness of some coastal ports in China. Wang et al. [14] established an evaluation index system to measure the competitiveness of port logistics, introduced the entropy weight TOPSIS analysis method to calculate the evaluation index of eight major ports in China, and ranked the ports according to the calculation results. Song [15] et al. used factor analysis to evaluate the competitiveness of listed port logistics enterprises in different regions of China. Li [16] based on the analysis of port logistics resources, from the physic-geographical environment of port, the infrastructure conditions of port, the scale of port logistics development, the comprehensive strength of port city four aspects to build the port logistics competitiveness evaluation index system, and then evaluate the port logistics competitiveness of 7 big ports in Bohai rim by using the entropy TOPSIS method, give the analysis of its competitive situation. Wang [17] comprehensively evaluated the five main factors by using the factor analysis method as the first principal component and proposed the comprehensive evaluation of port logistics competitiveness based on international trade and factor analysis method.

As a generalization of fuzzy set, Smarandache [18, 19] put forward the concept of neutrosophic set (NS) by using non-standard real unit interval [0–, 1 +], the NS has three membership functions: the true membership function, the uncertain membership function, and the false membership function. In order to use the NS more conveniently, the concept of single value neutrosophic set(SVNS) was proposed and defined in literature [20], at the same time some basic operations and integration operators of intelligence set in single value were presented. The SVNS can be regarded as a generalization of intuitionistic fuzzy set, and its three subjection functions are independent of each other and take values on the closed interval [0, 1]. At present, many results have been obtained in the study of the NS. Majumdar et al. [21] studied the similarity and entropy of SVNS. Ye [22, 23] proposed the correlation coefficient of the SVNS and applied it to the multi-attribute decision-making problem. Sahin et al. [24] proposed the axiomatic definition of the inclusion degree of the single-valued neutrosophic set and gave an inclusion degree of the single-valued neutrosophic set. Peng et al. [25] defined a new operation of the single-valued neutrosophic set and proposed a ranking of multi-criteria decision problems with simplified neutrosophic numbers methods; Ye [26] proposed improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Fan [27] et al. proposed the cosine measure of refined-single valued neutrosophic sets and refined-interval neutrosophic sets for multiple attribute decision-making. Avishek Chakraborty [28] et al. proposed the Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications. Abdul Alamin [29] et al. proposed Solution and Interpretation of Neutrosophic Homogeneous Difference Equation and so on [30].

In order to determine the competitiveness of port logistics, scientific, reasonable, and diversified evaluation methods should be adopted, establishing mathematical models to rank to solve the multi-index evaluation problem. This paper mainly studies on port logistics competitiveness evaluation, using neutrosophic cosine measure method to establish evaluation mechanism, according to the score function the port logistics competitiveness can be ranked, thus the main problems of our country port logistics can be gotten, some suggestions and reference for the improvement of China’s port logistics competitiveness can be offered.

3 Construction and evaluation of port logistics competitiveness evaluation index system

Port competitiveness is determined by a variety of factors, such as geographical location, economic hinterland strength, port infrastructure, port operation level and related port service level, etc. The importance degree of each factor is not exactly the same, so we should consider each aspect factor, establishes the appropriate scientific indicator system. The evaluation index system of logistics competitiveness of major coastal ports in China is shown in Table 1 [31]. This paper makes a hierarchy analysis on many index variables of the port logistics competitiveness and selects the first 7 evaluation indexes to evaluate the port logistics competitiveness for reducing the analysis index to facilitate the calculation and reducing the loss of information contained in the original index.

Table 1
Evaluation indexes

First-level indicators Second-level indicators

The capability of port logistics hardware facility Number of loading, unloading and transportation machinery and equipment in the port area

The 10,000-ton berth in the port

Portland area

The capacity of port logistics scale Port cargo throughput

Port container throughput

The number of routes covered by the port

The capability of port logistics operation Survey on automation level and operation capability of port machinery and equipment

The capacity of port gathering and distributing

The capacity of port waste treatment

The capacity of port logistics hinterland economic Total retail sales of consumer goods in the port city

Port city GDP

The capacity of port hinterland transport

The capacity of port logistics information processing Ship traffic command system automation level

Rapid response capability of the production scheduling system

Completeness of information service functions

Port logistics coordination and support capability Policy guidance and coordination ability of government departments

Regulatory and service capabilities of customs and maritime departments

The formulation of managing port regulations

First-level indicators	Second-level indicators
The capability of port logistics hardware facility	Number of loading, unloading and transportation machinery and equipment in the port area
	The 10,000-ton berth in the port
	Portland area
The capacity of port logistics scale	Port cargo throughput
	Port container throughput
	The number of routes covered by the port
The capability of port logistics operation	Survey on automation level and operation capability of port machinery and equipment
	The capacity of port gathering and distributing
	The capacity of port waste treatment
The capacity of port logistics hinterland economic	Total retail sales of consumer goods in the port city
	Port city GDP
	The capacity of port hinterland transport
The capacity of port logistics information processing	Ship traffic command system automation level
	Rapid response capability of the production scheduling system
	Completeness of information service functions
Port logistics coordination and support capability	Policy guidance and coordination ability of government departments
	Regulatory and service capabilities of customs and maritime departments
	The formulation of managing port regulations

4 Research methodology

4.1 Basic concepts of SVNS

Definition 1. Let U be an object set, then a NS A in U can be defined: $A = {〈 u, T_{A} (u), I_{A} (u), F_{A} (u) 〉 | u \in U} .$

In which T_A (u) , I_A (u) , F_A (u) express truth-membership function, indeterminacy-membership function, and falsity-membership function, individually. T_A (u) , I_A (u) , F_A (u) is]0–, 1 + [standard or non-standard subset.

Definition 2 [19, 20]. Let U be an object set, then a SVNS A in U can be defined as: $A = {〈 u, T_{A} (u), I_{A} (u), F_{A} (u) 〉 | u \in U} .$

In which T_A : U → [0, 1] , I_A : U → [0, 1] , F_A : U → [0, 1] express truth-membership function, indeterminacy-membership function and falsity-membership function, individually, T_A (u) , I_A (u) , F_A (u) ∈ [0, 1].

Definition 3 [20]. Let A_c be the complement of a SVNS A and can be defined as: $A_{c} = {〈 u, F_{A} (u), 1 - I_{A} (u), T_{A} (u) 〉 | u \in U} .$

Definition 4 [20]. Let A and B be two SVNSs in U, A ⊆ B if and only if T_A (u) ⩽ T_B (u), I_A (u) ⩾ I_B (u), and F_A (u) ⩾ F_B (u) for every u in U.

Definition 5 [20]. Let A and B be two SVNSs in U, A = B if and only if A ⊆ B and B ⊆ A.

4.2 Cosine measure of SVNS

Definition 6 [26]. Let U ={ u₁, u₂, … u_n } be a universe of discourse, A = {〈u, T_A (u_i) , I_A (u_i) , F_A (u_i) 〉|u_i ∈ U} and B = { 〈x, T_B (u_i) , I_B (u_i) , F_B (u_i) 〉|u_i ∈ U } betwoSVNSs. The cosine measure method of A and B can be defined as:

$\begin{matrix} D (A, B) = \frac{1}{n} \sum_{i = 1}^{n} cos {\frac{π}{6} (| T_{A} (u_{i}) - T_{B} (u_{i}) | \\ + | I_{A} (u_{i}) - I_{B} (u_{i}) | \\ + | F_{A} (u_{i}) - F_{B} (u_{i}) |)} \end{matrix}$ (1)

D (A, B) have the following properties [26]:

0 ⩽ D (A, B) ⩽ 1;

D (A, B) = 1ifandonlyifA = B ;

D (A, B) = D (B, A);

Considering the weights w_i ∈ [0, 1] of attributes G_i (i = 1, 2, …, n), $\sum_{i = 1}^{n} w_{i} = 1$ , the weighted cosine measure formula of SVNS can be defined as:

$\begin{matrix} W (A, B) = \sum_{i = 1}^{n} w_{i} (cos {\frac{π}{6} (| T_{A} (u_{i}) - T_{B} (u_{i}) | \\ + | I_{A} (u_{i}) - I_{B} (u_{i}) | \\ + | F_{A} (u_{i}) - F_{B} (u_{i}) |)}) \end{matrix}$ (2)

4.3 The weight of information entropy is determined

The cosine measures of SVNS consider the importance of each element and can get reasonable and effective results. The difficult part of this method is the determination of index weight. We choose the entropy weight method, which is an objective weighting method. The smaller the information entropy of the index is, the greater the variation degree of the index is, the more information it provides, the greater the role it plays in the comprehensive evaluation, and the higher the weight should be. On the contrary, the hher the information entropy is, the lower the weight of this index should be.

In the evaluation matrix with n evaluation objects and m evaluation indexes, the information eropy value of the number i evaluation index can be expressed as: $E_{i} = - \frac{1}{ln n} \sum_{j = 1}^{n} q_{ij} ln q_{ij}, i = 1, 2, \dots, m,$ (3)

In which $q_{ij} = \frac{r_{ij}}{\sum_{j = 1}^{n} r_{ij}}, i = 1, 2, \dots, m$ , Is the normalization result of the evaluation matrix R = (r_ij) _m×n.

According to the entropy value of the evaluation index, its weight can be determined. The objective weight of the index C_i: $ω_{i} = \frac{1 - E_{i}}{\sum_{k = 1}^{m} (1 - E_{k})}, i = 1, 2, . ., m .$ (4)

Therefore, the objective weight vector of each index is W = (ω₁, ω₂, …, ω_m) ^T.

4.4 Decision-making method using the cosine of SVNSs

Let A = {〈u, T_A (u) , I_A (u) , F_A (u) 〉|u ∈ U} three functions T_A (u) , I_A (u) , F_A (u) can be denoted by SVNSs in form of the decision matrix, which is shown in Table 2.

Table 2
The SVNS decision matrix

G ₁ … G _n

P ₁ 〈T₁₁, I₁₁, F₁₁〉 … 〈T_1n, I_1n, F_1n〉

P ₂ 〈T₂₁, I₂₁, F₂₁〉 … 〈T_2n, I_2n, F_2n〉

… … … …

P _m 〈T_m1, I_m1, F_m1〉 … 〈T_mn, I_mn, F_mn〉

	G ₁	…	G _n
P ₁	〈T₁₁, I₁₁, F₁₁〉	…	〈T_1n, I_1n, F_1n〉
P ₂	〈T₂₁, I₂₁, F₂₁〉	…	〈T_2n, I_2n, F_2n〉
…	…	…	…
P _m	〈T_m1, I_m1, F_m1〉	…	〈T_mn, I_mn, F_mn〉

Step 1: Setting T^max, I^minandF^minas the maximum truth value, the minimum indeterminate and falsity values in each column of the decision matrix, individually, the ideal solution can be expressed as $P_{x}^{*}$ . $P_{x}^{*} = 〈 T_{x}^{\max}, I_{x}^{\min}, F_{x}^{\min} 〉, for x = 1, 2, \dots n .$ (5)

Step 2: According to the formula (3, 4), we put T_mn value into the calculation, and then the weight vector of each attribute can be obtained.

Step 3: According to the formula (2), the weighted cosine measure between each alternative P_r (r = 1, 2, … m) and the ideal alternative lated. Then the values of obtained.

Step 4: The alternatives can be ranked according to the values of W (P_r, P^*).

Step 5: End.

The flow chart of the algorithm is shown in Fig. 1.

Fig. 1

Flow chart of the algorithm.

5 Application method and results

5.1 The number of evaluations given by experts

In this part, we choose five sample ports for empirical research. We use port 1 to port 5 to represent five different ports. The raw data of the port logistics competitiveness evaluation index system is shown in Fig. 2. According to raw data in Fig. 2, the experts sorted out and analyzed the collected data, and provided the evaluation data with single value neutrosophic information, as shown in Table 3.

Fig. 2

The raw data of port logistics competitiveness evaluation index system. **Note: Data source: port cargo throughput (2015), port city GDP (2015) from the National Statistical Yearbook total retail sales of port consumer goods (2015), port container throughput (2015), relevant ports Statistical yearbook and statistical bulletin of economic and social development of provinces and cities in corresponding years.

Table 3

The evaluation data with SVNS information

Port	Port1	Port2	Port3	Port4	Port5
Number of loading, unloading and transportation machinery and equipment in port area	0.9,0.6,0	0.7,0.9,0.2	1,0,0	0.7,0.4,0.3	0.4,0.5,0.6
The 10,000-ton berth in the port	1,0,0	0.8,0.8,0.1	0.7,0.6,0.2	0.9,0.3,0.1	0.3,0.4,0.7
Port land area	0.1,0.2,0.9	0.5,0.9,0.4	0.4,0.3,0.6	1,0,0	0.2,0.5,0.7
Port cargo throughput	0.6,0.4,0.4	1,0,0	0.3,0.9,0.6	0.9,0.1,0.1	0.1,0.5,0.8
Port container throughput	0.2,0.8,0.7	0.6,0.4,0.4	0.2,0.8,0.7	1,0,0	0.01,0.1,1
The number of routes covered by ports	0.3,0.1,0.7	1,0,0	0.5,0.8,0.4	0.5,0.5,0.4	0.2,0.1,0.8
Survey on automation level and operation capability of port machinery and equipment	0.6,0.2,0.4	0.7,0.5,0.2	1,0,0	0.5,0,0.5	0.2,0.5,0.7

Then we established the decision matrix, as shown in Table 4:

Table 4

The SVNS decision matrix

	P ₁	P ₂	P ₃	P ₄	P ₅
G ₁	<0.9,0.6,0>	<0.7,0.9,0.2>	<1,0,0>	<0.7,0.4,0.3>	<0.4,0.5,0.6>
G ₂	<1,0,0>	<0.8,0.8,0.1>	<0.7,0.6,0.2>	<0.9,0.3,0.1>	<0.3,0.4,0.7>
G ₃	<0.1,0.2,0.9>	<0.5,0.9,0.4>	<0.4,0.3,0.6>	<1,0,0>	<0.2,0.5,0.7>
G ₄	<0.6,0.4,0.4>	<1,0,0>	<0.3,0.9,0.6>	<0.9,0.1,0.1>	<0.1,0.5,0.8>
G ₅	<0.2,0.8,0.7>	<0.6,0.4,0.4>	<0.2,0.8,0.7>	<1,0,0>	<0.01,0.1,1>
G ₆	<0.3,0.1,0.7>	<1,0,0>	<0.5,0.8,0.4>	<0.5,0.5,0.4>	<0.2,0.1,0.8>
G ₇	<0.6,0.2,0.4>	<0.7,0.5,0.2>	<1,0,0>	<0.5,0,0.5>	<0.2,0.5,0.7>

From the SVNS decision matrix and the formula (5), the ideal solution (ideal alternative) can be obtained: $\begin{matrix} P^{*} = {〈 1, 0, 0 〉, 〈 1, 0, 0 〉, 〈 1, 0, 0 〉, 〈 1, 0, 0 〉, \\ 〈 1, 0, 0 〉, 〈 1, 0, 0 〉〈 1, 0, 0 〉} . \end{matrix}$

According to the formula (3), we normalized the decision matrix and got R = (r_ij) _m×n: $R = [\begin{matrix} 0.243 & 0.270 & 0.045 & 0.207 & 0.100 & 0.120 & 0.200 \\ 0.189 & 0.216 & 0.227 & 0.345 & 0.299 & 0.400 & 0.233 \\ 0.270 & 0.189 & 0.182 & 0.103 & 0.100 & 0.200 & 0.333 \\ 0.189 & 0.243 & 9.455 & 0.310 & 0.498 & 0.200 & 0.167 \\ 0.108 & 0.081 & 0.091 & 0.034 & 0.005 & 0.080 & 0.067 \end{matrix}]$

The information entropy value E of the evaluation index in each port can be calculated as: $\begin{matrix} E = (0.9742, 0.9614, 0.8472, 0.8742, \\ 0.7418, 0.9114, 0.9362)^{T} \end{matrix}$

Then objective entropy weight of the index C_i: $\begin{matrix} W = (0.0342, 0.0512, 0.2027, 0.1669, \\ 0.3427, 0.1176, 0.0846)^{T} \end{matrix}$

With the weight vector and formula (2), the weighted cosine measure values between each alternative P_r (r = 1, 2, 3, 4) and the ideal alternation P* can be obtained, which are listed as follows: $\begin{matrix} W (P_{1}, P^{*}) = 0.5965, W (P_{2}, P^{*}) = 0.8215, \\ W (P_{3}, P^{*}) = 0.5674, W (P_{4}, P^{*}) = 0.9498, \\ and W (P_{5}, P^{*}) = 0.4864 . \end{matrix}$

According to the measure values, the ranking of port logistics competitiveness can be obtained, which is P₄ ≻ P₂ ≻ P₁ ≻ P₃ ≻ P₅.

From the ranking of port logistics competition can be seen, P4 and P2 are in the leading position in port logistics competitiveness, P5 is in the bottom position in port logistics competitiveness, and other ports are not far behind the leading port.

5.2 Suggestions on improving logistics competitiveness

Through analysis of seven evaluation indicators of the port, the 5th and 3rd index weights are 0.3427 and 0.2027, respectively, occupied the main part of the overall weight of the evaluation model, which illustrated that the above two indicators play an important role to enhance the competitiveness of port logistics competitiveness, so every port should focus on expanding the port area land area and the port container throughput in order to improve the hardware facilities. The 4th and 6th index weights are 0.1669 and 0.1176, respectively, which are suggested ports to expand port cargo area and the number of routes covered. The 1st, 2nd and 7th with smaller index weights have less impact on logistics competitiveness, which can be used as a supplement to improve logistics competitiveness after the port’s infrastructure construction and industrial-scale reach a higher level.

For the five ports in the model, P4 and P2, which have the most logistics competitiveness, P4 should make improvements in loading, unloading and transportation machinery and equipment in port area, so as to improve industrial operational efficiency and promote the further expansion of the scale. In addition, P4 can introduce the latest automated management system and information processing system to improve the efficiency of port operation. Finally, the port’s collection and distribution capacity is relatively low, for which, the number of collection cards and the ability to communicate with customers can be increased to improve the collection and distribution capacity. P2 should make improvements in loading, unloading, and transportation machinery and equipment in port area, in addition, P2 should expand portland area, improve port container throughput and strengthen the publicity to attract investment and consumption, and overcome these weaknesses to enhance its port logistics competitiveness. For P1 and P3 with strong logistics competitiveness, P1 should expand the portland area, improve port container throughput and enhance communication with other foreign port cities to improve their route coverage, P3 should expand the portland area, improve port cargo throughput and port container throughput. For P5 with weak logistics competitiveness, due to its small land area and small number of routes, it is suggested to expand the port construction scale to establish a good foundation for the operation of cargo throughput and container throughput.

6 Conclusions

The evaluation and empirical research on the port logistics competitiveness are of great significance. This paper has carried out an analysis of port logistics competitiveness and built an index system of port logistics competitiveness by referring to the data collected from previous studies. On this basis, five sample ports have been selected for empirical study to establish the index system of port logistics competitiveness, and the subjective and objective weights of each index have been determined through the entropy value theory. And then the weighted cosine method of SVNS has been used to gain the score ranking of the five ports to verify the unbalanced development of port logistics. The results show that among the above ports, P2 and P4 have advantages and greater development potential, while P5 has a certain gap with other ports due to its limited infrastructure and industry. P1 and P3 have advantages, respectively. Based on the above analysis, the evaluation model established based on neutrosophic cosine method is a reliable and effective method, which can provide some suggestions for the evaluation and sorting of port logistics competitiveness. Finally, some reliable countermeasures are put forward for the cultivation of port logistics competitiveness.

In the future, we shall use other methods under the SVNS environment to deal with related issues of ports, such as port pollution and port management, and so on.

Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 61703280 and 51879156), the Science and Technology Planning Project of Shaoxing City of China(Grant No. 2017B70056 and 2018C10013, the General Research Project of Zhejiang Provincial Department of Education (Grant No. Y201839944, the Public Welfare Technology Research Project of Zhejiang Province (Grant No. LGG19F020007), and High-level talent project funding plan of transportation industry supported by the Ministry of Transport of the People’s Republic of China (Grant No. 2019-012).

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Single-value neutrosophic cosine measure for evaluation of port logistics competitiveness

Abstract

Keywords

1 Introduction

2 Literature review

3 Construction and evaluation of port logistics competitiveness evaluation index system

4.1 Basic concepts of SVNS

4.2 Cosine measure of SVNS

Table 2 The SVNS decision matrix G 1 … G n P 1 〈T11, I11, F11〉 … 〈T1n, I1n, F1n〉 P 2 〈T21, I21, F21〉 … 〈T2n, I2n, F2n〉 … … … … P m 〈Tm1, Im1, Fm1〉 … 〈T mn , I mn , F mn 〉

5.1 The number of evaluations given by experts

6 Conclusions

References

Table 2
The SVNS decision matrix

G ₁ … G _n

P ₁ 〈T₁₁, I₁₁, F₁₁〉 … 〈T_1n, I_1n, F_1n〉

P ₂ 〈T₂₁, I₂₁, F₂₁〉 … 〈T_2n, I_2n, F_2n〉

… … … …

P _m 〈T_m1, I_m1, F_m1〉 … 〈T_mn, I_mn, F_mn〉