An integration approach of multi-source heterogeneous fuzzy spatiotemporal data based on RDF

Abstract

With the growing importance of the fuzzy spatiotemporal data in information application, there is an increasing need for researching on the integration method of multi-source heterogeneous fuzzy spatiotemporal data. In this paper, we first propose a fuzzy spatiotemporal RDF graph model based on RDF (Resource Description Framework) that proposed by the World Wide Web Consortium (W3C) to represent data in triples (subject, predicate, object). Secondly, we analyze and classify the related heterogeneous problems of multi-source heterogeneous fuzzy spatiotemporal data, and use the fuzzy spatiotemporal RDF graph model to define the corresponding rules to solve these heterogeneous problems. In addition, based on the characteristics of RDF triples, we analyze the heterogeneous problem of multi-source heterogeneous fuzzy spatiotemporal data integration in RDF triples, and provide the integration methods FRDFG in this paper. Finally, we report our experiments results to validate our approach and show its significant superiority.

Keywords

RDF multi-source heterogeneous fuzzy spatiotemporal data data integration

1 Introduction

With the prompt development of the Internet, the data generated in each area is exponentially increased. Aiming at the problem of how to efficiently utilize massive data, researchers study the methodology of data integration [9 , 22]. There are three mature technologies for the integration of multi-source heterogeneous data, namely federated database [2], data warehouse [7] and middleware technology [20]. Federated databases [1 , 25] are an early and less difficult way to integrate heterogeneous data. A federated database is a collection of independent but cooperative unit databases, that is, data sources are independent of each other and mapped one by one through interfaces defined by data exchange. For example, Haas et al. [8] use information from various life science databases to achieve data management through federated database technology. So the biggest advantage of federated databases is that they are relatively easy to implement, but require a large number of interfaces for data interaction, which is a huge workload. The principle of data warehouse technology [12] implementation is to preprocess and convert data copies of multiple data sources, and then unify the technology in accordance with the pattern of the data warehouse and store the processed data into the data warehouse. The data warehouse is actually a subject oriented data set that has integrated and relatively stable features. The data integration of the middleware technology [6, 15] is similar to the data warehouse, but there is some difference between their architectures. In middleware technology, the data is still stored in heterogeneous data sources, and the integration system provides a virtual integrated view to handle the query functionality of the view. In the development of middleware technology, such as Yang et al. [29], who study the heterogeneous data based on mediators and wrapper machines. Using the design of the transformation algorithm, the data is converted into a unified XML format to eliminate isomerism.

In real-world applications, there is a large amount of spatiotemporal information which is often vague or ambiguous. A lot of researches on fuzzy spatiotemporal data have come out and most of the previous works focus on fuzzy spatiotemporal data modeling and querying [4 , 24]. Sözer et al. [24] use a meteorological database application in an intelligent database architecture, which combines an object-oriented database with a knowledgebase for modeling and querying spatiotemporal objects. Cheng et al. [4] propose a novel model for representing fuzzy spatiotemporal objects and their topological relations. Based on this model, they investigate how to design basic and complex fuzzy query operators so that it is possible to describe the evolution of fuzzy spatiotemporal objects over time. Ma et al. [16] extend XML Schema so that it is possible to describe fuzzy spatiotemporal data and capture the structural information in fuzzy XML document. Unfortunately, these models are weak in representing topological relations among data.

RDF (Resource Description Framework) [13], a language proposed by the World Wide Web Consortium (W3C), which is inclusive, exchangeable and easy to extend, control and integrate in data processing. Therefore, it is of great significance in data modeling of spatiotemporal data based on RDF and there are some works about it [5 , 26]. For example, stRDF is proposed in [11] which regulates the representation principle of spatiotemporal data in RDF and makes the spatiotemporal data querying more standardized. Di et al. [5] combine spatiotemporal information with RDF and present a novel representation model of spatiotemporal RDF. Unfortunately, there is no ambiguity involved in the works mentioned above. Then, a fuzzy RDF model and its algebra are formally put forward by Ma et al. [18]. It provides a solution to the expression of fuzzy information in RDF. Besides, Wang et al. [27] propose an uncertain spatiotemporal data model and define the corresponding constraint framework for the model. The research on modeling and querying isomorphism fuzzy spatiotemporal data is approaching maturity.

In fact, fuzzy spatiotemporal information is often heterogeneous and multi-source. There are some works on integrating heterogeneous data [17, 28], spatial data [3], temporal data [23], and spatiotemporal data [10]. Little attention has been paid to integration of multi-source heterogeneous fuzzy spatiotemporal data, so how to integrate and store them is expected to be solved. For this purpose, being similar to the study of isomorphism fuzzy spatiotemporal data as mentioned above, RDF is a good choice for integrating multi-source heterogeneous fuzzy spatiotemporal data. Therefore, in this paper we aim at investigating how to model and integrate multi-source heterogeneous fuzzy spatiotemporal data based on RDF.

The contributions of this paper are the following:

We define the concept of fuzzy spatiotemporal data and construct the corresponding model to represent the multi-source heterogeneous fuzzy spatiotemporal data based on RDF.

We analyze the semantic conflicts of integration and give the corresponding solutions. Then, the integration algorithms FRDFG and FSTR are put forward, which divide nodes into 4 categories for processing.

We conduct a comprehensive experiment to demonstrate the benefits of our proposed approach over previous approaches.

The remainder of this paper is organized: Section 2 devises a fuzzy spatiotemporal data model based on RDF. The integration method of fuzzy spatiotemporal data is presented in Section 3 and Section 4. Experimental evaluation is given in Section 5 and Section 6 concludes the paper.

2 Fuzzy spatiotemporal data model based on RDF

According to the characteristics of multi-source heterogeneous fuzzy spatiotemporal data, this section introduces some tuples to construct fuzzy spatiotemporal data model based on RDF.

Definition 1. (Fuzzy Spatiotemporal Data Model, FSTD). FSTD is represented by a 6-tuple (Oid, Attr, Motion, Rs, Sp, T) where

Oid: the identification of fuzzy spatiotemporal data, which describes the changing states;

Attr: the name of attribute set of fuzzy spatiotemporal data, which denotes the general properties;

Motion: it describes the next motions of fuzzy spatiotemporal data;

Rs: it describes the resource of fuzzy spatiotemporal data;

Sp: it describes the spatial information of fuzzy spatiotemporal data;

T: it describes the temporal information of fuzzy spatiotemporal data.

Definition 2. (Fuzzy Spatiotemporal RDF Graph, FSRG) Fuzzy Spatiotemporal RDF Graph is a 5-tuple FSRG = (Vet, E, Level, μ, ρ). Here

Vet is a finitude set of vertices;

E ⊂ Vi×Vj is a set of directed edges, where Vi, Vj ⊂V;

Level is the set of labels at vertices and edges;

μ: V⟶[0, 1] is a fuzzy subset of V;

ρ: E⟶[0, 1] is a fuzzy relation on fuzzy subset μ.

Definition 3. (Temporal Information of Fuzzy spatiotemporal RDF Graph, T) Temporal information of fuzzy spatiotemporal RDF graph is a 3-tuple T = (Tp, T_i, p), where

Tp is time point of the temporal information;

T_i = [t_s, t_e] is time interval for representing the temporal information, where t_s represents start time of T and t_e represents end time of T;

p Î [0,1] represents the possibility of temporal information of fuzzy spatiotemporal data.

Definition 4. (Spatial Information of Fuzzy spatiotemporal RDF Graph, Sp) Spatial information of fuzzy spatiotemporal RDF graph is a 3-tuple Sp = (la, lo, p), where la and lo denote the latitude and longitude, and p Î [0, 1] denotes the possibility of spatial information.

Definition 5. (Fuzzy Spatiotemporal RDF sub-graph, ASPO) Fuzzy Spatiotemporal RDF graph is a 5-tuple ASPO = (Vet’, E’, Level’, μ’, ρ’) where

Vet’ is a copy of a Vet which represents a finite set of vertices;

E’ is a copy of E;

Level’ is a copy of the set of vertices and edges;

μ’:Vet’⟶[0, 1] is the fuzzy subset of Vet’;

ρ’:E’⟶[0, 1] is the fuzzy relation of fuzzy subset μ’.

Example 1. In Fig. 1, it describes some information of film1. Here the genre of the film1 is “tragedy” with the possibility is 0.9, and the audience rating is 20.3. The time of film1 is (2018.08.10, [2018.07.01, 2018.09.30]), where the “2018.08.10” and “0.8” represent someone watching a movie at this time with the possibility is 0.8. The possibility of film1 that locates in city 1 ([120°E, 45°N]) is 0.7.

Fig. 1

Fuzzy spatiotemporal RDF graph.

The next two sections propose the integration method of multi-source heterogeneous fuzzy spatiotemporal data, and the flowchart is shown in Fig. 2.

Fig. 2

Flowchart of the integration method.

3 Semantic conflicts and corresponding solutions

This section summarizes semantic conflicts and corresponding solutions in multi-source heterogeneous fuzzy spatiotemporal data integration. There are 5 types of semantic conflicts, namely integration of fuzzy spatiotemporal data from the same source, Data source conflict, Nodes/labels naming conflicts, Nodes value conflicts and Fuzzy value conflicts.

Conflict 1: Supposed that two fuzzy spatiotemporal RDF sub-graphs G and G’ describe the same fuzzy spatiotemporal data from the same data source. Their states are different and other nodes and labels are similar. In short, the two RDF graphs of fuzzy spatiotemporal data contain state conflict.

Rule 1. Given a graph G (Oid, Attr, Rs, Sp, T) where G is the root based on FSRG (In Definition 2). If G’ (Oid’, Attr’, Rs’, Sp’, T’) exists and similarity between G’ and G is lower than the threshold θ _sim , then saving two root nodes G and G’ and child nodes of them remain unchanged:

If there is a node that represents the same data as G’, then G’ can be added after node G_ft (G_ft represents the last node that has the same type as G) and the member properties in G’ are preserved;

Otherwise adding G’ as the last child node of the root in existing FSRG and remaining properties of it.

Step 1: A new node motion is created and the same attribute nodes in the two fuzzy RDF sub-graphs are selected to form a triplet relationship with m otion.

Step 2: The two fuzzy spatiotemporal RDF sub-graphs are taken as the sub-graphs of the new nodes, and the other attribute nodes and the information contained in the child nodes remain unchanged.

Example 2. Here the two fuzzy spatiotemporal RDF sub-graphs shown in Fig. 3(a) and (b), which describe the same fuzzy spatiotemporal data from the same data source in different states. So we add the node motion to merge the two RDF sub-graphs. The result of integration is shown in Fig. 3(c).

Fig. 3

Fuzzy spatiotemporal RDF graph of Example 2.

Conflict 2: Supposed that two fuzzy spatiotemporal RDF sub-graphs G and G’ describe the same fuzzy spatiotemporal data from different data sources. There is a source conflict between the two fuzzy spatiotemporal RDF subgraphs.

Rule 2. Given a graph G (Oid, Attr, Rs, Sp, T) where G is the root. If G’ (Oid’, Attr’, Rs’, Sp’, T’) exists and the node similarity between G’ and G is higher than the threshold θ _sim , then we select one of the root nodes G or G’ to save and merge other nodes:

Adding the node ASPOgt (according to ASPO in Definition 5) to graph G, and the existing graph and the corresponding fuzzy values remain unchanged.

Step 1: Creating a new node and assigning the same properties in both RDF sub-graphs to it, with the labels and values remaining unchanged.

Step 2: Regarding two fuzzy spatiotemporal RDF sub-graphs as children of new nodes, where properties of other child nodes remain unchanged.

Example 3. Here the two fuzzy spatiotemporal RDF sub-graphs shown in Figs. 3(a) and 4(a), which describe the same fuzzy spatiotemporal data in different states with different data sources. We can move the nodes and labels describing the data source information to the corresponding motion nodes and convert them into motion object nodes. The result of integrating two fuzzy spatiotemporal data is shown in Fig. 4(b).

Fig. 4

Fuzzy spatiotemporal RDF graph of Example 3.

Conflict 3: Supposed that two fuzzy spatiotemporal RDF sub-graphs G and G’ describe the same fuzzy spatiotemporal data which have similar nodes and labels and the same values. However, there are partial naming conflicts between their nodes or labels.

Rule 3. Given a graph G (Oid, Attr, Rs, Sp, T) where G is the root. If gt (Oid_gt, Attr_gt, Rs_gt, Sp_gt, T_gt) exists and the similarity between gt and G is higher than the threshold θ _sim , then there is a duplicate candidate ASPO_gt (containing duplicate attribute nodes) in two graphs. We can ignore other nodes and extract the corresponding node name in ASPO_gt:

Creating a new node and assigning the same properties in the two RDF sub-graphs to it, then taking a node value of conflicting nodes as final value.

Regarding two sub-graphs as children of the new node, and other attributes of them remain unchanged.

Conflict 4: Supposed that two sub-graphs describe the same object, and their possibility degree of node name and value are equal and there are conflicting values in their properties.

Rule 4. Given a graph G (Oid, Attr, Rs, Sp, T) where G is the root. If gt (Oid_gt, Attr_gt, Rs_gt, Sp_gt, T_gt) exists and the node similarity between gt and G is higher than the threshold θ _sim , then there is a duplicate candidate ASPO_gt (containing duplicate attribute nodes) in two graphs. We ignore other nodes and extract the corresponding node value in ASPO_gt:

ASPO_gt is considered as a possible instance to describe a specific type, so we need to add the node ASPO_G. By using the data structure pattern of RDF graph G of the existing fuzzy spatiotemporal data, candidate ASPO_gt and ASPO_G of fuzzy objects are retained and corresponding fuzzy degree values in the RDF graph need to be integrated.

Determining whether the fuzzy values of node properties are equal or not. If they are equal, the property values are merged into the same node. Otherwise the problem will be discussed in Conflict 5.

Example 4. Here are the two fuzzy spatiotemporal RDF sub-graphs shown in Figs. 3(b) and 5(a), which describe the same fuzzy spatiotemporal data with different data sources and there is a value conflict of type node with the equal fuzzy degree. Then merging the values, and the value of type node is ST, STS shown in Fig. 5(b).

Fig. 5

Fuzzy spatiotemporal RDF graph of Example 4.

Conflict 5: Due to the different sources and the different calculation or statistical methods of the fuzzy sets of fuzzy spatiotemporal data, there is a conflict related to the fuzzy value. Fuzzy value conflicts occur at the node level, including inconsistent membership and inconsistent fuzzy sets.

For the two fuzzy spatiotemporal RDF sub-graphs, they describe the same fuzzy spatiotemporal data from same data resources. But there are different fuzzy degrees in similar nodes. Here it is assumed that there are no naming and attribute value conflicts because they can be solved beforehand. For example, the membership degree conflict can be solved by Zadeh’s intersection operator [30].

Rule 5. Given a graph G (Oid, Attr, Rs, Sp, T) where G is the root. If gt (Oid_gt, Attr_gt, Rs_gt, Sp_gt, T_gt) exists and the node similarity between gt and G is lower than the threshold θ _sim , then there is a duplicate candidate ASPO_gt (containing duplicate attribute nodes) in two graphs. We ignore other nodes and extract the conflicting fuzzy values σ _gt and σ _G in ASPO_gt:

If there is fuzzy value conflict of similar data nodes between fuzzy spatiotemporal RDF graph gt and G, then ASPO_gt is a duplicate of ASPO_G_. Assuming that the membership degrees of similar data nodes in ASPO_gt and ASPO_G are σ_gt and σ_G, then the fuzzy degree of ASPO_G after integrating is min( σ _gt _, σ _G ₎.

Example 5. Here the two fuzzy spatiotemporal RDF sub-graphs shown in Figs. 3(b) and 6(a), which describe the same fuzzy spatiotemporal data with different data sources. There is a fuzzy value conflict of type label between them. The solution is to add the different values up and average them and the result after integrating is 0.7 in Fig. 6(b).

Fig. 6

Fuzzy spatiotemporal RDF graph of Example 5.

In the above, the heterogeneous problem is analyzed and represented by the fuzzy RDF graph model, and the corresponding solutions are proposed. The analysis and classification process of heterogeneous conflict problems are shown in the Algorithm 1:

Algorithm 1 FRDFG
Input: foreign RDF graph gt, existing fuzzy spatiotemporal RDF graph G
Output: pre-integrated fuzzy spatiotemporal RDF graph G
01 for each foreign RDF graph f in gt
02 if (gt is identified as a “new” fuzzy RDF graph)
03 integrate gt_n into G and generate the integrated RDF graph G’ by applying
04 Rule 1
05 else if (there is resource conflict between gt and G)
06 integrate gt_n into G and generate the integrated RDF graph G’ by applying
07 Rule 2
08 else if (there is node naming conflict between gt and G)
09 integrate gt_n into G and generate the integrated RDF graph G’ by applying
10 Rule 3
11 else if (there is node value conflict between gt and G)
12 integrate gt_n into G and generate the integrated RDF graph G’ by applying
13 Rule 4
14 else if (there is fuzzy value conflict between gt and G)
15 integrate gt_n into G and generate the integrated RDF graph G’ by applying
16 Rule 5
17 end for
18 return G’

4 Integration of fuzzy spatiotemporal RDF graph

4.1 Integration of root nodes in the fuzzy spatiotemporal RDF graph

Before integration, the similarity of objects described by the RDF graph of fuzzy spatiotemporal data should be determined. Each fuzzy spatiotemporal data has a unique identifier Oid, which can be used to determine the similarity.

Rule 6. Given a graph G (Oid, Attr, Rs, Sp, T) where G is the subject node, and the properties (Oid, Attr, Rs, Sp, T) are taken as the object nodes of G. If it exists G_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺), then taking G as root to build fuzzy spatiotemporal RDF graph.

In Rule 6, the Oid_i node values in the graph are extracted, and the similarity of Oid_i nodes in two RDF graphs is calculated by formula (1): $Sim s (G 1, G 2) = {\begin{matrix} 1, if {Oid}_{i} = {Oid}_{i + 1} \\ 0, if {Oid}_{i} \neq {Oid}_{i + 1} \end{matrix}, (i = N^{+})$ (1)

In formula (1), G1 and G2 are name variables of fuzzy spatiotemporal RDF graph. If Oid_i = Oid_i +1, it means two graphs represent the same object. If Oid_i ≠ Oid_i +1, it means that the two graphs describe different objects, and a new node needs to be added to transform the two RDF graphs into one.

Rule 7. Given a graph G (Oid, Attr, Rs, Sp, T), and there are multiple G_i(Oid_i, Attr_i, Rs_i, Sp_i, T_i)(i = N⁺) in the integration process. Where G is the subject node in the RDF graph, and (Oid_i, Attr_i, Rs_i, Sp_i, T_i) is the object node of G_i. If the calculated value of the similarity of Oid_i is 0 or 1, carrying out the similarity analysis of the nodes in figure G (Oid, Attr, Rs, Sp, T).

Rule 6 and Rule 7 aim to judge whether the nodes in the fuzzy spatiotemporal RDF graph are similar, and to realize the integration processing of root nodes in the fuzzy spatiotemporal RDF graph. The implementation of is shown in Example 6.

Example 6. Fuzzy spatiotemporal RDF graphs Fig. 7(a) and (b) describes fuzzy spatiotemporal data cloud1 and cloud2, respectively. By comparing Oid of cloud1 and cloud2 through formula (1), it can be obtained: Sim s (G1, G2) = 0. Transforming these two graphs into Fig. 7(c), then the integration of root nodes describing different objects is completed.

Fig. 7

Fuzzy spatiotemporal RDF graph of Example 6.

4.2 The integration of subject nodes in fuzzy spatiotemporal RDF graphs

The fuzzy spatiotemporal objects described by RDF can be taken as subjects. However, according to the characteristics of the fuzzy spatiotemporal data changing with time, there are fuzzy spatiotemporal data describing different states in the same subject. Therefore, this section focuses on solving the problem of subject nodes with multiple states.

Case 1: Supposed there are two RDF sub-graphs C1 and C2 that describe same fuzzy spatiotemporal RDF sub-graph. (t₁, t₂) and (t₃, t₄) are time intervals of C1 and C2 respectively, where (t₁, t₂) Ç (t₃, t₄) ≠ Æ.

Rule 8. Given the fuzzy spatiotemporal RDF graph C (Oid, Attr, Rs, Sp, T), there are multiple C_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. C is the subject node in the RDF graph, and (Oid_i, Attr_i, Rs_i, Sp_i, T_i) is the object node of C_i. If the similarity of Oid_i is 1, then value of the subject node T_i in C_i is selected and the T_i node is taken as the reference of integration.

Step.1 It assumes that i = 1, 2 and the intersection of T_i node is (t₁, t₂) ∩ (t₃, t₄) ≠ Ø, where t₁ < t₂ < t₃ < t₄ or t₃ < t₄ < t₁ < t ₂. It means C_i has different states, so creating S as object node of the fuzzy spatiotemporal RDF graph C_i.

Step.2 As shown in Fig. 8, creating the new right object node of S which represent as S_i +1, S_i +2, S_ki..., where k_i represents the subject node at k_i state.

Fig. 8

Fuzzy spatiotemporal RDF graph of Example 7.

Example 7. By using the fuzzy spatiotemporal data in Fig. 7(a), Fig. 8(a) and Fig. 8(b), the Oid value calculate by formula (1) is the same, so all three RDF graphs represent the same fuzzy spatiotemporal data cloud1. If t₁ < t₂ < t₅ < t₆ < t₇ < t₈, then the result of integration as Fig. 8(c) shows.

Case 2: If it exists (t₁, t₂) ∩ (t₃, t₄) ≠ Ø where t₁ < t₃ < t₄ < t₂, then (t₁, t₂) ∩ (t₃, t₄) = (t₃, t₄) can be obtained.

Rule 9. Given the fuzzy spatiotemporal RDF graph C (Oid, Attr, Rs, Sp, T), there are multiple C_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. If the similarity of Oid_i is 1, then value of the subject node T_i in C_i is selected and S is defined as the left object node of C.

Step. 1 It assumes that i = 1, 2 and the intersection of T_i node is (t₁, t₂) ∩ (t₃, t₄) ≠ Ø, where t₁ < t₃ < t₄ < t₂, then S is taken as subject node of C₁ and C₂.

Step. 2 Creating new left sub-nodes of S which represent as S_{i +1 . j +1}, S_{i +1 . j +2},..., S_i +1 . kj where kj represents the kj state of subject node at i + 1 state in the same RDF graph, as S₁, S_1.1 shown in Fig. 9.

Fig. 9

Fuzzy spatiotemporal RDF graph of Example 8.

In Rule 9, the integration of subject nodes in the fuzzy spatiotemporal RDF graph with similarity but in different intersecting sub-states is studied.

Example 8. As shown in Figs. 7(a) and 9(a), if t₁ < t₃ < t₄ < t₂, then the two RDF graphs represent the same fuzzy spatiotemporal data cloud1 at different states. Therefore, it can be obtained that the state in Fig. 9(a) is a sub-state of Fig. 7(a). The integration result is shown in Fig. 9(b).

Case 3: If (t₁, t₂) ∩ (t₃, t₄) ≠ Ø where t₁ < t₃ < t₂ < t₄ between the two fuzzy spatiotemporal RDF graphs, then (t₁, t₂) ∩ (t₃, t₄) = (t₃, t₂) can be obtained.

Rule 10. Given the fuzzy spatiotemporal RDF graph C (Oid, Attr, Rs, Sp, T), there are multiple C_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. If S_i (i = N⁺) nodes already exists, then ignoring other nodes and taking S_i . j as the right subject node of T_i in C_i.

Step. 1 It assumes that i = 1, 2 and the intersection of T_i is (t₁, t₂) ∩ (t₃, t₄) = (t₃, t₂) , then S is created as subject node of C₁ and C₂.

Step. 2 Creating new left sub-nodes of S which represent as S_{i +1 . j +1 . l +1}, S_{i +1 . j +2 . l +2},... i + 1.j+1 represents the j + 1 state of the subject node at i + 1 state in the same fuzzy spatiotemporal RDF graph, as S₁, S_1.1, S_1.1.1... shown in Fig. 10.

Fig. 10

Fuzzy spatiotemporal RDF graph of Example 9.

According to Rule 10, FSTR is guaranteed the integrity of information integration processing different states of fuzzy spatiotemporal data.

Example 9. As shown in Fig. 7(a), Figs. 9(a) and 10(a), these three graphs describe the same fuzzy spatiotemporal data cloud1 because their Oid are the same. After integration, a new fuzzy spatiotemporal RDF Fig. 10(b) is obtained. Finally, combining the integrated Fig. 7(c), 8(c), 9(b) and 10(b), a new fuzzy spatiotemporal RDF graph is obtained as shown in Fig. 10(c).

4.3 The integration of property nodes in fuzzy spatiotemporal RDF graphs

In formula (1), the method of judging the similarity of two fuzzy RDF graphs describing the same fuzzy spatiotemporal data is proposed. Although Oid values of the same fuzzy spatiotemporal data in the above examples are the same. However, each fuzzy spatiotemporal data has a fuzzy value, which is used to describe the possible degree of fuzzy spatiotemporal data. As a result, there is conflict between subjects and corresponding properties. Therefore, this subsection proposes a method to deal with it.

Rule 11. Given a graph G (Oid, Attr, Rs, Sp, T), there are multiple G_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Then, extracting the fuzzy values in G_i with P_i (i = N⁺).

Assume that the fuzzy information in the property nodes s1 and s2 is extracted; the similarity of the property nodes is calculated with the formula (2):

$\begin{matrix} Sim sp (s 1, s 2) = 0, if Oid 1 \neq Oid 2 [] \\ Sim sp (s 1, s 2) = 1 - | P 1 - P 2 |, if Oid 1 = Oid 2 \\ Sim sp (s 1, s 2) = P 1, if Oid 1 = Oid 2, P 1 = P 2 \end{matrix}$ (2)

Rule 11 is a supplement to the integration method FSTR in the property node. In the formula (2), s1 and s2 represent property nodes, Oid1 and Oid2 are property node names, and P1 and P2 are fuzzy values.

Rule 12. Given a graph G (Oid, Attr, Rs, Sp, T), there are multiple G_i(Oid_i, Attr_i, Rs_i, Sp_i, T_i)(i = N⁺) in the integration process. After the processing of formula (2), extracting the fuzzy values in G_i with P_i (i = N⁺). This subsection analyzes the heterogeneous situation in the integration of property nodes, judges the different states of the fuzzy spatiotemporal data described in the fuzzy spatiotemporal RDF graph based on the characteristics of the fuzzy spatiotemporal data, and processes the fuzzy spatiotemporal data of different states. Rules 11 and 12 are part of the integration method FSTR, whose main function is to accomplish the integration of property nodes.

4.4 The integration of object nodes in fuzzy spatiotemporal RDF graphs

Due to the spatial characteristics and temporal characteristics of spatiotemporal data, the similarity measurement method is divided into two directions: the integration of fuzzy temporal information and the integration of fuzzy spatial information.

In Definition 3, temporal information of the fuzzy spatiotemporal RDF graph is represented by T (T_p, T_i, p). In general, p can be inferred based on the fuzziness degree and state of Tp and Ti. Therefore, it is assumed that there are fuzzy spatiotemporal RDF subgraphs F1 and F2 from different data sources, and F1 ((t₁, t₃), T_i1) and F2 ((t₂, t₄), T_i2) are fuzzy temporal information of the same fuzzy spatiotemporal data where t₁≤T_i1≤t₃, t₂≤T_i2≤t₄.

Case 4: For the object nodes O1 and O2 of fuzzy spatiotemporal RDF graphs F1 and F2, it exists Sim s (O1, O2) = 0, (t₁, t₂) ∩ (t₃, t₄) = Ø and T_i1 ≠ T_i2. There are two rules as follows:

Rule 13. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Where F is the subject node in the RDF graph, and (Oid_i, Attr_i, Rs_i, Sp_i, T_i) is the object node of F_i. According to formula (1), Oid_i in graph F_i is calculated to obtain Sim f (F_i, F_i +1) = 1. Taking different T_i in F_i as object nodes, and F_i is integrated according to Rule 8 - Rule 10.

Rule 14. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. According to formula (1), Oid_i in graph F_i is calculated to obtain Sim f (F_i, F_i +1) = 0. Ignoring the other nodes and combine multiple graphs F_i into one graph according to Rule 7.

Case 5: For the fuzzy spatiotemporal RDF graphs F1 and F2, the fuzzy temporal object node T exists: (t₁, t₂) ∩ (t₃, t₄) ≠ Ø where t₁≤t₂≤t₃≤t₄. There are three rules as follows:

Rule 15. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i, where there is t₂ = t₃ ⇔ (t₁, t₂] ∩ [t₃, t₄) = t₃. Formula (3) is used to integrate the fuzzy value of the object nodes in graph F: $Simo (O 1, O 2) = 1 - | P 1 - P 2 |$ (3)

Rule 16. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i, where there is t₃ < t₂ ⇔ (t₁, t₂] ∩ [t₃, t₄) = (t₃, t₂). Therefore, the two fuzzy time intervals T_i of F_i can be divided into three nodes with fuzzy temporal attributes, and then three valid fuzzy time intervals (t₁, t₃), [t₃, t₂), [t₂, t₄] can be obtained. Finally, the fuzzy values of the new nodes can be calculated by formula (4).

$\begin{matrix} Sim o (O 1, O 2) \\ = \frac{(Tm - Tn) (P 1 - P 2 - | P 1 - P 2 |)}{Tj - Ti} (i ⩽ n ⩽ m ⩽ j) \end{matrix}$ (4)

Rule 17. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i, where there is t₁ = t₃ and t₂ = t₄ and it can be inferred that (t₁, t₂) ∩ [t₃, t₄) = (t₁, t₂)/(t₁, t₄)/(t₃, t₂)/(t₃, t₄). Then, a fuzzy temporal object boundary node is reserved in the two fuzzy time interval T_i, and fuzzy value of the new node can be calculated by formula (5). $Sim o (O 1, O 2) = P 1$ (5)

Case 6: For the fuzzy spatiotemporal RDF graphs F1 and F2, the fuzzy temporal object node T exists: (t₁, t₂) ∩ (t₃, t₄) ≠ Ø and (t₁, t₂) ∩ (t₃, t₄) = (t₃, t₄) where t₁≤t₃≤t₄≤t₂ can be obtained. There are three rules defined as follows:

Rule 18. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i, where t₃ = t₄ and it can be inferred that (t₁, t₂] ∩ [t₃, t₄) = (t₁, t₂). Finally, the fuzzy value of T_i is calculated by formula (5).

Algorithm 2 FSTR
Input: several fuzzy spatiotemporal RDF graph G
Output: integrated fuzzy spatiotemporal RDF graph G
01 for each RDF graph G
02 if (Oid meets Rule 6)
03 if (similarity is 1 according to Rule 7)
04 integrate subject nodes (different states of fuzzy spatiotemporal data)
05 if (it satisfies Case 1) execute Rule 8
06 else if (it satisfies Case 2) execute Rule 9
07 else if (it satisfies Case 3) executeRule10
08 integrate property nodes (processing of fuzzy values)
09 execute Rule 11 and Rule 12
10 integrate object nodes (processing of temporal nodes and spatial nodes)
11 if (it satisfies Case 4) execute Rule 13 and Rule 14
12 else if (it satisfies Case 5) execute Rules 15-17
13 else if (it satisfies Case 6) execute Rules 18-20
14 else if (it satisfies Case 7) execute Rules 21-22
15 integrate according to Rule 7
16 else if (similarity is 0 according to Rule 7) integrate according to Rule 7
17 execute Algorithm 1
18 end for
19 return G

Rule 19. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i, where t₁ < t₃ < t₄ < t₂ and it can be inferred that (t₁, t₂) ∩ [t₃, t₄) = (t₃, t₄). Then, the two fuzzy time intervals T_i are divided into three valid fuzzy time intervals (t₁, t₂), (t₃, t₄), (t₄, t₂). Finally, the fuzzy value of new fuzzy temporal object node T_i can be calculated by formula (6).

$\begin{matrix} Sim o (O 1, O 2) \\ = \frac{(Tm - Tn) (P 1 - P 2)}{Tj - Ti} (i ⩽ n ⩽ m ⩽ j) \end{matrix}$ (6)

Rule 20. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in graph F_i, where there is t₁ = t₃ and t₄ = t₂ and it can be inferred that (t₁, t₂) ∩ [t₃, t₄) = (t₁, t₂)/(t₁, t₄)/(t₃, t₂)/(t₃, t₄). Then a new fuzzy temporal object node T_i is established to merge the two fuzzy time intervals, and fuzzy value of T_i can be calculated by formula (5).

In addition, this subsection studies the integration method of fuzzy spatial object nodes. In Definition 4, the fuzzy spatiotemporal RDF graph G is formed by Sp (la, lo, p). Because the spatial variation of fuzzy spatiotemporal data varies with the temporal information, the integration of the spatial information must consider the temporal information. Sp1 and Sp2 discribe spatial information of two RDF subgraphs of the same fuzzy spatiotemporal data. Therefore, the integration of fuzzy spatial information can be based on the following rules:

Case 7: When processing the integration of spatial object nodes, the corresponding fuzzy temporal information in the two fuzzy spatiotemporal RDF graphs F1 and F2 is judged and it exists (t₁, t₂) ∩ (t₃, t₄) ≠ Ø where t₁≤t₃≤t₂≤t₄. Here, the following two rules are defined to solve the problem:

Rule 21. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i where t₂ = t₃. Then the value of fuzzy spatial object node Sp_i are la = min la₁, la₂ and lo = max lo₁, lo₂.

Rule 22. Given a graph F (Oid, Attr, Rs, Sp, T), there are multiple F_i (Oid_i, Attr_i, Rs_i, Sp_i, T_i) (i = N⁺) in the integration process. Extracting the object node T_i in the graph F_i, there is t₃ < t₂ and it can be inferred that (t₁, t₂] ∩ [t₃, t₄) = (t₃, t₂). Then three valid fuzzy time intervals (t₁, t₃), [t₃, t₂), [t₂, t₄] can be obtained. Finally, the integration of Sp_i is as follows:

If la₁ ≠ la₂ or lo₁ ≠ lo₂, then the fuzzy spatial node Sp_i should store the fuzzy spatiotemporal data and corresponding fuzzy values.

If t₁ = t₃ and t₂ = t₄, which means (t₁, t₂) ∩ [t₃, t₄) = (t₁, t₂)/(t₁, t₄)/(t₃, t₂)/(t₃, t₄). Then, a new fuzzy temporal object node T is established to merge the two fuzzy time intervals. The value of the integrated fuzzy spatial object node Sp_i is: Sim o (O1, O2) = P1, la = min la₁, la₂, lo = maxlo₁, lo₂.

Cases 4–6 are the integration of fuzzy temporal object nodes and Case 7 is the integration of fuzzy spatial object nodes. Through the definition of Rules 13–22, it improves the integration method FSTR in the integration of object nodes.

The core work of this section is to study the integration method FSTR of multi-source heterogeneous fuzzy spatiotemporal data in fuzzy spatiotemporal RDF graph. The implementation process of integration method FSTR is shown in Algorithm 2. The integration operations are shown as Example 10.

Example 10. In Fig. 11, the four RDF graphs (a), (b), (c) and (d) describe the same fuzzy spatiotemporal data cloud1 whose states are different, and Fig. 11(e) depicts fuzzy spatiotemporal data cloud2. Figure 11(f) is the integration result of them. According to formula (1), the similarity of Fig. 11(a) and (e) is 0. Therefore, it can be concluded that the two graphs respectively describe cloud1 and cloud2. According to Rule 14, there is no fuzzy temporal conflict between cloud1 and cloud2 in the fuzzy spatiotemporal property values, then Fig. 11(a) and (e) are merged into Fig. 11(g) based on Rule 7. There is t₁ < t₂ < t₅ < t₆ in Fig 11(a) and (d), so the two graphs describe the same fuzzy spatiotemporal data cloud1 at different states. In addition, by comparing the fuzzy spatiotemporal property values can get that the state of Figure (d) is the next state of Figure (a) or a different state from Figure (a). There is no fuzzy temporal conflict between them, so a fuzzy spatiotemporal RDF graph with Clouds as the subject node is obtained, as shown in Fig. 11(h). Finally, merging Fig. 11(f), (g) and (h) into Fig. 11(l) by executing the Algorithm 2.

Fig. 11

Fuzzy spatiotemporal RDF graph of Example 10.

5 Experiment

5.1 Experimental setup

In this subsection, we will present evaluations on the basis of the meteorological application. All the evaluations have been implemented in eclipse4.4.1 and JDK 1.8, and performed on 3.2 GHz Intel Core i5 processor with 8 GB RAM on Windows 7 system. We implement some groups of querying experiments in Java and MYSQL.

For this assessment, a meteorological information database was established, containing 55,000 tuples from global meteorological information sites. Our test used two different data sets. The first data set is an unintegrated data set, described as a UIDB, and the second data set is an integrated data set, described as IFDB. In addition, the experiment of this paper is divided into three groups, in the two groups of experiments FSTR need to be compared with other processing method of spatiotemporal data. The method of data processing τ-SPARQL [28] and Deep integration [17] needs to be reconstructed, so two data sets should be added after pretreatment based on UIDB: one is temporal data set τ-SPARQL and the other is spatial data set Deep integration, respectively.

In this experiment, the feasibility and effectiveness of the integrated method FSTR are verified by data set query. The experimental query conditions are divided into three types, and the three types of query conditions contain no less than 12 query tuples. The setting of these query tuples should reflect the characteristics of multi-source heterogeneous fuzzy spatiotemporal data, including general attributes, temporal attributes and spatial attributes of fuzzy spatiotemporal data. In addition, as the spatial attributes of fuzzy spatiotemporal data change with time, the query conditions can be set in the form of combining the attributes of fuzzy spatiotemporal data with the temporal attributes. The query conditions are shown in Table 1.

Table 1
The query condition of users query

Groups Types Practical Query Example

G1 General query cloud[subject=’Tianjin’]

G2 cloud[subject="Tianjin"][predicat=’Sunny’]Ù

G3 Temporal query Temperature Î[8, 12]

G4 TsÎ[1226,]Ù[subject="Tianjin"]Ù[type = Sunny]

G5 TsÎ[1224]Ù[subject="shanghai"]

G6 TsÎ[1224,1226]Ù[subject="shanghai"]

G7 TsÎ[1226,1228]Ù[subject="shanghai"]

G8 TsÎ[1224,1228]Ù[subject="shanghai"]

G9 Spatial query SpÎ(39.47N,116.63E)Ù[subject="beijing"]

G10 SpÎ(38.98N,117.22E)Ù[subject="Tianjin"]

G11 SpÎ(31.05N120.84E)Ù[subject="shanghai"]

G12 SpÎ(39.85N,119.59E)Ù[subject="Qinhuangdao"]

Groups	Types	Practical Query Example
G1	General query	cloud[subject=’Tianjin’]
G2		cloud[subject="Tianjin"][predicat=’Sunny’]Ù
G3	Temporal query	Temperature Î[8, 12]
G4		TsÎ[1226,]Ù[subject="Tianjin"]Ù[type = Sunny]
G5		TsÎ[1224]Ù[subject="shanghai"]
G6		TsÎ[1224,1226]Ù[subject="shanghai"]
G7		TsÎ[1226,1228]Ù[subject="shanghai"]
G8		TsÎ[1224,1228]Ù[subject="shanghai"]
G9	Spatial query	SpÎ(39.47N,116.63E)Ù[subject="beijing"]
G10		SpÎ(38.98N,117.22E)Ù[subject="Tianjin"]
G11		SpÎ(31.05N120.84E)Ù[subject="shanghai"]
G12		SpÎ(39.85N,119.59E)Ù[subject="Qinhuangdao"]

5.2 The experimental results

5.2.1 Comparison of FSTR between data sets UIDB and IFDB

This section uses G1, G2, G3 and G4 query conditions, which are mainly focused on the general attribute query of fuzzy spatiotemporal data. The corresponding query results are obtained by using respectively on UIDB and IFDB. In Fig. 12, the Precision, Recall and F-score of the experimental results of IFDB are greater than UIDB. In Fig. 13, the Execution Time and Memory Cost values corresponding to the four query conditions -on IFDB were lower than on UIDB. Therefore, the experimental comparison in this section shows that the method of multi-source heterogeneous fuzzy spatiotemporal data integration is effective and accurate.

Fig. 12

The Precision, Recall and F-Score of the Queries in the UIBD, IFDB.

Fig. 13

Execution Time and Memory Cost of G1 - G4.

5.2.2 Comparison of FSTR and τ-SPARQL in temporal integration

Because fuzzy spatiotemporal data is different from general data, most of researches on the integration of fuzzy spatiotemporal data are focused on the temporal or spatial attributes of the fuzzy spatiotemporal data. For example, Tappolet et al. propose an integrated method τ-SPARQL to combine RDF and temporal data, which is of great significance to the research of spatiotemporal data integration. In this section, the experiment will compare the FSTR and τ-SPARQL to verify the superiority and effectiveness of FSTR proposed in this paper.

This section uses G5, G6, G7 and G8 query conditions, which are mainly focused on the temporal attribute query of fuzzy spatiotemporal data. In Fig. 14, the Precision, Recall and F-score of the experimental results of FSTR are higher than τ-SPARQL.

Fig. 14

The Precision, Recall, F-Score of the Temporal Queries in the IFDB.

In Fig. 15, the Execution Time and Memory Cost of FSTR are lower than τ-SPARQL. Therefore, the experimental comparison in this section shows that FSTR has better effectiveness and accuracy in temporal data integration than τ-SPARQL.

Fig. 15

Execution Time and Memory Cost of G5 - G8.

5.2.3 Comparison of FSTR and Deep integration in spatial integration

The experimental content in this section is mainly to compare FSTR with the spatial attribute processing method Deep Integration proposed by Brodt et al [38]. This section uses G5, G6, G7 and G8 query conditions, which are mainly focused on the spatial attribute query of fuzzy spatiotemporal data. In Fig. 16, the Precision, Recall and F-score of the experimental results of FSTR are higher than Deep integration. In Fig. 17, the Execution Time and Memory Cost of FSTR are lower than Deep integration. Therefore, the experimental comparison in this section shows that FSTR has better effectiveness and accuracy in spatial data integration than Deep integration.

Fig. 16

The Precision, Recall, F-Score of the Spatial Queries in the IFDB.

Fig. 17

Execution Time and Memory Cost of G9 - G12.

5.3 Discussion

By calculating the experimental results, the Precision, Recall and F-Score of the query results were obtained, as well as the comparison between the Execution Time and Memory Cost in the experimental process fully consistent with the expected effect of the integrated method. Finally, through the analysis of the above experimental results, the multi-source heterogeneous fuzzy spatiotemporal data integration method studied in this paper meets the purpose and achieves expected effect.

However, the research on the multi-source heterogeneous fuzzy spatiotemporal data integration method proposed in this paper has some imperfections. On the one hand, this work mainly focuses on the study of fuzzy spatiotemporal data. We only take the fuzziness into consideration, which is a kind of uncertain information. There is also some other uncertain information has been ignored, such as inconsistency, imprecision, vagueness, uncertainty, ambiguity and so on. On the other hand, there are more heterogeneous problems in the integration method of multi-source heterogeneous fuzzy spatiotemporal data that we omit. For example, more in-depth and comprehensive researches can be carried out in the aspects of system heterogeneity and pattern heterogeneity. We will solve these problems in future work.

6 Conclusion

This paper proposes an integration method of multi-source heterogeneous fuzzy spatiotemporal data. To accomplish the study of integration, a fuzzy spatiotemporal RDF model was proposed. Then an integration algorithm FRDFG is proposed, which concerns 5 types of semantic conflicts and corresponding solutions, can solve the heterogeneous problems. What’s more, we put forward the methodology of integrating subject nodes, property nodes and object nodes in RDF graphs to improve FRDFG. Finally, experimental results confirm the superiority of our approaches.

Future work mainly concentrates on the following aspects: (i) This paper mainly focus on fuzzy data, so we will take more uncertain information (e.g. inconsistency and imprecision) into consideration. (ii) Our model only deals with semantic heterogeneity, so more heterogeneous problems (e.g. system heterogeneity and pattern heterogeneity) will be considered.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (61402087), the Natural Science Foundation of Hebei Province (F2019501030), the Natural Science Foundation of Liaoning Province (2019-MS-130), the Key Project of Scientific Research Funds in Colledges and Universities of Hebei Education Department (ZD2020402), and the Fundamental Research Funds for the Central Universities (N2023019).

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