Recommendation decision-making algorithm for sharing accommodation using probabilistic hesitant fuzzy sets and bipartite network projection

With the rapid development of emerging technologies and continuous upgrade of municipal and rural tourism consumption and services, sharing accommodation has gradually gone into people’s sight. Figure 1 indicates the high growth of sharing accommodation orders in some Chinese cities. Sharing accommodation has characteristics of diversified supply subjects and service contents and socialized user experience, which can meet diverse accommodation need. At the same time, sharing accommodation can reduce the information asymmetry and transaction risk between the landlords and the tenants. It offers a better service experience to landlords [1]. Not only that the economic development of sharing accommodation plays a positive role in expanding employment and entrepreneurship channels, increasing the income of urban and rural residents, and helping rural revitalization [2]. In 2017, Airbnb created over 20,000 employment opportunities in Beijing and Shanghai. According to a survey of Airbnb’s domestic landlords, landlords can significantly improve their daily living standards by house sharing income. More than that, Airbnb participates in the innovative tourism targeted poverty alleviation project, explores new models for rural housing poverty relief, and helps rural poor families get rid of poverty. Sharing accommodation has made great contributions to social development.

The report on development of China’s sharing accommodation shows that the market scale of sharing accommodation industry will maintain a growth rate of 50% in the next 3 years, as well as the number of online housing resource will get an increase [1]. In such a trend, it is more difficult to obtain the required housing resource information by users themselves. This situation is bad for the development of sharing accommodation. Therefore, it is worth thinking about how to response to this trend and provide accurate accommodation information for users.

Recommender systems are used as decision support systems to overcome information overload in online environments [3]. Collaborative filtering (CF) [4] recommender system is one of the most popular types of recommender systems [5]. It is mainly used as information retrieval system based on past users’ activities and ratings on the items. Content-based recommendation is the continuation and development of CF recommendation. It does not rely on users’ historical activities and ratings on the items, but calculates the similarity degree between users based on product content information [6]. Besides, according to online review information, scholars have put forward some recommendation systems based on users’ historical information [7, 8]. By extracting the online review information, the text information needs to be transformed into computable data, and it will inevitably lead to the loss of information. Therefore, it is necessary to propose a new recommendation method to solve the existed problems.

Without considering the content characteristics of users and products, the network-based recommendation algorithm directly regards them as abstract nodes. Owing to the relatively clear data structure, bipartite networks have attracted widespread attention. They have been successively applied to cluster analysis [9‐11], pattern recognition [12‐14], recommender systems [15‐18], and other fields. Zhou et al. presented a bipartite network algorithm based on resource-allocation dynamics [19]. The similarity degree among homogeneous nodes is utilized to implement personal recommendation for users. Subsequently, Liu et al. analyzed the similarities and differences between weighted and unweighted bipartite graph networks by combining collaborative filtering with network reasoning [20]. It is concluded that recommendation accuracy of the weighted bipartite graph network is higher than that of the unweighted one under the same amount of calculations. The attendant problem is how to determine the weights of adjacent edge for improving algorithm accuracy. Wang et al. introduced a half cumulative distribution method to normalize the weights of adjacent edges, and mapped the original scores to the probability of users’ preference [21]. Pan et al. defined the weights of edges based on the distribution of degree between user and object [22]. Then, they applied the weights of edges in the quality diffusion to improve the accuracy of recommendation algorithm. Li et al. used monotonic saturation function to calculate the weights of edges [23]. An approach to calculate the weights which is based on balance factor was proposed by Song et al. [24]. In the existed methods, the connection degree and the distribution of two kinds of nodes are two commonly used tools to calculate the weights of adjacent edges, which are based on users’ ratings or historical usage. As the amount of information increases, users are accustomed to utilize key words or attributes to filter information and services. Besides, when we determine the recommended content based on the users’ historical data, it will not only focus on the direct evaluation on object, but also analyze the root cause of users’ choices, because users pay attention to the characteristics of the content, which is one of the research contents in this paper.

Users often passively accept recommendations rather than making their own decisions; that is to say, the information service platform recommends information or services to users depending on their historical data. In some cases, decision-makers are not always able to obtain “certain information” when evaluating alternatives because of the diversification of users’ demands. How to depict the evaluation information more reasonably is another urgent problem. To describe the uncertainty, Zadeh proposed the concept of fuzzy sets [25, 26]. With the continuous process of human practice and increasingly complicated decision-making environment, some extended forms of fuzzy sets have been proposed to model uncertainty, such as the interval-valued fuzzy sets [27], the intuitionistic fuzzy sets [28‐30], the type-2 fuzzy sets [31, 32], the fuzzy multi-sets [33], the Pythagorean fuzzy sets [34, 35], the hesitant fuzzy sets (HFSs) [36, 37], the dual hesitant fuzzy soft sets [38], the probabilistic hesitant fuzzy sets [39], and so on. Since the hesitant fuzzy set was proposed, it has been widely applied in many fields, such as decision-making [40‐43], emergency management [44, 45], online reviews [46], supply chain management [47], and so on. When defining the membership of an element, the difficulty of establishing the membership degree is not because we have a margin of error [as in intuitionistic fuzzy sets (IFSs)], but because we have a set of possible values [36]. For example, a decision organization that contains ten experts is authorized to assess the degree that an alternative should satisfy an attribute. Some of them think that 0.9 is most appropriate and the rest insist that it is 0.5, and these two different groups of experts cannot persuade each other. It is noted that the HFE {0.5, 0.9} can describe the above situation more objectively than the fuzzy number 0.5 (or 0.9) or the interval-value fuzzy set [0.5, 0.9]. Therefore, HFSs can express the decision-makers’ judgments more informative and reliable in this case. Probabilistic hesitant fuzzy set (PHFS), as an extension of HFS, not only contains different membership degrees, but also gives the occurrence probabilities associated with membership degrees, which reserves more original information than HFSs. Therefore, it can fully describe the uncertainty of decision-making information, which has attracted more and more scholars’ attention. Zhou and Xu defined the basic operation of PHFSs [48]. Furthermore, the operation rules and aggregation operators of PHFSs are defined by Zhang et al. [49]. Subsequently, it was applied to various fields such as decision-making [50, 51], supply chain management [52], project investment [53], and so on. Due to the uncertainty of users’ recommendation content, PHFS which can be thought as an effective tool for modeling the uncertainty is utilized to present the evaluation information in this paper. Considering those advantages of PHFS, we introduce it into the bipartite network projection, and establish a novel bipartite graph network which integrates users’ decision information and experts’ evaluation information simultaneously.

In addition, the satisfaction degree of PHFE is proposed, and the weights of adjacent edges are determined in this paper. We combine bipartite network with PHFS to address complex decision-making problems in recommendation system. The main contributions and innovation of this paper are mainly reflected in the following aspects:

The remaining sections of this paper are organized as follows. Some basic concepts related to PHFS and bipartite network projection are introduced in Sect. 1. In Sect. 2, we establish a bipartite graph connecting users and alternatives. Then, the satisfaction degree of probabilistic hesitant fuzzy element is defined. In Sect. 3, an illustrative example of recommending a hotel for Airbnb user is used to explain the feasibility and effectiveness of the proposed method. And conclusions are drawn in Sect. 4.

Some basic concepts related to PHFS and the preliminaries used throughout this paper are introduced in this section.

Airbnb is one of the leading rental communities, where users can post or search vacation rental information and complete online booking programs via its web or mobile apps. It is convenient to obtain house information on Airbnb mobile application. Then, an eligible list will be shown for users on the website after inputting destination, dates, guests’ number, etc. It can be further set property prices, community facilities, and other search results for secondary screening. By clicking on a link in the message, user could obtain more detailed information, including description, photos, and reviews of previous guests. The search page of Airbnb mobile software is shown in Fig. 4.

In 2015, Airbnb settled in China. Due to the fierce competition in the Chinese market, it did not get the expected growth in time. To get a breakthrough in the Chinese market, Airbnb needs to carry out adequate public relations activities and adopts precise market positioning and marketing strategies [55]. According to the report released by Airbnb in 2019 [56], the disposable income of residents has been continuously increasing in recent years and the consumption structure of residents has been gradually optimized. Moreover, the consumption of education and entertainment continues to grow. In recent years, tourism market presents sound and rapid development momentum, with 4.0 domestic per capita trips and 10.7 outbound trips per 100 people. With comprehensive penetration of the Internet, people’s lifestyle and consumption habits are constantly changing. At the same time, the tourism market is increasingly delivered over the Internet.

The millennials (who were born in 1982–2000) constitute nearly 80% of online travelers, and become the main force of tourism market. They pursue a high-quality and fashion lifestyle, but also explore the unknowns without neglecting to interact with family members. Nearly half of millennials have a higher expense on accommodation than before. In addition, the pursuit of comfortable sleep and the general relaxation environment like home and a colorful accommodation experience will greatly enhance travel happiness. With the development of the sharing economy and the popularity of sharing accommodation, the specialty home stays and the short-term rentals are ever more popular among millennial travelers. However, it is hard to obtain an accurate house information in travel. Hence, we propose a method to recommend accommodation for Airbnb users in this paper.

A handful of studies on tourists’ motivations for choosing Airbnb have been investigated. Quinby and Gasdia found that home amenities and space were the two main motivations for users to choose sharing accommodation [57]. Several studies show that price (or economic benefits) has been recognized sometimes as the most important factor [57‐59]. Nowak et al. considered location to be the second most important factor [59]. Besides, some scholars analyzed the user’s intention of using Airbnb [60‐62]. According to the above literatures and attributes collected from Airbnb community (https://​www.​airbnb.​cn), factors influencing user’s decision are shown in Table 1.

Five different houses near Nanjing Confucius Temple are to be evaluated (as shown in Table 2). Four users who have stayed at the five houses are randomly selected. According to their habits of booking rooms at Airbnb and taking those houses as an example, we illustrate how to select a recommendation alternative using the proposed method in this paper.

Step 1. According to requirements of users, the absolute frequency matrix is shown in Table 3.

The corresponding requirement relative frequency matrix is shown in Table 4.

The alternative is evaluated by experts based on the required attributes of users (https://​share.​weiyun.​com/​5J3KcW8), and the corresponding probabilistic hesitant fuzzy evaluation matrix is obtained which is shown in Table 5.

Step 2. Calculate the satisfaction degree of PHFE according to Eq. (14), and they are shown in Table 6.

Step 3. We establish bipartite network between users and alternatives based on PHFEs. Users’ requirements for attributes and the satisfaction degree of PHFEs are considered simultaneously. Specific steps of recommendation method are as follows:

First, determine the set of adjacent edges according to Eq. (18):

Then, calculate the weight of adjacent edge according to Eq. (19) as shown in Table 7.

Step 4. In the established bipartite graph network, the recommended user \( U_{ 3} \) was filled with gray. If the alternatives have been connected with user \( U_{ 3} \), its initial resource would be assigned a unit resource, otherwise zero. As shown in Fig. 5a, initial resource of alternative \( A_{3} \) is 1, and initial resource of the other alternatives is 0. First, the resource flows from alternative to user, and the resource allocation is shown in Fig. 5b. Then, resource flows back to alternative, and the resource allocation is shown in Fig. 5c.

It is easy to see from Fig. 5 that \( g\left( {U_{h} } \right) = g\left( {U_{4} } \right) \) and \( F\left( {A_{o} } \right) = f^{\prime}(A_{2} ) \).

Step 5. Finally, it is prior to recommend alternative \( A_{2} \) for user \( U_{ 3} \). Because user \( U_{ 3} \) is similar to user \( U_{ 4} \) and user \( U_{ 4} \) gives a high evaluation for alternative \( A_{2} \).

Step 6. End.

Based on users’ decision-making information and experts’ evaluation information, a bipartite network between users and alternatives is established in this paper. And a probabilistic hesitant fuzzy recommendation decision-making method based on bipartite network projection is proposed. The proposed method is utilized to recommend accommodation for Airbnb users in this paper. It is worth mentioning that the satisfaction degree of PHFE is applied to calculate the edge weight of bipartite network. And the priority recommendation of alternative is determined by the resource allocation. We consider the uncertainties of recommendation decision-making information and catch the root cause of users’ choice. Thus, a more reasonable recommendation result could be obtained by our method.

In future research, we will continue to focus on bipartite network projection, and expand the application fields of the proposed method, such as online book recommendation, gourmet recommendation, and so on. In addition, we will extend the proposed method to accommodate probabilistic dual hesitant fuzzy or probabilistic linguistic environments, and apply the proposed method to pattern recognition and online reviews.