Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information
Graphical abstract
Introduction
With the explosive development of the internet and information, it is very common to select an optimal alternative from some available alternatives with respect to a set of attributes, based on the mass related evaluation information [1]. For example, according to physiological and economic condition, a respiratory system disease patient should choose an appropriate hospital for his/her rehabilitation with referring to the advises from doctors and the evaluation information from some other patients [2]. Recommender system (RS), which exploits the past behaviors and the user similarities to provide the personalized recommendations, is a good tool to deal with selection problems. Some authors paid attention to the missing rating prediction for particular users on unknown items [3]. Some other studies focused on developing the measures [4] and recommender methods [5] to improve the recommendation precision. A few of practical applications of RSs with linguistic information can be seen in some papers such as Refs. [5], [6].
As for the preference information related to RS, people usually express them by linguistic terms such as “fine” or “slightly good” to evaluate an object. But it is indeed a challenge to accurately simulate the evaluators’ opinions, especially in group decision situations, due to the different evaluators’ knowledge backgrounds and the information extraction methods [7]. The hesitant fuzzy linguistic term set (HFLTS) was proposed [8] and developed [9], [10], [11] to improve the flexibility of linguistic preference information within hesitant situations. Probabilistic linguistic term set (PLTS) is an extended expression of HFLTS by adding probability parameter to prevent the loss of original linguistic information [12]. The PLTS is a good tool to represent the evaluator’s hesitancy, but it is still not precisely enough to express the evaluator’s all preference information between these hesitant options as the evaluator may be hesitant not only in the linguistic terms but also in the preference variability corresponding to each term. When such information is used in a group decision making situation, its non-precise degree is magnified by the number of evaluators. Therefore, the PLTSs with the change degree of each linguistic term should be much more applicable than the HFLTSs.
Due to the advantage and convenience of linguistic information in describing the preferences of experts, the linguistic RS has been investigated from different points of view such as the methods of capturing the uncertainty of user’s preferences [13], [14] and detecting the noise by measures [15]. Herreara et al. [16] investigated a fuzzy linguistic RS through the preference relation method on the basis of linguistic hierarchy and similarity measure. After this, a new fuzzy linguistic RS to characterize the users’ profiles was presented and applied into the university digital libraries [17], [18].
In our opinion, the utilization of linguistic terms can be improved if we consider the sensitivity change parameter, which can ameliorate the effect of linguistic RS. The sensitivity change should be considered because it is different from person to person. Suppose that and are two evaluators required to make evaluations on an object together. They both give the linguistic evaluation . But is subtler compared to , which is implied in the expressions that expresses his/her opinion by using a LES with nine terms but expresses his/her opinion through a five terms LES. So, the semantics of for and respectively are different even though they give the same linguistic descriptor . In other words, only using cannot describe the evaluators’ opinions comprehensively and accurately enough when different LESs are used by a group of experts to deal with a MAGDM. The purpose of this paper is to depict the sensitivity change.
Compared with the existing linguistic approaches for dealing with the MAGDM problems, the innovations and contributions of this paper are summarized as follows:
- (1)
We firstly propose a vector formula of probabilistic hesitant fuzzy LETs, called PLVTSs, which considers not only the score but also the change degree of each LET. It allows the experts to use their own LET sets to express personal opinions flexibly according to their knowledge. We will define the PLVTS as a new tool to express the expert’s preferences in a multi-attribute group decision making problem in Section 3.
- (2)
The operations and the operators are the necessary techniques to apply the PLVTSs in a multi-attribute group decision making problem. Then we will define some related concepts and operators for PLVTS after giving the definition of PLVTS in Section 3.
- (3)
We put forward an algorithm to deal with the MAGDM problem. In this algorithm, we construct a value function with some parameters, which can consider both the weight vectors of recommenders and the user’s selection weights. This is the specific method to obtain a ranking of all alternatives in a multi-attribute group decision making problem, based on the concept of PLVTS and the related operators. We will interpret the algorithm in Section 4.
The remainder of the paper is arranged as follows: Section 2 briefly reviews some preliminary knowledge of linguistic scales and PLTS. Section 3 defines the concept of PLVT and gives several basic operations to carry out the computing over multi-granular uncertain linguistic information. Section 4 presents an algorithm to accomplish the process of group evaluation and selection. Additionally, an illustrative example about visiting hospital selection in a personalized recommendation system with linguistic evaluation information is introduced in Section 5. We compare the novel expression of multi-granular linguistic information with the traditional method in this section as well. Finally, Section 6 makes a summary and outlook of the paper.
Section snippets
Preliminaries
The linguistic variables [19], [20] have been widely explored from distinct aspects such as linguistic computations [21] and properties [22], [23]. This section briefly reviews the related LESs and the concept of probabilistic linguistic term set (PLTS).
Probabilistic linguistic vector-term set (PLVTS)
In this section, we propose the concept of PLVTS, and then investigate some basic operations of PLVTs.
Approach to MAGDM with PLVTSs
In this section, we first describe the MAGDM problem with probabilistic linguistic information, then present an algorithm for conducting the ranking-oriented recommender system.
Application in personal hospital selection-recommender system
In recent decades, climatic deterioration and the multiple phenomenon of respiratory diseases make people pay attention to the relation between them. The associations between socioeconomic, environment and health provide a research topic that has a bearing on a long-term development. High morbidity and wide prevalence in respiratory diseases lead to more people going to the hospital for medical treatment. Therefore, the management, configuration and application of medical resources are more
Conclusions
The PLVTS proposed in this paper is helpful to deal with multi-granular multi-attribute group decision making problems with uncertain linguistic information. In this paper, we have first introduced the concept of PLVTS and given their basic operations. This expression improves the accuracy of multi-granular linguistic information in the MAGDM problems. Then an algorithm has been developed to aid MAGDM with multiple LESs. The advantage of this approach is that the influence factors considered
Acknowledgements
The authors thank the Associate Editor and the anonymous reviewers for their helpful comments and suggestions, which have led to an improved version of this paper. The work was supported by the National Natural Science Foundation of China (Nos. 61273209, 71571123, 71532007), and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).
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