Two-sided matching decision making with multi-granular hesitant fuzzy linguistic term sets and incomplete criteria weight information
Introduction
In our daily life, it is common that people will be involved in decision making problems which aim to find an appropriate matching between two sets of objects, such as marriage matching (Boudreau & Knoblauch, 2016), colleges admissions (Roth, 1985), person–job matching (Golec & Kahya, 2007) and knowledge service matching (Chang et al., 2019, Chen et al., 2016), to name but a few. This type of decision making problems is called two-sided matching decision making (TSMDM), which was initially studied by Gale and Shapley (Gale & Shapley, 1962) to deal with college admissions and stable marriage matching problems. Due to extensive applications, TSMDM problems has received more and more attention from scholars.
Followed by Gale and Shapley’s pioneer work, a lot of work has been conducted to study the existence and resolution algorithm of stable matching (Irving et al., 2008, Nguyen and Vohra, 2019), TSMDM problems with different preference structures (Delorme et al., 2019, Fan et al., 2018, Zhang et al., 2019, Zhang et al., 2020b), and the application of TSMDM models (Jiang et al., 2019, Li et al., 2019, Liu et al., 2018). In these studies, it is usually assumed that matching objects on one side will directly provide preferences/assessments over matching objects on the other side from a global perspective. However, for practical TSMDM problems, it is possible that matching objects will consider different aspects and provide multi-criteria assessments about matching objects on the other side (Chen et al., 2016, Liu and Li, 2017, Yin and Li, 2018, Yu and Xu, 2020). For instance, in a person–job matching problem, the candidates may provide their assessments about job positions by considering some criteria, such as developing space, working environment and salary level, while the employers may also provide their assessments over the candidates by considering their work experience, language and computer skills. Therefore, how to determine an appropriate matching for these multi-criteria TSMDM problems becomes a hot topic in the studies of TSMDM.
In the literature, there are some studies about multi-criteria TSMDM problems. For instance, Jiang et al. (2016) developed a multi-objective nonlinear model to deal with one-shot multi-attribute exchange problems for electronic brokerages and designed a meta-heuristic algorithm to solve the model. Chen et al. (2016) studied knowledge service matching problems in which linguistic assessments are provided by matching objects and proposed a TSMDM approach based on axiomatic design. Liang et al. (2019) studied multi-criteria TSMDM problems in which q-Rung orthopair fuzzy information is provided by matching objects and developed a Choquet integral aggregation operator-based two-sided matching model. Miao et al. (2019) proposed a TSMDM approach to match overseas demanders and domestic suppliers for B2B export cross-border e-commerce by considering the satisfaction of different stakeholder. Lin et al. (2019) developed an approach to deal with multi-attribute TSMDM problems with 2-tuple linguistic multi-attribute preference information. Chen et al. (2019) proposed a two-stage method to determine the matching between patients and healthcare service providers based on knowledge rules and the OWA-NSGA-II algorithm.
Although these approaches are effective to deal with practical multi-criteria TSMDM problems, there are still some research gaps.
First, due to the imprecise knowledge of matching objects, it is natural that matching objects will provide linguistic assessments over matching objects on the other side (Rodríguez & Martínez, 2013). Different linguistic approaches have been proposed to deal with such situations, for instance, the linguistic 2-tuple model (Herrera & Martínez, 2000), granular computing approaches (Cabrerizo et al., 2020) and linguistic approach based on discrete fuzzy numbers (Massanet et al., 2014). However, in most of existing studies, it is usually assumed that a single linguistic term is provided. For TSMDM problems with high uncertainty, matching objects may hesitate among some linguistic terms and provide linguistic assessments like “between good and very good”. In this case, the hesitant fuzzy linguistic term sets (HFLTSs) proposed by Rodríguez et al. (2012) can be an alternative tool for matching objects to provide assessments. Moreover, due to the difference of culture and knowledge backgrounds, matching objects may use linguistic term sets with different granularities to elicit his/her HFLTSs (Morente-Molinera et al., 2015, Yu et al., 2020, Zhang et al., 2020c). For instance, for a person–job matching problem, one candidate may provide his/her satisfaction degrees over job positions using a linguistic term set , while another candidate may provide HFLTSs using a linguistic term set . As a result, it is necessary to consider multi-granular HFLTSs in multi-criteria TSMDM problems. However, to the best knowledge of the authors, such TSMDM problems have not been considered in the literature.
Second, the criteria weight vector which reflects the importance of criteria used by matching objects plays an important role for multi-criteria TSMDM problems. For some TSMDM problems, matching objects may have limited knowledge about the importance of criteria and thus provide incomplete criteria weight information (Liu et al., 2019, Zhang and Guo, 2012). For instance, a candidate may provide weight information like “developing space is more important than working environment” for a person–job matching problem. How to model heterogeneous decision making contexts where we have weights associated with criteria becomes a challenge for practical TSMDM problems (Cabrerizo et al., 2013). However, it seems that this problem has not been fully discussed in existing studies about multi-criteria TSMDM problems. Therefore, how to determine criteria weight vectors for matching objects in multi-criteria TSMDM problems with multi-granular HFLTSs becomes another research gap.
Finally, stability is an important property for TSMDM problems (Fan et al., 2018, Zhang et al., 2019), since unstable matchings will make matching objects give up current matching and try to match with others. In existing studies about TSMDM problems with linguistic information, the stable matching condition has also not been considered extensively.
In order to fill these research gaps, the aim of this paper is to propose a comprehensive approach to deal with TSMDM problems with multi-granular HFLTSs and incomplete criteria weight information by considering the stable matching condition. The main contributions of the paper are as follows. First, we provide some further results about the aggregation of HFLTSs and the unification of multi-granular linguistic distribution assessments (the aggregation results of HFLTSs), which will lay a good foundation for the proposed TSMDM approach. Second, based on the distance measure of HFLTSs, we propose some optimization models to determine criteria weight vectors for TSMDM problems with multi-granular HFLTSs. Finally, based on these results, an optimization model which takes the maximization of matching objects’ satisfaction degrees and the stable matching condition into account is developed to determine the matching between matching objects.
The rest of this paper is organized as follows. In Section 2, we provide some preliminaries about TSMDM and linguistic decision making. Section 3 presents the procedure of the stable TSMDM approach with multi-granular HFLTSs and incomplete criteria weight information. A numerical example is provided to illustrate the proposed approach in Section 4. Furthermore, we discuss the characteristics of the proposed TSMDM approach in Section 5. Finally, we conclude this paper in Section 6.
Section snippets
Preliminaries
In this section, some basic knowledge about stable two-sided matching is firstly revised, and then we introduce some related studies about HLFTSs and linguistic distribution assessments (LDAs). Finally, we discuss the aggregation of HLFTSs and the unification of multi-granular LDAs.
The proposed TSMDM approach
In this section, we first give the formulation of the TSMDM problem with multi-granular HFLTSs and then develop an approach to determine the optimal matching of matching objects. For convenience, let , and .
An illustrative example
In this section, an example for the matching of green building technology supply and demand (adapted from Yin and Li (2018)) is provided to demonstrate the proposed approach.
E Technical Service Center (E Center for short) is a nonprofit-driven broker which aims to promote effective matching between suppliers and users in Northeast China. Recently, E center received some matching requests of green roof technology from four building enterprises (denoted by ) and five academic
Comparisons and discussions
In this section, we discuss the characteristics of the proposed TSMDM approach through comparison with existing studies.
First, through the literature review, one can find that there are two types of TSMDM problems, including TSMDM problems with different preference structures and multi-criteria TSMDM problems. For TSMDM problems with different preference structures, matching objects need to provide his/her preference information over matching objects on the other side from a global perspective,
Conclusions
In this paper, an approach to TSMDM with multi-granular HFLTSs and incomplete criteria weight information is developed. By using the distance measures of HFLTSs, the maximizing deviation method is extended to determine criteria weight vectors for matching objects. To obtain matching objects’ satisfaction degrees about matching objects on the other side, multi-granular HFLTSs are aggregated and transformed into LDAs defined on a unified linguistic term set. Based on the satisfaction degree
CRediT authorship contribution statement
Zhen Zhang: Conceptualization, Methodology, Funding acquisition, Supervision, Formal analysis, Writing - original draft, Writing - review & editing. Junliang Gao: Formal analysis, Writing - original draft, Writing - review & editing. Yuan Gao: Formal analysis, Writing - review & editing. Wenyu Yu: Methodology, Formal analysis, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank the Editor-in-Chief and the anonymous referees for their insightful and constructive comments that have led to an improved version of this paper. This work was partly supported by the National Natural Science Foundation of China (NSFC) under Grant 71501023, Grant 71971039 and Grant 71771034, the Fund for Creative Research Groups of China under Grant 71421001, the Key Program of the NSFC, PR China under Grant 71731003, the Scientific and Technological Innovation
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