A probabilistic linguistic evaluation-based multi-stage medical scheme selection process related to referral system

https://doi.org/10.1016/j.eswa.2020.114523Get rights and content

Highlights

  • A transformation function to keep the symmetry of preferences.

  • Consider individual problems and portray the mutual measures among information.

  • Log-normal distribution-based increase model and TOPSIS-entropy-based programming model.

  • Comparison analyses and simulation experiment.

Abstract

This paper provides a multi-stage medical scheme selection process to obtain the suitable scheme in the referral system. Firstly, considering the uncertainty of the experts and physicians, the preference relations (PRs) under the probabilistic linguistic term environment are introduced to the system. Then, this paper checks the consistency of the PRs and selects out the inconsistent PRs. For the inconsistent one, this paper provides alternative evaluations by repairing the most inconsistent element. Then, let experts choose from the alternative evaluation set. Next, by introducing the Bonferroni mean (BM) operator and Choquet integral, this paper integrates the historical data and the evaluations with stage weights to obtain the comprehensive assessment. The weights are calculated by the provided discrete and continuous stage weight functions or the programming model. Finally, the medical scheme selection process for the lung cancer and its simulation experiment are investigated to demonstrate the effectiveness and application of provided methods. The simulation experiments on sensitivity analysis and comparative analysis with existing methods are also conducted to validate the provided method.

Introduction

With the development of information technology, some new types of technologies such as big data (Badiezadeh, Saen, & Samavati, 2018) and cloud computing (Saren & Remes, 2019) have been gradually applied to medical and health fields and promoted the development of “Internet + medical” (Papanagnou & Matthews-Amune, 2018). The intelligent technologies can effectively address the shortage of medical resources and improve the sharing of public resources. They also provide the convenience for physicians and patients (Hui et al., 2020).

However, with the increase of human being demands, there still exists a serious shortage of sources, especially, the relatively low medical level and backward health facilities in rural areas. The current situation not only affects the revitalization of rural areas, but also results inadequate treatment of patients (since 40% of population in China is in rural areas). The applications and developments of the advanced internet technologies contribute to alleviate the problems. Thus, the further development of the medical technology plays a key role in the future.

When the patient suffering from a disease has received a treatment or has exacerbation, he/she needs to be transferred into another hospital because of the limited medical equipment and limited work experience of physician. The related physician who specialize and master in the related field, usually come from different hospitals located in different cities or countries. However, the patients usually do not know which physician is the right choice. Then, the intelligent referral system is helpful (this system is only suitable for those patients who only need follow-up treatment, disease monitoring, rehabilitation guidance, nursing and other services) (Macklin et al., 2019). It contains all information of physicians, including the specializations, historical data (for example, the re-hospitalization rate for previous treated patients), geographic locations, etc.

This paper conducts some novel methods related to the process after the referral system receiving and distributing a patient the related physicians. The aim of this paper is to improve the accuracy of patients locating physicians. The processes can be descripted as following two aspects: (a) Physicians provide medical schemes and upload them to the system. The system distributes them to peer experts for evaluation. The evaluation contains two parts, i.e., the preference relations (PRs) by pairwise comparison between alternative schemes and therapeutic effects of schemes; (b) Integrating evaluations and historical data of physicians, the system offers the best scheme.

As far as we known, each physician equips with individual work experience and cognitive level, and they incline to express the evaluation with linguistic information, such as good and verygood (Guo et al., 2017, Li et al., 2020, Xu, 2012, Zadeh, 1975). In order to portray these characteristics and reduce influences of work environments on decision-making results, this paper introduces the associated probabilistic information (Zhang, Dong, & Xu, 2014). In the view of the uncertainty, Pang, Wang, and Xu (2016) firstly provided the concept of the probabilistic linguistic term sets (PLTSs). As a useful tool in the field of decision-making management, it not only represents above characteristics, but also visualizes irresolute evaluations with probability distributions and keeps complete original evaluations. Thus, evaluations and corresponding data presented in this paper are in the form of PLTSs. In addition, (1) For (a) (provided in last paragraph), illogic PRs will result in irrational results, we have to check their consistencies and logics (Herrera-Viedma et al., 2004, Li et al., 2019); (2) For (b), some major diseases (such as, lung cancer and breast cancer) have multiple stages, i.e., earlier stage and later stage. The data of each stage will have different influence degrees on final decision-making results. Thus, we need to obtain the weight of each stage; (3) Integrating all data into comprehension is also a vital procedure (Wei, Zhao, & Tang, 2014).

Furthermore, existing literature has substantial works involved to the check and modification of PRs (Dong et al., 2019, Dong et al., 2013, Gao et al., 2019, Xie et al., 2018, Zhang et al., 2016), integrated operators (Bai et al., 2017, Bonferroni, 1950, Gou and Xu, 2016, Liang et al., 2018, Pang et al., 2016, Wu et al., 2018, Xia et al., 2013) and stage/time weights (Mao et al., 2014, Sun and Xu, 2016, Xu and Yager, 2008, Yager, 1988). However, there are still some deficiencies that need to be improved:

  • i.

    For the check and modification of PRs in the forms of PLTSs, Zhang et al. (2016) firstly provided the concept of probabilistic linguistic preference relations (PLPRs), consistency index, acceptably consistent PLPRs and unacceptably consistent PLPRs. An intelligent algorithm was used to modify unacceptably consistent PLPRs. Then, to avoid that the calculated linguistic terms may be beyond the range of linguistic term sets (LTSs), multiplicatively consistent PLPRs (Gao et al., 2019) were developed. The new consistency index and goal programming model-based consistency reaching process were constructed by introducing priority weights (Tanino, 1984), positive and negative deviations. Besides, the Analytic Hierarchy Process (AHP) (Saaty, 1977) was introduced into the reaching process (Xie et al., 2018), and the construction of index criteria improved the effectiveness of process. Nevertheless, they run the procedure based on scores of PLTSs, which violates the original feature: PRs should be symmetric. In addition, after these processes, the PRs were normalized into the type of precise values, and then these values were as inputs of next procedures. Thus, we cannot figure out which original element is discordant.

  • ii.

    Since the concept of PLTSs proposed by Pang et al. (2016), the operation and aggregation among PLTSs has been a hot topic. After that, Gou and Xu (2016) introduced the transformation function to the hesitant fuzzy and probabilistic linguistic term environment and presented some basic operation laws. However, he did not present corresponding operators. If we extend the laws to obtain operators, the number of elements in PLTSs will grow in multiples. Then, more effective operations were provided (Wu et al., 2018), which reduced the load of calculation. Considering the interrelationship, the geometric Bonferroni mean (BM) (Bonferroni, 1950, Xia et al., 2013) was introduced into operations, and probabilistic linguistic geometric Bonferroni mean (PLGBM) operator and weighted probabilistic linguistic geometric Bonferroni mean (WPLGBM) operator were provided (Liang et al., 2018). Whereas, they neglected the dependency and non-additivity among information.

  • iii.

    Previous studies introduced kinds of methods to determine stage weights (Mao et al., 2014, Sun and Xu, 2016, Xu and Yager, 2008, Yager, 1988) including BUM function, normal distribution-based method, exponential distribution-based method, average age method, the exponential decay model, the logarithm increase model, etc. However, they all need to be improved to avoid following disadvantages: (1) they are only based on the sequence information. For example, for T=t1,t2,t3,t4,t=1,5,10,20,21 (t is the final decision-making time, i.e., 21st year or month), they take the sequence of 1,2,3,4 into account; (2) the weights are determined based on the same time span; (3) the given weight functions are monotonous. In fact, the weight characteristics for individual problems are diverse.

Therefore, this paper proposes a series of novel methods and achieves the promotion of the referral system. The contributions of this paper can be summarized as follows:

  • i.

    This paper proposes a new transformation function to keep the symmetry of PRs. Then, the consistency check and modification process are presented, i.e., dividing original PRs to obtain the divided matrices with maximal consistencies by constructing the programming model; introducing a threshold to select the inconsistent divided matrix; selecting the discordant element and presenting the modified alternative elements. The final forms of PRs are still PLPRs

  • ii.

    We take BM operator (Bonferroni, 1950) into account and portray the mutual measures among information by introducing Choquet integral (Verma & Hanmandlu, 2010). Thus, the probabilistic linguistic Bonferroni mean (PLBM) operator, weighted probabilistic linguistic Bonferroni mean (WPLBM) operator, probabilistic linguistic Choquet-Bonferroni mean (PLCBM) operator, weighted probabilistic linguistic Choquet-Bonferroni mean (WPLCBM) operator, probabilistic linguistic Choquet geometric Bonferroni mean (PLCGBM) operator and weighted probabilistic linguistic Choquet geometric Bonferroni mean (WPLCGBM) operator are given.

  • iii.

    This paper proposes two kinds of methods to determine stage weights: (1) A new weight model, called log-normal distribution-based increase model is given. It not only remedies defects of existing methods, but also is of great flexibility by adjusting values of variance and attenuation factor. (2) We present a TOPSIS-entropy-based (Abdel-Basset et al., 2019, Beg and Tabasam, 2013, Zhang et al., 2014) programming model. It allows peer experts to provide evaluations about importance degrees of stages, which removes restrictions of parameter values.

This paper is organized as follows: Section 2 reviews some basic knowledges about PLTSs and the PLPRs. Then, the whole selection process is provided in Section 3, to be specific, the consistency check and modification process of the PLPRs by constructing programming models and present the alternatives linguistic terms or the probability information, respectively; the series of operators; the log-normal distribution-based increase model and the programming model. In Section 4, a case about selecting the best scheme for a lung cancer patient and its simulation are used to demonstrate the effectiveness and the rationality of the provided method. Besides, the sensitive analyses and comparison analyses also validate the method.

Section snippets

Preliminaries

To demonstrate the uncertainty and bounded rationality of the experts, the PLTS is first provided by Pang et al. (2016) based on the LTS S1={sαα=-τ,,-1,0,1,,τ} or S2={sαα=1/τ, 1/τ-1,,1/2,1,,τ-1,τ} (τ is a positive integer). The PLTS can be denoted as:L(p)=L(ι)(p(ι))L(ι)S1orS2,0p(ι)1,ι=1#L(p)p(ι)1where L(ι)(p(ι)) is the ι- th probabilistic linguistic element (PLE) and #L(p) is the number of PLE. If ι=1#L(p)pι<1, the normalized PLE is L¯(ι)(p¯(ι)), satisfying p¯(ι)=p(ι)/ι=1#L(p)p(ι).

Multi-stage medical schemes selection process

Because of the complicated situation, limited medical equipment and limited work experience of physician, patients usually need to be transferred to another hospital. How to effectively and accurately transfer the patient to the hospital in which the physician specialized in this disease and let the patient receive professional therapies are important. Thus, choosing the most suitable physician and scheme plays a key role in the system. The whole selection process can be demonstrated in Fig. 1.

Case study and simulation

The lung cancer is one of the malignant tumors threatening the health and life of human being with the characteristics of high incidence and mortality rate. In the last 50 years, the incidence and mortality rate of lung cancer have significantly increased. It goes through five stages (including stage-I, stage-II, stage-IIIA, stage-IIIB, stage-IV). If someone is affected by lung cancer unfortunately, he/she needs to receive the timely and effective therapy so that the pain of the illness can be

Conclusions

The presented whole selection not only guarantees the complete original information, but also improves the effectiveness and rationality from three ways: (1) the new transformed function assures the symmetry of PLPRs and replaces the position of score in the consistency check and modification processes. Then, modification elements are transmitted to peer experts as alternative information. In this paper, alternative linguistic terms are provided by the determined probability information. On the

CRediT authorship contribution statement

Bo Li: Conceptualization, Methodology, Software, Writing - original draft. Zeshui Xu: Methodology, Writing - review & editing. Yixin Zhang: 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.

Acknowledgements

This study was funded by the National Natural Science Foundation of China (No. 71771155, 71571123), the scholarship under the UK-China Joint Research and Innovation Partnership Fund PhD Placement Programme (No. 201806240416) and the Teacher-Student Joint Innovation Research Fund of Business School of Sichuan University (No. H2018016).

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