Regret Theory-Based Three-Way Decision Model in Hesitant Fuzzy Environments and Its Application to Medical Decision

In real world, a typical decision-making problem in the medical field can be seen as an uncertain hesitant fuzzy multiattribute decision-making problem when existing experiences of decision-makers are insufficient. A three-way decision model is an effective tool to deal with uncertain decision-making problems, which can realize the classification of objects. However, different psychological behaviors of decision-makers are likely to affect decision-making results in actual decision-making processes. In order to address this challenge, we first propose a regret-theory-based three-way decision model in hesitant fuzzy environments, which mainly combines regret theory with hesitant fuzzy sets to calculate the perceived utility value of objects. Second, since one of the core ingredients for regret theory is the regret–rejoice function, we put forward a new regret–rejoice function that preserves the original indecisive uncertainty in hesitant fuzzy environments. In addition, according to the inherent relationship of the used data, this article provides a three-way classification method based on the preference ranking organization method for enrichment evaluations I method. Finally, the practicability, rationality, and superiority of the proposed method are shown via the case analysis and comparative analysis in the medical field.

I. Introduction

Due to the complexity and diversity in real world, practical multiattribute decision-making (MADM) problems are often uncertain [1]–[5]. For instance, the underlying background of healthcare is uncertain [6], [7]. Some specific manifestations of medical uncertainties are listed as follows: the same disease may have multiple symptoms [8], the same drug may have different drug reactions due to differences of individual physical qualities, and so forth. Thus, a decision-making problem in the medical diagnosis background can be seen as a hesitant fuzzy multiattribute decision-making (HF-MADM) problem [7], [9], [10]. According to the National Bureau of Statistics,¹

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it is known that the number of visits in medical institutions was 8.72 billion, the number of visits in hospitals was 3.842 billion, and the number of visits in general hospitals was 2.779 billion in 2019. The annual population base in medical care is very large. Therefore, it is vital to make correct decisions under uncertain medical conditions. Some existing HF-MADM methods [11]–[14] can realize the ranking of objects. However, actual decision-making processes are often rational, and decision-making results are more ideal. In response to the above challenges, Zhang et al. [15], Yang et al. [16], and Liang and Wang [17] added regret theory (RT) to decision-making processes for describing a decision-maker’s (DM) psychological behaviors. Although these methods [15]–[17] avoid the complete rationality of decision-making processes, they do not achieve the classification of objects. Hence, how to use RT and three-way decision (T-WD) theory to reasonably and effectively solve HF-MADM problems in the medical field is a challenging issue. This has certain practical significance and is also the focus of this article. Thus, this article plans to introduce an RT-based T-WD model in hesitant fuzzy (HF) environments and discusses its medical applications. In what follows, we briefly summarize the development of hesitant fuzzy sets (HFSs), RT, and T-WD theory, respectively.