Cardiovascular disease is a global leading cause of death, and timely monitoring can determine its extent. Clinicians use these diagnostic indicators to make scientific and reasonable decisions. However, when decision-makers (DMs) encounter risks in complex environments, their limited rationality may affect decision behaviors. Therefore, the paper explores a new three-way multi-attribute decision making method based on regret theory (3W-MADM-R), which uses heart disease data to make decisions in fuzzy environments. There are three main steps in developing 3W-MADM-R, i.e., (i) we propose the notion of relative outcome functions and corresponding aggregated regret-based utility functions of each object; (ii) we estimate the conditional probability via an outranked set defined by an outranking relation based on the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE II); (iii) we construct three-way decision rules to solve the problems of clustering and ranking of objects in data analysis. In order to demonstrate the usefulness of 3W-MADM-R, we apply it to analyze heart disease data. By comparing with results of other methods, we show the feasibility, stability and superiority of the presented 3W-MADM-R method.
Multi-attribute decision making (MADM) refers to a decision problem in which the importance of different attributes is considered and the decision scheme is ranked or the optimal one is selected. There are many applications of MADM methods in management, engineering design, economics and other fields. For instance, Churchman et al.  first used a simple weighting method to solve the problem of “choosing the investment policy of enterprises”. At present, the classic MADM methods, including the TOPSIS method , the ELECTRE method , the PROMETHEE-II method  and others. Meanwhile, many types of uncertainties have been considered in MADM methods, including randomness , fuzziness  and roughness . According to the behavior characteristics of a DM, stochastic, fuzzy-set, and rough-set-based MADM models have been proposed and investigated , , , , .
With the rise of MADM techniques, their applications in the medical field  have become more and more widespread. A case in point is that the MADM method can be applied to solve cardiovascular and cerebrovascular diseases that seriously threaten human health. According to a report released by World Health Organization (WHO), 18 million people die from cardiovascular diseases each year, and 85% of which are due to heart disease and stroke. Data from the National Bureau of Statistics (https://data.stats.gov.cn/) show that the proportion of deaths due to heart disease in the total number of deaths is increasing year by year and has reached 23.65% in 2019. Therefore, the prevention and control of heart disease need joint efforts of all individuals. Early monitoring, diagnosis and treatment can effectively reduce the morbidity and mortality of heart disease and improve the life quality of patients. One of the key problems in the field of life sciences is how to quickly and effectively diagnose heart disease. At present, routine detection items for this disease mainly include blood pressure, electrocardiogram, blood routine, blood lipids, blood glucose, hemorheology, and so forth. These tests will help clinicians to determine the location and extent of cardiovascular diseases. However, in complex environments, facing with limited rationality owned by DMs and different forms of biomedical data, there are two issues that need to be addressed. One is how to effectively and reasonably deal with ambiguities in psychological and medical data along with the bounded rationality of DMs, and the other one is how DMs with limited rationality apply these data to diagnose a variety of diseases. In real world, clinical decision making and other aspects remain to be explored.
In recent years, the researches on MADM problems and 3WD models have become the mainstream. On this basis, we have combined RT with the traditional PROMETHEE-II method to construct a new 3W-MADM-R method to solve the decision making problems with behavioral psychology in real life. The effectiveness and superiority of our proposed method have been verified by an illustrative example and comparative analysis of other methods. In addition, in order to demonstrate the stability and feasibility of the 3W-MADM-R method, parameter analysis has been carried out and another three data sets have been added for further verification. The main contributions of this paper are summarized as follows:
(1) Based on the net-flow of the traditional PROMETHEE-II method, we have constructed a new outranking relation and objectively given the membership degree of the membership function to calculate the conditional probability, which solves the deficiency of the existing methods [38,39].