A three-way decision method with prospect theory to multi-attribute decision-making and its applications under hesitant fuzzy environments

Nowadays, various uncertain information can be found in real world, and it is imperative to explore viable countermeasures for uncertain decision-making problems. Hesitant fuzzy set (HFS) theory is an efficient expression of uncertain information. Thus, the solution of hesitant fuzzy multi-attribute decision-making (HF-MADM) problems acts as a key topic in decision sciences. The purpose of this paper is to build a model with ranking and classification functions to reasonably solve HF-MADM problems, preferably aiming at the following situations: (1) decision-makers (DMs) are not risk-averse in all situations. (2) Decision results with acceptance, rejection or deferment are more important than merely ranking when there are many objects involved. First, prospect theory (PT) is used to quantify the psychology of DMs with gains and losses. Taking into account the particularity of HF environments, the gain and loss values of objects are estimated via using the flow of HF Preference Ranking Organization method for Enrichment Evaluations (HF-PROMETHEE). Subsequently, the concept of relative outcome matrices is proposed. Second, by means of three-way decision (TWD), a TWD model based on PT is established in HF environments. Third, the comparative analysis of ranking and classification is respectively constructed. The rationality and validity of the proposed model can be verified via the results of Spearman correlation coefficients with other ranking methods are greater than 0.75, and the classification error rate (CER) indicator is 33.61% smaller than other existing classification methods. Finally, parameter experiments and case experiments under different data sets are constructed. The consistent optimal results under different parameters demonstrate the stability of the proposed model. Under the four different datasets, the CER values of 14.44%, 11.11%, 4.72% and 7.41% show that the proposed model is better than the other existing methods.