**1. Introduction**

P2P network lending is a new type of lending model. As a website that provides intermediary services, it connects capital applicants and providers together. Due to its relatively high rate of return while low threshold, requirement and cost, P2P online lending provides an important channel for borrowers who have di fficulty in obtaining financing from the traditional financial industry. This lending model has been popularized nationwide. In 2007, the first P2P platform in China was established in Shanghai, then there was a blowout in 2015. In fact, there was little interference in P2P by regulators before 2018. But with the continuous upgrading of financial regulation after that, P2P continued to su ffer from explosion, suspension, losing contact, withdrawal di fficulties, platform fraud and other problems, and those phenomena disrupted the normal financial order. By November 2019, the total loan balance of normal operating platforms of P2P was 540.828 billion yuan, and the transaction volume was 50.623 billion yuan. Compared with the November of last year, the total loan balance declined by 33.33 percent, and the transaction volume dropped by 54.58 percent. Recently, some provinces, such as Hunan, Shandong, Chongqing, and Sichuan have announced a crackdown on non-compliant P2P business. At present, the biggest risk of P2P lending is default risk, which has become the main bottleneck of the development of P2P industry. How to evaluate the borrower's default risk is particularly important for the normal operation of P2P. Therefore, this article attempts to propose a new method to evaluate the borrower's default risk in P2P online lending.

In recent years, a lot of researchers studied on the personal default risk in the P2P online lending. Malekipirbazari [1] established a credit risk assessment model based on random forest classification method. Serrano-cinca [2] exceeded the traditional credit model, established the profit scoring model, and proved that the profit scoring model based on multiple regression was superior to the credit scoring system based on the logistic model. Oreski S. [3] proposed a personal credit assessment method combining genetic algorithm and neural network. Guo et al. [4] verified that the instance-based credit risk assessment model was superior to the score-based model.

Wei and Lu [5] proposed the dual hesitant Pythagorean fuzzy set (DHPFS), the definitions and basic algorithms of DHPFS were given in their paper. In DHPFS, both membership and non-membership are represented by sets. It is clear that DHPFS can ge<sup>t</sup> more valuable decision information from decision makers. Pythagorean fuzzy sets and dual hesitant fuzzy sets have their own outstanding advantages and application prospects. The combination of the two will make grea<sup>t</sup> contribution to the extension of fuzzy sets and make a di fference in decision-making process [6].

MADM is an important part of decision science and expected utility theory is the theoretical basis of traditional MADM research. Expected utility theory believes that complete rationality is the characteristic of decision makers, and those persons' goal is to maximize benefits. In real life, the practical option of decision makers and best option based on rational decision theory have a certain deviation, owing to cognitive ability, emotion, psychology and other factors [7]. At present, some scholars have studied the MADM method which takes the psychological behavior of decision makers into account. Knhneman and Tversky put forward prospect theory [8], which is regarded to be the most influential theory in the field of behavioral decision making and has been widely used in MADM problems [9]. The theory mainly draws the following conclusions. First, most people have a risk-averse attitude to gains and a risk-appetite attitude to losses. Second, people are more sensitive to loss than gain. The pain of loss greatly exceeds the pleasure of gain, which is called "loss aversion". Third, most people tend to rely on reference points for their judgment of gains and losses, which is called "reference dependence". Gomes and Lima [10] proposed a TODIM decision making method based on prospect theory, which is a typical multi-attribute decision making method that takes the psychological behavior of decision makers into account. The TODIM method's main concepts are as follows. First, calculating the advantages of alternatives over other alternatives in various attributes based on the decision maker's reference dependence and the psychological behavior characteristics of loss avoidance. Then, the overall advantage of each scheme over other schemes is calculated, and finally, the objective function which can maximize the overall advantage and the optimal model is established respectively. The TODIM method has been deeply studied and applied to various decision-making problems by many scholars, such as choosing the best destination for natural gas storage [11] and evaluating green supply chain [12]. In order to describe both the uncertainty of MADM problems and the attitude of lenders to avoid risks, some scholars have successively proposed fuzzy TODIM method [13], intuitionistic fuzzy TODIM [14], Pythagoras fuzzy TODIM [15] and hesitant fuzzy TODIM [16]. Wei [17] proposed picture fuzzy TODIM method for MADM problems. Huang and Wei [18] proposed the Pythagoras binary semantic TODIM method. Ji et al. [19] applied the project-based multi-valued neutrophil set TODIM method to personnel selection. Tian et al. [20] proposed an extended TODIM based on cumulative prospect theory, and then applied it in venture capital. Yin et al. [21] proposed an extended TODIM to evaluate the competency of project manager, which combines lambda-fuzzy measure with Choquet integral. However, the dual hesitant Pythagoras fuzzy TODIM method has not been studied.

Although there are a large number of methods for evaluating personal default risk, they do not take people's attitude to risk into account. At the same time, the decision environment contains too

much uncertain information. So, risk and uncertainty are two important factors that should be taken into consideration when evaluating personal credit default risk. Previous research has found that TODIM is an effective method that can reflect people's attitude to risk, and dual hesitant Pythagoras fuzzy set can ge<sup>t</sup> more information from decision maker. Therefore, we are trying to apply TODIM method with dual hesitant Pythagoras fuzzy number to the personal default risk evaluation in P2P online lending. Our goal is to demonstrate the applicability of this approach in individual default risk evaluation and, more broadly, to apply it to more similar MADM problems.

In the next section, we will introduce the process of traditional TODIM approach, the concepts of Pythagorean fuzzy set, dual hesitant fuzzy set and dual hesitant Pythagorean fuzzy set. In Section 3, we shall propose the dual hesitant Pythagorean TODIM approach. In Section 4, a numerical example for evaluating personal credit risk in the P2P online lending platform with dual hesitant Pythagorean fuzzy information is used to demonstrate the approach's applicability. In Section 5, we will draw the conclusions about this paper.
