Risk appetite dual hesitant fuzzy three-way decisions with TODIM

In our real life, the decision maker is always of bounded rationality under risk and uncertainty. The decision result also can be impacted by the risk appetite of the decision maker. However, the existing research works of three-way decisions rarely involve the risk appetite of the decision maker. To address this drawback and enrich the application, we introduce the risk appetite into three-way decisions. More specifically, under the dual hesitant fuzzy environment, we utilize TODIM (an acronym in Portuguese for Interactive Multi-Criteria Decision Making) as a valuable tool to handle the risk appetite character to construct risk appetite dual hesitant fuzzy three-way decisions. This study takes into account the risk appetite of decision maker and designs a series of decision analysis methodologies for three-way decisions. It can preferably satisfy the practical situation and vastly extend the range of applications. Firstly, based on the dual hesitant fuzzy loss functions, we mainly study dual hesitant fuzzy entropy and cross-entropy measures for determining the conditional probability. In this scenario, the conditional probability information can be objectively learned from the loss function matrix with the aid of the power average (PA) aggregated operator. Then, considering the different comparison methods of dual hesitant fuzzy elements (DHFEs), we further design two types of strategies to deduce risk appetite dual hesitant fuzzy three-way decisions in the framework of TODIM, i.e., Strategies 1 and 2, which mainly rely on the pairwise comparison of loss functions with DHFEs. Strategy 1 is designed based on the score function of DHFEs. Strategy 2 is the likelihood of DHFEs. Meanwhile, some properties are carefully investigated. Finally, the project investment evaluation of online peer-to-peer (P2P) is applied to illustrate and validate these proposed strategies.