An outranking method for multicriteria decision making with probabilistic hesitant information

Abstract

Defects of hesitant fuzzy set (HFS) manifest in actual decision‐making process, so adding probabilities to the values in HFS is necessary. The probabilistic HFS (PHFS) is a useful tool to describe the uncertainty of elements in HFS by introducing occurrence probabilities. However, some important issues in PHFS utilization remain to be addressed. In this study, an outranking method for multicriteria decision making (MCDM) with probabilistic hesitant information is presented. First, the binary relations between two probabilistic hesitant fuzzy elements (PHFEs) are defined on the basis of the elimination and choice translating reality method. Some outranking relations between the alternatives are then introduced. Second, we provide a Hausdorff distance between two PHFEs. The main characteristic of the proposed Hausdorff distance is that it does not require the same length and arrangement of the PHFEs. Third, a maximizing Hausdorff distance deviation method is developed to obtain the evaluation criteria weights under a probabilistic hesitant fuzzy environment. Finally, an illustrative example in conjunction with comparative analysis is used to demonstrate that the proposed method is feasible for practical MCDM problems.

A novel MCGDM technique based on correlation coefficients under probabilistic hesitant fuzzy environment and its application in clinical comprehensive evaluation of orphan drugs

“…Hao et al [23] introduced the concept of probabilistic dual hesitant fuzzy sets. In recent years, an increasing number of researchers have focused on PHFSs, including their fusion operator [24][25][26], preference relationships [27,28], measures based on PHFSs [29][30][31][32], and decision methods based on PHFSs [32][33][34][35], etc. Although PHFSs have been extensively investigated, certain unresolved issues remain.…”

“…In recent years, with the proposal of PHFSs, compared to other fuzzy sets, they have excellent advantages in preserving DMs' preferences information. Many scholars have begun to study MCDM methods in probabilistic hesitant fuzzy environments [30,53,[80][81][82]. Most fuzzy MCDM approaches rely on information measurements, such as distance, similarity, and correlation coefficients.…”