An ORESTE approach for multi-criteria decision-making with probabilistic hesitant fuzzy information

Multi-Attribute Decision-Making Method Based Distance and COPRAS Method with Probabilistic Hesitant Fuzzy Environment

“…Li et al [21] defined a distance between h 1 (p) and h 2 (p), then the Euclidean distance among them was developed as follows:…”

“…Li et al [21] proposed the distance after normalization of PHFEs, so it is not the original PHFEs after normalization. PHFEs are different before and after normalization, so the distance will be different.…”

“…Email: czclph@163.com improve the rationality and credibility of the result. In recent years, scholars have done some works to extend PHFS theory [17][18][19][20][21][22][23]. It is worth noting that the sum of the probabilities of all membership degrees in the same probabilistic hesitant fuzzy element (PHFE) is required to be one in these studies.…”

“…In probabilistic hesitant fuzzy environment, most existing distances have some disadvantages. For example, distance proposed by Wu and Xu [39] does not satisfy the reflexivity of the definition of distance measure; Hamming distance proposed by Zhang et al [40] and the Euclidean distance proposed by Ding et al [41] do not consider the difference in length and probability of PHFEs; The Euclidean distance proposed by Li et al [21] is based on the normalized PHFEs, which is not the original PHFEs. Therefore it has a certain influence on the decision result.…”

“…1. In order to make up for these existing distances [21,[39][40][41] that do not take into account the differences in length, membership degrees and probability between PHFEs, this study proposes some new distances based on PHFEs.…”