Abstract
The Bonferroni mean (BM) can be used in situations where the aggregated arguments are correlated. BM is very useful for solving decision-making problems. For describing fuzziness and vagueness more accurately, the interval-valued hesitant fuzzy set (IVHFS), which is a generalization of the hesitant fuzzy set (HFS), can be used to describe the membership degrees with interval numbers. The aim of this paper is to propose the interval-valued hesitant fuzzy Bonferroni mean (IVHFBM) for aggregating interval-valued hesitant fuzzy information. Furthermore, the weighted form of IVHFBM (IVHFWBM) is forwarded and, hereby, a multi-criteria group decision-making (MCGDM) method is established. A case study on the problem of evaluating research funding applications in China is analyzed. A comparison between the proposed method and existing ones demonstrates its practicability.
Highlights
The Bonferroni mean (BM) is a typical class of average mean, which was first proposed by Bonferroni [1]
The aim of this paper is to introduce some new interval-valued hesitant fuzzy aggregation operators such as the interval-valued hesitant fuzzy BM (IVHFBM) and the weighted forms of interval-valued hesitant fuzzy Bonferroni mean (IVHFBM) (IVHFWBM)
The interval-valued hesitant fuzzy set (IVHFS) introduced by Chen et al [17] represents an extension of the hesitant fuzzy set theory [24]
Summary
The Bonferroni mean (BM) is a typical class of average mean, which was first proposed by Bonferroni [1]. Xia et al [13] introduced a series of generalized intuitionistic fuzzy BM operators. Xu and Chen [14] extended the BM operator to an interval-valued intuitionistic fuzzy environment. Some aggregation operators for aggregating interval-valued hesitant fuzzy information have been proposed, such as the interval-valued hesitant fuzzy weighted averaging (IVHFWA) operator, IVHFWG, GIVHFWA, GIVHFWG and their ordered and induced forms [17,18,19]. The existing interval-valued hesitant fuzzy aggregation operators do not consider the relationships between the aggregated arguments. The aim of this paper is to introduce some new interval-valued hesitant fuzzy aggregation operators such as the interval-valued hesitant fuzzy BM (IVHFBM) and the weighted forms of IVHFBM (IVHFWBM).
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