Ye Jun
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, 312000 Zhejiang Province People's Republic of China.
Springerplus. 2016 Sep 5;5(1):1488. doi: 10.1186/s40064-016-3143-z. eCollection 2016.
An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.
区间中智集（INS）是中智集的一个子类，也是区间值直觉模糊集的一种推广，其特征由其真隶属度、不确定隶属度和假隶属度的区间数独立描述。然而，在区间中智决策问题中，所有现有的区间中智集指数运算定律及其相应的指数聚合算子的指数参数（权重）都是精确值。作为补充，本文首先引入了区间中智集的新指数运算定律，其中底数为精确值或区间数，指数为区间中智数（INN），区间中智数是区间中智集中的基本元素。然后，基于这些指数运算定律，我们提出了区间中智加权指数聚合（INWEA）算子和对偶区间中智加权指数聚合（DINWEA）算子，并引入了基于INN和对偶INN的余弦测度函数的比较方法。进一步地，我们开发了基于INWEA和DINWEA算子的决策方法。最后，给出了一个关于全球供应商选择问题的实例，以说明所提方法的适用性和合理性。
