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Keywords = exponential operational laws of interval neutrosophic numbers

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22 pages, 863 KB  
Article
Exponential Aggregation Operator of Interval Neutrosophic Numbers and Its Application in Typhoon Disaster Evaluation
by Ruipu Tan, Wende Zhang and Shengqun Chen
Symmetry 2018, 10(6), 196; https://doi.org/10.3390/sym10060196 - 1 Jun 2018
Cited by 21 | Viewed by 3763
Abstract
In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interval neutrosophic set (INS) is a subclass [...] Read more.
In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interval neutrosophic set (INS) is a subclass of a neutrosophic set (NS). However, the existing exponential operations and their aggregation methods are primarily for the intuitionistic fuzzy set. So, this paper mainly focus on the research of the exponential operational laws of interval neutrosophic numbers (INNs) in which the bases are positive real numbers and the exponents are interval neutrosophic numbers. Several properties based on the exponential operational law are discussed in detail. Then, the interval neutrosophic weighted exponential aggregation (INWEA) operator is used to aggregate assessment information to obtain the comprehensive risk assessment. Finally, a multiple attribute decision making (MADM) approach based on the INWEA operator is introduced and applied to the evaluation of typhoon disasters in Fujian Province, China. Results show that the proposed new approach is feasible and effective in practical applications. Full article
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
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11 pages, 236 KB  
Article
Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making
by Zhikang Lu and Jun Ye
Information 2017, 8(2), 62; https://doi.org/10.3390/info8020062 - 7 Jun 2017
Cited by 25 | Viewed by 4624
Abstract
As an extension of an intuitionistic fuzzy set, a single-valued neutrosophic set is described independently by the membership functions of its truth, indeterminacy, and falsity, which is a subclass of a neutrosophic set (NS). However, in existing exponential operations and their aggregation methods [...] Read more.
As an extension of an intuitionistic fuzzy set, a single-valued neutrosophic set is described independently by the membership functions of its truth, indeterminacy, and falsity, which is a subclass of a neutrosophic set (NS). However, in existing exponential operations and their aggregation methods for neutrosophic numbers (NNs) (basic elements in NSs), the exponents (weights) are positive real numbers in unit intervals under neutrosophic decision-making environments. As a supplement, this paper defines new exponential operations of single-valued NNs (basic elements in a single-valued NS), where positive real numbers are used as the bases, and single-valued NNs are used as the exponents. Then, we propose a single-valued neutrosophic weighted exponential aggregation (SVNWEA) operator based on the exponential operational laws of single-valued NNs and the SVNWEA operator-based decision-making method. Finally, an illustrative example shows the applicability and rationality of the presented method. A comparison with a traditional method demonstrates that the new decision-making method is more appropriate and effective. Full article
(This article belongs to the Section Information Theory and Methodology)
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