Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-06-01
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| Series: | Information |
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| Online Access: | http://www.mdpi.com/2078-2489/8/2/62 |
| _version_ | 1818062862211350528 |
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| author | Zhikang Lu Jun Ye |
| author_facet | Zhikang Lu Jun Ye |
| author_sort | Zhikang Lu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T14:10:57Z |
| format | Article |
| id | doaj.art-9876c4030bfa481a974d29f5ad2ff23d |
| institution | Directory Open Access Journal |
| issn | 2078-2489 |
| language | English |
| last_indexed | 2024-12-10T14:10:57Z |
| publishDate | 2017-06-01 |
| publisher | MDPI AG |
| record_format | Article |
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| spelling | doaj.art-9876c4030bfa481a974d29f5ad2ff23d2022-12-22T01:45:29ZengMDPI AGInformation2078-24892017-06-01826210.3390/info8020062info8020062Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision MakingZhikang Lu0Jun Ye1Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang Province, ChinaDepartment of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang Province, ChinaAs 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.http://www.mdpi.com/2078-2489/8/2/62single-valued neutrosophic setexponential operational lawsingle-valued neutrosophic weighted exponential aggregation (SVNWEA) operatordecision making |
| spellingShingle | Zhikang Lu Jun Ye Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making Information single-valued neutrosophic set exponential operational law single-valued neutrosophic weighted exponential aggregation (SVNWEA) operator decision making |
| title | Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making |
| title_full | Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making |
| title_fullStr | Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making |
| title_full_unstemmed | Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making |
| title_short | Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making |
| title_sort | exponential operations and an aggregation method for single valued neutrosophic numbers in decision making |
| topic | single-valued neutrosophic set exponential operational law single-valued neutrosophic weighted exponential aggregation (SVNWEA) operator decision making |
| url | http://www.mdpi.com/2078-2489/8/2/62 |
| work_keys_str_mv | AT zhikanglu exponentialoperationsandanaggregationmethodforsinglevaluedneutrosophicnumbersindecisionmaking AT junye exponentialoperationsandanaggregationmethodforsinglevaluedneutrosophicnumbersindecisionmaking |