The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广)
距离测度是毕达哥拉斯（Pythagorean）模糊决策的一个基本概念，其在用权重向量进行有序集成运算、有序加权距离和相似度构造时具有重要作用。然而，早期发表于International Journal of Intelligent Systems中的文章Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets，在首次引入海明距离测度时，对距离公理化条件的证明存在不妥。为此，通过反例和分析指出了其在证明公理化条件的有界性和三点不等式时存在的错误，并统筹考虑犹豫度的绝对值项和其他绝对值项...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Zhejiang University Press
2023-07-01
|
| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2023.04.002 |
| _version_ | 1797232910556725248 |
|---|---|
| author | 李丹(LI Dan) 李丹(LI Dan) |
| author_facet | 李丹(LI Dan) 李丹(LI Dan) |
| author_sort | 李丹(LI Dan) |
| collection | DOAJ |
| description | 距离测度是毕达哥拉斯（Pythagorean）模糊决策的一个基本概念，其在用权重向量进行有序集成运算、有序加权距离和相似度构造时具有重要作用。然而，早期发表于International Journal of Intelligent Systems中的文章Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets，在首次引入海明距离测度时，对距离公理化条件的证明存在不妥。为此，通过反例和分析指出了其在证明公理化条件的有界性和三点不等式时存在的错误，并统筹考虑犹豫度的绝对值项和其他绝对值项，通过分情况讨论给出了海明距离测度的严格证明，进一步，证明了其推广形式（欧几里得距离测度）的公理化条件。 |
| first_indexed | 2024-04-24T16:07:47Z |
| format | Article |
| id | doaj.art-81ddb46f9ecd41c8ac9d92e2cd75abee |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:07:47Z |
| publishDate | 2023-07-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-81ddb46f9ecd41c8ac9d92e2cd75abee2024-04-01T01:52:11ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972023-07-0150440240810.3785/j.issn.1008-9497.2023.04.002The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广)李丹(LI Dan)0https://orcid.org/0000-0002-9903-4408李丹(LI Dan)1https://orcid.org/0000-0003-2124-5595(1三亚学院 理工学院，海南 三亚 572000)(2天津师范大学 数学科学学院，天津 300387)距离测度是毕达哥拉斯（Pythagorean）模糊决策的一个基本概念，其在用权重向量进行有序集成运算、有序加权距离和相似度构造时具有重要作用。然而，早期发表于International Journal of Intelligent Systems中的文章Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets，在首次引入海明距离测度时，对距离公理化条件的证明存在不妥。为此，通过反例和分析指出了其在证明公理化条件的有界性和三点不等式时存在的错误，并统筹考虑犹豫度的绝对值项和其他绝对值项，通过分情况讨论给出了海明距离测度的严格证明，进一步，证明了其推广形式（欧几里得距离测度）的公理化条件。https://doi.org/10.3785/j.issn.1008-9497.2023.04.002 |
| spellingShingle | 李丹(LI Dan) 李丹(LI Dan) The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广) Zhejiang Daxue xuebao. Lixue ban |
| title | The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广) |
| title_full | The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广) |
| title_fullStr | The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广) |
| title_full_unstemmed | The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广) |
| title_short | The proof and generalization of Hamming distance measure in the Pythagorean fuzzy environment(毕达哥拉斯模糊环境下海明距离测度的证明及推广) |
| title_sort | proof and generalization of hamming distance measure in the pythagorean fuzzy environment 毕达哥拉斯模糊环境下海明距离测度的证明及推广 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2023.04.002 |
| work_keys_str_mv | AT lǐdānlidan theproofandgeneralizationofhammingdistancemeasureinthepythagoreanfuzzyenvironmentbìdágēlāsīmóhúhuánjìngxiàhǎimíngjùlícèdùdezhèngmíngjítuīguǎng AT lǐdānlidan theproofandgeneralizationofhammingdistancemeasureinthepythagoreanfuzzyenvironmentbìdágēlāsīmóhúhuánjìngxiàhǎimíngjùlícèdùdezhèngmíngjítuīguǎng AT lǐdānlidan proofandgeneralizationofhammingdistancemeasureinthepythagoreanfuzzyenvironmentbìdágēlāsīmóhúhuánjìngxiàhǎimíngjùlícèdùdezhèngmíngjítuīguǎng AT lǐdānlidan proofandgeneralizationofhammingdistancemeasureinthepythagoreanfuzzyenvironmentbìdágēlāsīmóhúhuánjìngxiàhǎimíngjùlícèdùdezhèngmíngjítuīguǎng |