Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread
Uncertainty or vagueness is usually used to reflect the limitations of human subjective judgment on practical problems. Conventionally, imprecise numbers, e.g., fuzzy and interval numbers, are used to cope with such issues. However, these imprecise numbers are hard for decision-makers to make decisi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/15/10/355 |
| _version_ | 1797475993273761792 |
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| author | Chin-Yi Chen Jih-Jeng Huang |
| author_facet | Chin-Yi Chen Jih-Jeng Huang |
| author_sort | Chin-Yi Chen |
| collection | DOAJ |
| description | Uncertainty or vagueness is usually used to reflect the limitations of human subjective judgment on practical problems. Conventionally, imprecise numbers, e.g., fuzzy and interval numbers, are used to cope with such issues. However, these imprecise numbers are hard for decision-makers to make decisions, and, therefore, many defuzzification methods have been proposed. In this paper, the information of the mean and spread/variance of imprecise data are used to defuzzify imprecise data via Mellin transform. We illustrate four numerical examples to demonstrate the proposed methods, and extend the method to the simple additive weighting (SAW) method. According to the results, our method can solve the problem of the inconsistency between the mean and spread, compared with the center of area (CoA) and bisector of area (BoA), and is easy and efficient for further applications. |
| first_indexed | 2024-03-09T20:52:34Z |
| format | Article |
| id | doaj.art-6b76a6b3a8954fe7a6f20b6b9f88b61a |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-09T20:52:34Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-6b76a6b3a8954fe7a6f20b6b9f88b61a2023-11-23T22:30:12ZengMDPI AGAlgorithms1999-48932022-09-01151035510.3390/a15100355Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and SpreadChin-Yi Chen0Jih-Jeng Huang1Department of Business Administration, Chung Yuan Christian University, No. 200 Chung Pei Road, Chung Li District, Taoyuan 320, TaiwanDepartment of Computer Science & Information Management, SooChow University, No. 56 Kueiyang Street, Section 1, Taipei 100, TaiwanUncertainty or vagueness is usually used to reflect the limitations of human subjective judgment on practical problems. Conventionally, imprecise numbers, e.g., fuzzy and interval numbers, are used to cope with such issues. However, these imprecise numbers are hard for decision-makers to make decisions, and, therefore, many defuzzification methods have been proposed. In this paper, the information of the mean and spread/variance of imprecise data are used to defuzzify imprecise data via Mellin transform. We illustrate four numerical examples to demonstrate the proposed methods, and extend the method to the simple additive weighting (SAW) method. According to the results, our method can solve the problem of the inconsistency between the mean and spread, compared with the center of area (CoA) and bisector of area (BoA), and is easy and efficient for further applications.https://www.mdpi.com/1999-4893/15/10/355imprecise dataMellin transformdefuzzificationcenter of area (CoA)bisector of area (BoA) |
| spellingShingle | Chin-Yi Chen Jih-Jeng Huang Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread Algorithms imprecise data Mellin transform defuzzification center of area (CoA) bisector of area (BoA) |
| title | Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread |
| title_full | Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread |
| title_fullStr | Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread |
| title_full_unstemmed | Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread |
| title_short | Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread |
| title_sort | defuzzify imprecise numbers using the mellin transform and the trade off between the mean and spread |
| topic | imprecise data Mellin transform defuzzification center of area (CoA) bisector of area (BoA) |
| url | https://www.mdpi.com/1999-4893/15/10/355 |
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