Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment
With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SN...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/8/1058 |
| _version_ | 1818037184349863936 |
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| author | Muhammad Akram Sumera Naz Florentin Smarandache |
| author_facet | Muhammad Akram Sumera Naz Florentin Smarandache |
| author_sort | Muhammad Akram |
| collection | DOAJ |
| description | With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment. |
| first_indexed | 2024-12-10T07:22:48Z |
| format | Article |
| id | doaj.art-659af00c5bc943aaabcb2fd9762119dd |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T07:22:48Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-659af00c5bc943aaabcb2fd9762119dd2022-12-22T01:57:47ZengMDPI AGSymmetry2073-89942019-08-01118105810.3390/sym11081058sym11081058Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy EnvironmentMuhammad Akram0Sumera Naz1Florentin Smarandache2Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, PakistanDepartment of Mathematics, Government College Women University Faisalabad, Punjab 38000, PakistanScience Department 705 Gurley Ave., University of New Mexico Mathematics, Gallup, NM 87301, USAWith the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment.https://www.mdpi.com/2073-8994/11/8/1058simplified neutrosophic hesitant fuzzy setmulti-attribute decision-makingmaximizing deviationTOPSIS |
| spellingShingle | Muhammad Akram Sumera Naz Florentin Smarandache Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment Symmetry simplified neutrosophic hesitant fuzzy set multi-attribute decision-making maximizing deviation TOPSIS |
| title | Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment |
| title_full | Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment |
| title_fullStr | Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment |
| title_full_unstemmed | Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment |
| title_short | Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment |
| title_sort | generalization of maximizing deviation and topsis method for madm in simplified neutrosophic hesitant fuzzy environment |
| topic | simplified neutrosophic hesitant fuzzy set multi-attribute decision-making maximizing deviation TOPSIS |
| url | https://www.mdpi.com/2073-8994/11/8/1058 |
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